viscosity studies of high-temperature metallurgical slags
TRANSCRIPT
Viscosity Studies of High-Temperature Metallurgical Slags
Relevant to Ironmaking Process
Chen Han
Bachelor of Engineering
A thesis submitted for the degree of Doctor of Philosophy at
The University of Queensland in 2017
School of Chemical Engineering
Abstract:
Slags are molten oxides presenting in a number of high-temperature processes. In ironmaking
process, the metallurgical properties of blast furnace slags are determined largely by its
viscosity. Understanding and controlling the behavior of the slag phase is crucial in
improving the operational and economical efficiencies. However, high-temperature viscosity
measurement is practically difficult, time- and cost-consuming. There is a necessity to
develop a reliable mathematical model for the viscosity prediction through the review of
experimental data and fundamental theory.
As foundation work, abundant viscosity measurements and models have been examined and
evaluated, including over 3000 viscosity data in the CaO-MgO-Al2O3-SiO2 system and 16
viscosity models. Over the past 10 years, there has been increasing attentions on wide
composition range of slag viscosity due to the continuous consumption of complex iron ores.
In addition, the impacts of eight minor elements (including F, Ti, B, Fe, Mn, Na, K, and S) on
slag viscosity have been studied for practical purpose.
Slag viscosity is determined by its structure, which is the theoretical base of the mathematical
model. The structures of the quenched silicate slags were quantitatively investigated utilizing
Raman spectroscopy. It is accepted that the application of Raman spectroscopy can disclosure
the vibration units of molten slag, which can be interpreted the structural of silicate melts
(amorphous glass phase).
In the blast furnace operations, some solid phases such as oxide precipitates, coke or Ti(CN)
can be present in the slag. In addition, the precipitation of solid particles was commonly
observed in iron, steel, copper and other pyrometallurgy process. These solids can
significantly increase the viscosity of the slag causing operating difficulty. There is a research
gap that the solid impact on suspension was limited investigated under high-temperature
condition due to uncertainty.
Referring to the research gap of viscosity study of blast furnace slag, the following goals have
been achieved by the Ph.D. candidate:
1. Review and evaluated the experimental methodologies, viscosity data, and models
relevant to the blast furnace slag in CaO-MgO-Al2O3-SiO2 system (Chapter 2)
2. Based on the collected data and models, an accurate viscosity model has been developed
to predict the viscosity of blast furnace slag in CaO-MgO-Al2O3-SiO2 system (Chapter 4-
5)
3. Research on the viscosity impact of minor elements on the blast furnace final slag in CaO-
MgO-Al2O3-SiO2 based system. (Chapter 4-5)
4. Quantitative investigation of the microstructural units of silicate slag utilizing Raman
spectroscopy. (Chapter 6)
5. Investigation of the solid phase impact on the viscosity of liquid slag. (Chapter 7)
Declaration by author
This thesis is composed of my original work, and contains no material previously published
or written by another person except where due reference has been made in the text. I have
clearly stated the contribution by others to jointly-authored works that I have included in my
thesis.
I have clearly stated the contribution of others to my thesis as a whole, including statistical
assistance, survey design, data analysis, significant technical procedures, and professional
editorial advice, and any other original research work used or reported in my thesis. The
content of my thesis is the result of work I have carried out since the commencement of my
research higher degree candidature and does not include a substantial part of work that has
been submitted to qualify for the award of any other degree or diploma in any university or
other tertiary institution.
I have clearly stated which parts of my thesis, if any, have been submitted to qualify for
another award. I acknowledge that an electronic copy of my thesis must be lodged with the
University Library and, subject to the General Award Rules of The University of Queensland,
immediately made available for research and study in accordance with the Copyright Act
1968.
I acknowledge that copyright of all material contained in my thesis resides with the copyright
holder(s) of that material. Where appropriate I have obtained copyright permission from the
copyright holder to reproduce material in this thesis.
Publications during candidature
1. Chen. Han, Mao. Chen, Weidong Zhang, Zhixing Zhao, Tim Evans, Anh V. Nguyen and
Baojun. Zhao*, “Viscosity Model for Iron Blast Furnace Slags in SiO2-Al2O3-CaO-MgO
system”, Steel Research International, 2015, vol.85 (6), pp. 678-685
2. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing. Zhao, Tim. Evans and Baojun. Zhao*,
“Evaluation of Existing Viscosity Data and Models and Developments of New Viscosity
Model for Fully Liquid Slag in the SiO2-Al2O3-CaO-MgO System”, Metallurgical and
Material Transactions B, 2016, Vol 47 (5), pp. 2861-2874
3. Chen. Han, Mao. Chen, Ron. Rasch, Ying. Yu and Baojun. Zhao*, “Structure Studies of
Silicate Glasses by Raman Spectroscopy”, Advances in Molten Slags, Fluxes, and Salts:
Proceedings of The 10th
International Conference on Molten Slags, Fluxes and Salts, Seattle,
United States, 2016, pp. 175-182
4. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans and Baojun. Zhao,
“Viscosity Model for Blast Furnace Slags Including Minor Elements”, The 10th
CSM Steel
Congress & The 6th
Baosteel Biennial Academic Conference 2015, Shanghai, China, 2015, pp.
95-103
5. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans, Anh V. Nguyen and
Baojun. Zhao*, “Development of viscosity model for SiO2-CaO-MgO-Al2O3-“FeO” slags in
ironmaking process”, High Temperature Processing Symposium, 2015, Melbourne, Australia,
pp. 103-106
Publications included in this thesis
1. Chen. Han, Mao. Chen, Weidong Zhang, Zhixing Zhao, Tim Evans, Anh V. Nguyen and
Baojun. Zhao*, “Viscosity Model for Iron Blast Furnace Slags in SiO2-Al2O3-CaO-MgO
system”, Steel Research International, 2015, vol.85 (6), pp. 678-685 – incorporated as
Chapter 4.1
Contributor Statement of contribution
Chen Han (Candidate) Wrote the paper (100%)
Baojun Zhao* Discussed and edited paper (45%)
Mao Chen Discussed and edited paper (45%)
Tim Evans Discussed and edited paper (5%)
Anh V Nguyen Discussed and edited paper (5%)
Weidong Zhang Provided industrial advices (50%)
Zhixing Zhao Provided industrial advices (50%)
2. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing. Zhao, Tim. Evans and Baojun. Zhao*,
“Evaluation of Existing Viscosity Data and Models and Developments of New Viscosity
Model for Fully Liquid Slag in the SiO2-Al2O3-CaO-MgO System”, Metallurgical and
Material Transactions B, 2016, Vol 47 (5), pp. 2861-2874 – incorporated as Chapter 4.2
Contributor Statement of contribution
Chen Han (Candidate) Wrote the paper (100%)
Baojun Zhao* Discussed and edited paper (45%)
Mao Chen Discussed and edited paper (45%)
Tim Evans Discussed and edited paper (5%)
Anh V Nguyen Discussed and edited paper (5%)
Weidong Zhang Provided industrial advices (50%)
Zhixing Zhao Provided industrial advices (50%)
3. Chen. Han, Mao. Chen, Ron. Rasch, Ying. Yu and Baojun. Zhao*, “Structure Studies of
Silicate Glasses by Raman Spectroscopy”, Advances in Molten Slags, Fluxes, and Salts:
Proceedings of The 10th
International Conference on Molten Slags, Fluxes and Salts, Seattle,
United States, 2016, pp. 175-182 – incorporated as Chapter 6
Contributor Statement of contribution
Chen Han (Candidate) Wrote the paper (100%)
Baojun Zhao* Discussed and edited paper (45%)
Mao Chen Discussed and edited paper (45%)
Ron Rasch Assisted in the Raman spectra analysis (50%)
Ying Yu Assisted in the Raman spectra analysis (50%)
4. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans and Baojun. Zhao,
“Viscosity Model for Blast Furnace Slags Including Minor Elements”, The 10th
CSM Steel
Congress & The 6th
Baosteel Biennial Academic Conference 2015, Shanghai, China, 2015, pp.
95-103 – incorporated as Chapter 4.2;
Contributor Statement of contribution
Chen Han (Candidate) Wrote the paper (100%)
Baojun Zhao* Discussed and edited paper (45%)
Mao Chen Discussed and edited paper (45%)
Tim Evans Discussed and edited paper (5%)
Anh V Nguyen Discussed and edited paper (5%)
Weidong Zhang Provided industrial advices (50%)
Zhixing Zhao Provided industrial advices (50%)
5. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans, Anh V. Nguyen and
Baojun. Zhao*, “Development of viscosity model for SiO2-CaO-MgO-Al2O3-“FeO” slags in
ironmaking process”, High Temperature Processing Symposium, 2015, Melbourne, Australia,
pp. 103-106 – incorporated as Chapter 5.2
Contributor Statement of contribution
Chen Han (Candidate) Wrote the paper (100%)
Baojun Zhao* Discussed and edited paper (45%)
Mao Chen Discussed and edited paper (45%)
Tim Evans Discussed and edited paper (5%)
Anh V Nguyen Discussed and edited paper (5%)
Weidong Zhang Provided industrial advices (50%)
Zhixing Zhao Provided industrial advices (50%)
Contributions by others to the thesis
Contributions by Professor Baojun Zhao in experiment design, concept, analysis,
interpretation, drafting, and writing in the advisory capacity.
Statement of parts of the thesis submitted to qualify for the award of another degree
None
Acknowledgements
I express my sincere gratitude to my advisor team Prof. Baojun Zhao (principal), Prof Anh
Nguyen and Dr. Tim.Evans for their guidance and support the research projects and this
thesis completion
I would like to acknowledge the Beijing Shougang Co., Ltd, China and Rio Tinto Iron Ore,
Australia for financial support.
I thank to Dr. Mao Chen for fruitful discussions and assistance in preparing this thesis.
I am very grateful to the lab assistant Ms, Jie Yu, for her help and support on the completion
of experimental work.
Key Words
Slag viscosity, viscosity modelling, blast furnace slag, Raman spectrum
Australian and Newzealand Standard Research Classifications (ANZSRC)
ANZSRC: 091407 Pyrometallurgy 100%
Fields of Research (FoR) Classification
FoR code: 0914 Resources Engineering and Extractive Metallurgy 100%
Table of Contents
Chapter 1 : Introduction ............................................................................................................. 1
1.1 Background Introduction ........................................................................................... 1
1.2 Research Gap ............................................................................................................... 2
1.3 Aim of the Study .......................................................................................................... 2
Chapter 2 : Literature reviews .................................................................................................... 4
2.1 The technical review of high-temperature viscosity measurement.............................. 4
2.1.1 Liquid Viscosity Definition .............................................................................. 4
2.1.2 Viscometer ........................................................................................................ 7
2.1.2.1 Rotational Viscometer ................................................................................... 9
2.1.2.2 Falling-Body Viscometer ............................................................................. 10
2.1.2.3 Oscillating Viscometer................................................................................. 12
2.1.2.4 Other Viscometers ....................................................................................... 13
2.1.3 Post-Experimental Analysis ............................................................................ 14
2.1.3.1 Composition Analysis .................................................................................. 15
2.1.3.2 Surface Morphology Study .......................................................................... 17
2.1.3.3 Internal Structure Study ............................................................................... 20
2.2 The review of viscosity data of sub binary, ternary of CaO-MgO-Al2O3-SiO2 system
.......................................................................................................................................... 26
2.2.1 Binary System ................................................................................................. 26
2.2.1.1 SiO2-CaO ..................................................................................................... 26
2.2.2.2 SiO2-Al2O3 ................................................................................................... 27
2.2.2.3 SiO2-MgO .................................................................................................... 28
2.2.2 Ternary System ............................................................................................... 29
2.2.2.1 SiO2-CaO-Al2O3 .......................................................................................... 29
2.2.2.2 SiO2-Al2O3-MgO ......................................................................................... 32
2.2.2.3 Conclusion ................................................................................................... 33
2.3 Evaluation of Quaternary system CaO-MgO-Al2O3-SiO2 ......................................... 34
2.3.1 Experimental Techniques in Viscosity Measurements ................................... 35
2.3.2 Data Consistency ............................................................................................ 36
2.3.3 Cross Reference Comparison .......................................................................... 38
2.3.4 Summary of Experimental Data...................................................................... 39
2.3.5 Random Network Structure ............................................................................ 45
2.3.5 Minor Element Impact .................................................................................... 47
2.3.5.1 “FeO” ........................................................................................................... 47
2.3.5.2 TiO2 .............................................................................................................. 49
2.3.5.2 Na2O and K2O .............................................................................................. 51
2.4 The review and evaluation of viscosity model for silicate melts of CaO-MgO-Al2O3-
SiO2 system ...................................................................................................................... 53
2.4.1 Bottinga Model ............................................................................................... 53
2.4.2 Neural Network Model ................................................................................... 54
2.4.3 Giordano Model .............................................................................................. 54
2.4.4 CSIRO Model ................................................................................................. 55
2.4.5 KTH Model ..................................................................................................... 56
2.4.6 Urbain Model .................................................................................................. 57
2.4.6.1 Riboud Model .............................................................................................. 60
2.4.6.2 Kondratiev and Forsbacka Model ................................................................ 61
2.4.7 Iida Model ....................................................................................................... 61
2.4.8 NPL (Mills) Model ......................................................................................... 63
2.4.9 Shankar Model ................................................................................................ 64
2.4.10 Hu Model ...................................................................................................... 64
2.4.11 Shu Model ..................................................................................................... 65
2.4.12 Zhang Model ................................................................................................. 66
2.4.13 Gan Model .................................................................................................... 68
2.4.14 Tang Model ................................................................................................... 69
2.4.15 Ray Model ..................................................................................................... 70
2.4.16 Li Model........................................................................................................ 71
2.4.17 Quasi-Chemical Viscosity Model ................................................................. 72
2.4.18 Factsage 7.0................................................................................................... 73
2.4.19 Summary ....................................................................................................... 73
2.5 The viscosity study review of suspension system...................................................... 81
2.5.1 Effects of liquid viscosity & Solid Fraction ................................................... 82
2.5.2 Effects of Particle Size .................................................................................... 84
2.5.3 The review of viscosity model of suspension system ..................................... 86
Chapter 3 : Experiment Methodology...................................................................................... 90
3.1 High-Temperature Viscosity Measurement ............................................................... 90
3.2 Room Temperature Viscosity Measurement ............................................................. 92
3.3 Raman Spectroscopy Study ....................................................................................... 92
Chapter 4 : Viscosity Model Development in CaO-MgO-Al2O3-SiO2 System Based on
Urbain Model ........................................................................................................................... 94
4.1 CaO-MgO-Al2O3-SiO2 system in blast furnace composition range .......................... 94
4.1.1 Introduction ..................................................................................................... 94
4.1.2 Experimental Data Used for Model Development.......................................... 95
4.1.3 Silicate Melt Structure .................................................................................... 95
4.1.4 Description of Model ...................................................................................... 96
4.1.5 Expressions of Activation Energy .................................................................. 97
4.1.6 Model Performances ..................................................................................... 100
4.1.7 Industrial Applications .................................................................................. 102
4.1.8 Conclusions ................................................................................................... 104
4.2.1 Introduction ................................................................................................... 104
4.2.2 Experimental Methodology .......................................................................... 105
4.2.3 Viscosity Database ........................................................................................ 106
4.2.3.1 Collected Reference ................................................................................... 106
4.2.3.2 Minor Element Impact ............................................................................... 106
4.2.4 Result & Discussion ...................................................................................... 107
4.2.4.1 Comparisons of viscosities ........................................................................ 107
4.2.4.2 Viscosity Model Description ..................................................................... 108
4.2.4.3 Industrial Application ................................................................................ 112
4.2.5 Conclusions ................................................................................................... 114
Chapter 5 : Viscosity Model Development Based on Probability Theorem .......................... 115
5.1 CaO-MgO-Al2O3-SiO2 system in full composition range ....................................... 115
5.1.1 Introduction ................................................................................................... 115
5.1.2 Silicate melt structure ................................................................................... 115
5.1.3 Pre-Exponential Factor A ............................................................................. 116
5.1.4 Network Modifier Probability ....................................................................... 118
5.1.5 Activation Energy EA .................................................................................... 119
5.1.6 Model Performance ....................................................................................... 122
5.1.6.1 CaO-MgO-Al2O3-SiO2 system................................................................... 122
5.1.6.2 Viscosity Trend Prediction ........................................................................ 124
5.1.6.3 Sub-Ternary & Sub-Binary System ........................................................... 125
5.1.7 Industrial Application ................................................................................... 128
5.1.7.1 Blast Furnace Slag ..................................................................................... 128
5.1.7.2 Ladle Slag in Steelmaking Process ............................................................ 130
5.1.8 Conclusions ................................................................................................... 131
5.2 CaO-MgO-Al2O3-SiO2-“FeO” system in full composition range ........................... 132
5.2.1 Introduction ................................................................................................... 132
5.2.2. Model Description ....................................................................................... 132
5.2.2.1 Silicate structure of SiO2-CaO-Al2O3-MgO-“FeO” system ...................... 132
5.2.2.2 Temperature dependence ........................................................................... 133
5.2.2.3 Pre-exponential Factor A ........................................................................... 134
5.2.2.4 Fe2+
and Fe3+
Determination ...................................................................... 134
5.2.2.5 Network Modify probability ...................................................................... 134
5.2.2.6 Activation Energy ...................................................................................... 135
5.2.3 Model Performance ....................................................................................... 138
5.2.4 Industrial Application ................................................................................... 140
5.2.4.1 Blast Furnace Slag ..................................................................................... 140
5.2.4.2 Coppermaking Slag .................................................................................... 141
5.2.5 Conclusion .................................................................................................... 142
Chapter 6 : Structure studies of silicate slag by Raman spectroscopy ................................... 143
6.1 Introduction .............................................................................................................. 144
6.2 Methodology ............................................................................................................ 145
6.2.1 Sample Preparation ....................................................................................... 145
6.2.2 Raman Analysis ............................................................................................ 150
6.3 Raman Results ......................................................................................................... 151
6.3.1 Structure of alumina silicate system ............................................................. 151
6.3.2.1 Raman Peak Shift ....................................................................................... 154
6.3.2.2 Peak Intensity ............................................................................................. 156
6.3.2.3 Temperature Impact ................................................................................... 157
6.3.3 Bond energy and the lattice energy ............................................................... 158
6.3.4. Summary ...................................................................................................... 159
6.4 Thermodynamic Analysis ........................................................................................ 160
6.4.1 Degree of Polymerization ............................................................................. 160
6.4.2 Density .......................................................................................................... 162
6.4.3 Viscosity & Activation Energy ..................................................................... 163
6.5 Conclusion ............................................................................................................... 164
Chapter 7 : Experimental and modeling study of suspension system .................................... 165
7.1 Introduction .............................................................................................................. 165
7.2 Methodology ............................................................................................................ 166
7.2.1 Calibration..................................................................................................... 166
7.2.2 Viscosity Study of Suspension at Room Temperature ................................. 167
7.2.3 Viscosity Study of Suspension at Smelting Temperature ............................. 169
7.3 Results ...................................................................................................................... 170
7.3.1 Room Temperature ....................................................................................... 170
7.3.2 Smelting Temperature ................................................................................... 175
7.3.3 Effect of liquid viscosity and solid fraction .................................................. 177
7.3.4 Effect of particle diameter ............................................................................ 178
7.3.5 Effect of Temperature ................................................................................... 179
7.3.6 Effect of Shear Rate ...................................................................................... 181
7.4 Model Simulation..................................................................................................... 182
7.4.1 Model Review and Evaluation ...................................................................... 182
7.4.2 Model Optimization ...................................................................................... 185
7.4.3 Model Application ........................................................................................ 188
7.5 Conclusion ............................................................................................................... 190
Chapter 8 : Conclusions ......................................................................................................... 191
Chapter 9 : Reference............................................................................................................. 192
List of Table
Table 1.1 Blast furnace composition range [1] .................................................................. 1
Table 2.1 Category of different types of fluids .................................................................. 6
Table 2.2 Summary of Reviewed Viscometers.................................................................. 8
Table 2.3 Summary of post-experiment techniques ........................................................ 14
Table 2.4 the assigned peaks after peak deconvolution in the region 800-1200 cm-1
[41]
.................................................................................................................................. 22
Table 2.5 Summary of viscosity study at binary system SiO2-CaO ................................ 27
Table 2.6 Summary of viscosity data of SiO2-Al2O3 system ........................................... 27
Table 2.7 Summary of viscosity data of SiO2-MgO system ............................................ 28
Table 2.8 Summary of SiO2-Al2O3-CaO viscosity study................................................. 30
Table 2.9 Summary of viscosity study at SiO2-Al2O3-MgO system ............................... 32
Table 2.10 Viscosity impact of oxide in their binary and ternary system with silica ...... 34
Table 2.11 The summary of existing viscosity study in CaO-MgO-Al2O3-SiO2 system 41
Table 2.12 Summary of Brokis study of expression of SiO2 unit at various concentration
[111].......................................................................................................................... 46
Table 2.13 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-”FeO” system ......... 47
Table 2.14 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-TiO2 system ............ 49
Table 2.15 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-Na2O and K2O system
.................................................................................................................................. 51
Table 2.16 the parameter D values of Bottinga model in CaO-MgO-Al2O3-SiO2
quaternary system [126] ........................................................................................... 54
Table 2.17 Model parameters for Giordano [128] ........................................................... 55
Table 2.18 Model parameters of Urbain Model [131] ..................................................... 59
Table 2.19 Equation parameters for Iida model [136, 137] ............................................. 62
Table 2.20 Model parameters of NPL model [138] ......................................................... 63
Table 2.21 The model parameters used to calculate E [145] ........................................... 67
Table 2.22 All possible condition in the CaO-MgO-Al2O3-SiO2 system, only the
condition 1 equations were included. The equations for other conditions is not
included due to text limitation [145]. ....................................................................... 68
Table 2.23 Model parameters of Gan model [147] .......................................................... 69
Table 2.24 Model parameters of Tang model [148] ........................................................ 70
Table 2.25 Model parameters of Li model [150] ............................................................. 71
Table 2.26 Summary of reviewed viscosity model in CaO-MgO-Al2O3-SiO2 system.... 77
Table 2.27 Summary of applicable oxides of existing viscosity model .......................... 79
Table 2.28 The brief review of viscosity study of suspension system at different system,
viscosity and temperature range, note: the relative viscosity means the ratio of
suspension viscosity to liquid viscosity .................................................................... 81
Table 2.29. Summary of 10 different viscosity model, f is the solid fraction within
suspension ................................................................................................................. 88
Table 4.1 Parameters B used in Equation 4-4 .................................................................. 99
Table 4.2 Model parameters N......................................................................................... 99
Table 4.3 Summary of typical BF composition range ................................................... 105
Table 4.4 Model parameters to calculate Ei of each minor element, the parameters of
SiO2, CaO, MgO, and Al2O3 were reported in the section 4.1.4 before ................. 109
Table 4.5 Optical basicity of oxide from Duffy ............................................................. 110
Table 4.6 Summary of model performance in BF slag composition range ................... 110
Table 5.1 Electronegativity χ of basic oxide cations and network former units ............ 119
Table 5.2 Activation energy parameters of all involved structural units in CaO-MgO-
Al2O3-SiO2 system .................................................................................................. 121
Table 5.3 The summary of model parameters in binary and ternary silicate system
containing CaO, MgO, and Al2O3. ......................................................................... 125
Table 5.4 Electronegativity χ of basic oxide cations and network former units ............ 135
Table 5.5 Activation energy parameters of all involved structural units in CaO-MgO-
Al2O3-SiO2 system .................................................................................................. 137
Table 5.6 The prediction deviation of viscosity models for CaO-MgO-Al2O3-SiO2-“FeO”
system ..................................................................................................................... 138
Table 6.2 The experiment designed condition and EPMA results ................................. 146
Table 6.3 The description of assigned peak information in Raman spectrum silicate
structural units, black ball is Si and white ball is O. white ball with – sign is O- .. 152
Table 6.4 Summary of the bond energy of each deconvoluted peaks ........................... 161
Table 7.1 Physical properties of silicon oil in present study ......................................... 167
Table 7.2: Experimental condition of viscosity measurement at room temperature ..... 167
Table 7.3. Viscosity measurements of suspension of solid proportion from 0-22 vol%
................................................................................................................................ 171
Table 7.4. Viscosity measurements of suspension of solid proportion from 25-32 vol %
................................................................................................................................ 172
Table 7.5. The elemental analysis of Baosteel and JingTang slag from EPMA analysis,
where the minor element include Na2O, K2O, FeO and etc ................................... 175
Table 7.6. Summary of optimized model....................................................................... 187
List of Figure
Figure 1.1 Technical description of blast furnace ironmaking process ............................. 1
Figure 2.1 Laminar shear of fluid between two plates....................................................... 5
Figure 2.2 Shear stress vs strain rate of Newtonian liquid and non-Newtonian fluid ....... 6
Figure 2.3 Schematic diagram of rotational cylinder viscometer ...................................... 9
Figure 2.4 geometry for rotational bob, (a) cylinder, (b) cylinder, (c) cone, (d) cone, (e)
parallel plate (f) parallel plate ................................................................................... 10
Figure 2.5 Schematic diagram of the falling sphere viscometer ...................................... 11
Figure 2.6 Counter balance viscometer [15] .................................................................... 11
Figure 2.7 Schematic diagram of the oscillating piston viscometer ................................ 12
Figure 2.8 Schematic diagram of the capillary viscometer.............................................. 13
Figure 2.9 Schematic diagram of ICP [31] ...................................................................... 17
Figure 2.10 Spherulite of aluminous enstalite under (a) natural and (b) polarized light
after the viscosity measurements [36] ...................................................................... 18
Figure 2.11 Bright-field TEM image [37] ....................................................................... 19
Figure 2.12 Raman spectrum of silica glass [38] ............................................................. 21
Figure 2.13 The Raman spectrum of SiO2-CaO system at different Ca/Si ratio [43] ...... 22
Figure 2.14 The pair distribution for the pure SiO2. A is the experimental curve, B is the
calculated curve [49] ................................................................................................ 24
Figure 2.15 (a) left, 29
Si NMR spectra of SiO2-Na2O glasses [52] .................................. 25
Figure 2.16 Activity of SnO plotted against mole fraction of SiO2 for the SiO2-SnO
system at 1100 oC. Kozuka experimental data and 1) Masson prediction, 2) Flory
expression k11=2.55. And 3) Flory expression with k11=1.443 [53] ........................ 26
Figure 2.17 isovicosity data by Licko in SiO2-CaO-MgO system at 1500 °C at 40 wt.%
and 50 wt.% SiO2 [56](b) The viscosity data of Bockris of SiO2-CaO and SiO2-
MgO system at 1750 °C [54] .................................................................................... 29
Figure 2.18 Examples showing viscosity measured below liquidus by Machin [74] and
Tang [99] .................................................................................................................. 37
Figure 2.19 Linearity comparison examples by Muratov [100], Machin[80], and
Yakushev [89]........................................................................................................... 38
Figure 2.20 Four sets viscosity measurement at 45 wt % SiO2, 15 wt% Al2O3, 30 wt%
CaO and 10 wt% MgO by Gul’tyai [83], Han [93], Kita [27] and Machin [27, 74, 83,
93] ............................................................................................................................. 38
Figure 2.21 Comparison of viscosity data by the present authors (UQ), Kim et al [35]
and Park et al [101] at composition of 36.5% SiO2, 17% Al2O3, 36.5% CaO and 10%
MgO .......................................................................................................................... 39
Figure 2.22 (a) Left, pure SiO2 structure. (b) Right, silicate mix with other basic oxide
solution ..................................................................................................................... 45
Figure 2.23 FeO replaced the CaO and MgO oxide at 40 wt% SiO2, 1500 oC for SiO2-
CaO-FeO system, 40 wt% SiO2, 1550 oC for SiO2-MgO-FeO system, by Bockris
[94], Chen [115], Ji [114]and Urbain [13] ................................................................ 48
Figure 2.24 The comparison between Urbain model of 1981 and 1987 version using the
viscosity database of before-evaluation, after-evaluation and BF composition [131,
132] ........................................................................................................................... 60
Figure 2.25 The shear stress enlarged from fully liquid system to solid/liquid system... 83
Figure 2.26 Viscosity deduced from data of van der Molten and Paterson (1979) [165]at
high solid fraction (circles) and from data of Mg3Al2Si3O12 by Lejeune (triangles)
[162] and other values at low solid fraction (squares) by Thomas [166] ................. 84
Figure 2.27 Experiment data of different particle size vs model prediction [167] .......... 85
Figure 2.28. The description of interaction between solid sphere and fluid particle ....... 87
Figure 3.1 Schematic diagram of furnace for viscosity measurement at high temperature
.................................................................................................................................. 91
Figure 3.2 Schematic diagram of crucible and spindle .................................................... 91
Figure 3.3 Schematic diagram of viscosity study at room temperature ........................... 92
Figure 3.4 (a) left, a photograph of phase equilibrium experiment. (b) Right, a schematic
diagram of a vertical tube furnace ............................................................................ 93
4.1 The linear relationship between EA and ln(A) ........................................................... 97
Figure 4.2 Comparison of the current viscosity model with others ............................... 101
Figure 4.3 Three model performance for 0 - 1 Pa.s, mean deviation for three models:
present model 12.5%, Zhang model 16.4% and Urbain model (1987 version) 16.3%
[131, 188]................................................................................................................ 102
Figure 4.4 Effect of MgO on viscosity of BF slag at 15 wt% Al2O3 and 1500 °C
predicted by the present model with comparisons to the experimental data [74] .. 103
Figure 4.5 Effects of Al2O3 concentration and temperature on slag viscosity at 40 wt%
SiO2 and 10 wt% MgO predicted by the present model with comparisons to the
experimental data of Gultyai [83], Hofmann [22] and Machin [68] ...................... 104
Figure 4.6 Comparison of viscosities for CaO-MgO-Al2O3-SiO2-TiO2 slag by Park [120]
and Liao [119] ........................................................................................................ 107
Figure 4.7 the model prediction vs experimental results of CaO-MgO-Al2O3-SiO2-TiO2
slag system of Park [120], Shankar [32] and present (A) left, present model and (B)
right, Urbain Model (1981 version) [132] .............................................................. 111
Figure 4.8 Increase of prediction deviation in CaO-MgO-Al2O3-SiO2-FeO system with
increasing FeO concentration by Bills [64] , Gorbachev [189], Higgins [190] and
present study ........................................................................................................... 112
Figure 4.9 The comparison of viscosity reduction ability of 8 minor elements on BF slag
viscosity .................................................................................................................. 113
Figure 4.10 Comparison of model prediction and Liao’s measurements [119] ............ 114
Figure 5.1 Interaction among Ca2+
cations, silica and alumina ..................................... 116
Figure 5.2 The linear relationship between EA and ln(A) .............................................. 118
Figure 5.3 The performance summary of viscosity models in, (i) full CaO-MgO-Al2O3-
SiO2 composition, (ii) BF slag composition and (iii): ladle slag composition ....... 123
Figure 5.4 Comparison between experimental viscosity and calculated viscosity by
present model (12.5% deviation), Zhang model (19.4 deviations) [145] and Urbain
model (19.3 % deviation) [131] .............................................................................. 124
Figure 5.5 Comparisons between model predictions and Gul’tyai [65] and Hofmann [22]
results, 1500 °C in the system CaO-MgO-Al2O3-SiO2 .......................................... 125
Figure 5.6 The linear relationship between EA and ln(A) for (A): SiO2-Al2O3-CaO and
SiO2-Al2O3-MgO system and ................................................................................. 126
Figure 5.7 Comparisons between experiment viscosity and model prediction in the
systems (A) SiO2-Al2O3-CaO, (B) SiO2-Al2O3-MgO, (C) SiO2-CaO, (D) SiO2-MgO
and (E) SiO2-Al2O3 ................................................................................................. 128
Figure 5.8 Effects of WCaO/WSiO2 and MgO on slag viscosity at 1500 °C and 15 Al2O3
by the present model in comparisons with the data from Kim [122], Gul’tyai [83]
and Machin’s [74] ................................................................................................... 129
Figure 5.9 The model prediction of the iso-viscosity diagram at 1500 °C and 15 wt.%
Al2O3 and experiment data of Gultyai [83], Li [150], and Machin [68, 74] ........... 130
Figure 5.10 Effects of WCaO/WSiO2 and temperature on slag viscosity at 5 wt.% MgO and
30 wt.% Al2O3 by present model in comparisons with Song’s data [107] ............. 131
Figure 5.11 The comparison between experimental viscosity and calculated viscosity
using Current, Urbain [131] and Zhang model [145]. ............................................ 139
Figure 5.12 40 wt% SiO2, 1500 oC for SiO2-CaO-“FeO” system by Chen [193], Bockris
[194] and Ji [114], 40 wt% SiO2, 1550 oC for SiO2-MgO-“FeO” system by Chen
[115], Ji [195] and Urbain [60] ............................................................................... 140
Figure 5.13 Comparisons of the viscosities between model predictions and experimental
data for different “FeO”-containing slags (in wt%) by Higgins [190]; Vyaktin [84]
and Machin [80]...................................................................................................... 141
Figure 5.14 Viscosity as a function of “FeO” at 1250 oC, base slag 52% SiO2, 13.3%
Al2O3, 29.3% CaO, 5.3% MgO by Higgins [190] .................................................. 142
Figure 6.1 Schematic diagram of equilibrium experiment settings ............................... 145
Figure 6.2 Typical deconvolution of Raman spectrum of a 52.6 mol% SiO2-47.4 mol%
CaO sample............................................................................................................. 150
Figure 6.3 the Raman spectrum of SiO2-CaO system, which covers the CaO/SiO2 ratio
from 0.55 to 1.1 ...................................................................................................... 155
Figure 6.4 the Raman spectrum of SiO2—MgO—CaO system under CaO/SiO2=1 and
1500 oC condition, which covers the different MgO concentrations. .................... 155
Figure 6.5 (a) left, the Raman spectrum of SiO2—Al2O3—CaO system under
CaO/SiO2=1 and 1500 oC condition, which covers the different Al2O3
concentrations. (b) Right, the peak deconvolution outcomes of left spectra .......... 156
Figure 6.6 The relative area occupancy of different peaks of (a) SiO2-CaO-MgO system
ranging of CaO/SiO2 =1, (b) right, relative area occupancy of different peaks of
SiO2-CaO-Al2O3 system ranging of CaO/SiO2 =1 ................................................. 157
Figure 6.7 Raman spectrum of 45 SiO2- 10 Al2O3- 45 CaO mol% sample at 1300, 1500
and 1600 oC and wollastonite [202] ....................................................................... 158
Figure 6.8 DP index again basicity of SiO2-CaO, SiO2-CaO-MgO, and SiO2-CaO-Al2O3
system ..................................................................................................................... 162
Figure 6.9 DP index against the estimated densities of slag samples ............................ 162
Figure 6.10 DP index of each Raman spectrum against the activation energy .............. 163
Figure 7.1 Schematic diagram of room temperature measurements .............................. 169
Figure 7.2 Schematic diagram of (a) left, high-temperature viscosity measurement (b)
right, equilibrium experiments ............................................................................... 170
Figure 7.3 The viscosity measurements of Baosteel and Jintang blast furnace slag
sample ..................................................................................................................... 176
Figure 7.4 The relative viscosity of oil-paraffin system at different solid fraction and
liquid viscosity at 25 oC .......................................................................................... 178
Figure 7.5 The suspension viscosity at different solid fraction and particle size at (a) top,
0.1 Pa.s liquid viscosity and (b) bottom, 1 Pa.s liquid viscosity ............................ 179
Figure 7.6 The temperature dependence on the oil-paraffin system suspension viscosity
(a) 0.05 liquid viscosity suspension at 5, 10, 15 and 20 vol% and (b) 15 vol%
suspension at liquid viscosity 0.05, 0.2 and 0.5 Pa.s by Wright [163] ................... 181
Figure 7.7 The measured torque at different rotational speed for (a) 5% solid fraction at
0.05 and 1 Pa.s silicon oil. (b) 10, 20 and 30 % solid fraction at 0.5 Pa.s silicon oil
................................................................................................................................ 182
Figure 7.8 The model prediction vs experimental results at (a) top, different models and
(b) bottom, 1 Pa.s liquid viscosity .......................................................................... 184
Figure 7.9 The model prediction vs experimental results of (a) top JingTang slag and (b)
bottom, Baosteel slag .............................................................................................. 185
Figure 7.10 The comparison between experimental data and model predictions by
Wright [163] and Wu [9] ........................................................................................ 188
Figure 7.11 The comparison of model prediction and other researchers results at (a)
room temperature by Chong [153] and Namburu [160], (b) high temperature by
Louise [159] and Wright [163] ............................................................................... 189
1
Chapter 1 : Introduction
1.1 Background Introduction
In the iron-making process, blast furnace (BF) is still the principle technology in the
production of pig iron, which contributed over 90% of pig iron [1]. As shown in Figure 1.1,
the iron ore, fuels and fluxes are fed from the top, flowed down and undergo the carbothermic
reduction with increasing temperature and carbonic gas. Molten pig iron and slag are tapped
from the bottom of the furnace. Molten oxides, known as slag, are composed of gangue
minerals and ash from fuels during the high-temperature smelting process. To achieve the
optimal processing, the chemical compositions of the slags are significantly varied over a
wide range. Viscosity, as one of the most important physical properties of the slag, has been
intensively studied in last decades. The ideal slag should have an appropriate viscosity, which
flows fluently and removes most of the gangue minerals.
Figure 1.1 Technical description of blast furnace ironmaking process [1]
The blast furnace slag is composed of four major components SiO2, CaO, Al2O3 and MgO [2].
The typical industrial blast furnace slag compositions are summarized in 错误!书签自引用
无效。.
Table 1.1 Composition range of blast furnace slag [1]
2
Major Constituents Mass% Minor Constituents Mass%
SiO2 30-40 TiO2 0-2
CaO 30-45 Na2O 0-0.3
Al2O3 10-20 K2O 0-0.7
MgO 5-10 CaO/SiO2 1-1.3
1.2 Research Gap
During the BF operation, slag viscosity plays a significant role in controlling the process,
which has a direct impact on the metal/slag separation efficiency and other operation benefits.
Understanding and controlling slag viscosity at different compositions and temperatures will
assist in improving operation efficiency and minimizing the energy usage.
Abundant studies have been conducted on the viscosity measurements and model simulation
in the past century for variable oxide systems. The viscosity measurement techniques were
continuously developed [3]. It was found that improper selection of crucible/spindle material
would significantly increase the measurement uncertainty and confirmed that use of graphite
crucible cannot report reliable viscosity data at high temperature [3]. Nowadays, the Mo
material replaced the graphite crucible to hold the molten sample. It is necessary to evaluate
the published viscosity data and mathematical models for fundamental study and industrial
application. The reliability of viscosity data from early publications (around 1950s) should be
critically reviewed to establish the database and determine the appropriate prediction range of
the existing viscosity models.
Different characterization techniques were utilized to determine the chemical and physical
properties of slags. The application of Raman spectroscopy can disclosure the vibration units
of molten slag, which can be interpreted the structure of silicate melts (amorphous glass
phase). Kim reported a mathematical correlation between the peak area of Raman peak and
the external physical properties, including density and viscosity [4]. However, the role of
Al2O3 was not well studied, which is necessary to utilize the Raman spectrum on the SiO2-
CaO-MgO-Al2O3 based slag (blast furnace slag) to investigate the silicate structure units.
In the blast furnace operations, some solid phases such as oxide precipitates, coke or Ti(CN)
can be present in the slag. In addition, the precipitation of solid particles was commonly
3
observed in iron, steel, copper and other pyrometallurgy process [5]. These solids can
significantly increase the viscosity of the slag causing operating difficulty. There is a research
gap that the solid impact on suspension was limited investigated under high-temperature
condition due to uncertainty.
1.3 Aim of the Study
There is an increasing focus on process optimization and energy usage efficiency of blast
furnace ironmaking. During the operation, slag viscosity plays a significant role in controlling
the process, which has a direct impact on the metal/slag efficiency. Understanding and
controlling slag viscosity at different compositions and temperatures will assist in improving
operation production, efficiency, minimizing energy usage.
Referring to the research gap, the aims of the study include:
1. Review the experimental methodologies, viscosity data, and models relevant to the blast
furnace slag in CaO-MgO-Al2O3-SiO2 system
2. Based on collected data and models, establish an accurate viscosity model to predict the
viscosity of blast furnace slag in CaO-MgO-Al2O3-SiO2 system
3. Research on the viscosity impact of minor elements on the blast furnace final slag in
CaO-MgO-Al2O3-SiO2 based system.
4. To improve the fundamental understanding of silicate structure, utilized the Raman
techniques to study the SiO2-CaO based system and determine its correlation with
external physical properties.
5. Study the solid impact on suspension systems under room and smelting temperature
regions.
4
Chapter 2 : Literature reviews
This section would introduce the reviewed literature, which includes the following sections.
The Section 2.1 introduced the viscosity measurement techniques under high temperature
condition, which would be utilized to evaluate the existing viscosity data to develop the
viscosity database of CaO-MgO-Al2O3-SiO2 system in Section 2.3. Section 2.4 is the
mathematical model review and evaluations for the slag of CaO-MgO-Al2O3-SiO2 system.
From section 2.2-2.4, it should be noted that the scoping of the viscosity study is fully liquid
slag at high temperature. The viscosity study of solid containing slag will be reviewed in the
Section 2.5.
1. The technical review of high-temperature viscosity measurement
2. The review of viscosity study of sub binary and ternary of SiO2-Al2O3-CaO-MgO system
3. The evaluation of the viscosity data of CaO-MgO-Al2O3-SiO2 system
4. The review and evaluation of existing viscosity model for CaO-MgO-Al2O3-SiO2 system
5. The review of experimental data and mathematical model of suspension system
2.1 The technical review of high-temperature viscosity measurement
Viscosity, one of the most important physiochemical properties of slag, has been theoretically
and experimentally investigated by abundant researchers over the last decades. The proper
measurement techniques could directly determine the measurements’ reliability. Therefore, in
the present section, the measurement techniques would be discussed for the preparation of
viscosity data evaluation in Section 2.3.
2.1.1 Liquid Viscosity Definition
In fully liquid, the viscosity is an internal property, which is defined as the internal friction of
a fluid. For example, as Figure 2.1 shown, assuming a liquid between two closely spaced
parallel plates, a force (F) is applied to top plate causes the fluid dragged in the direction of F
[6]. The applied force is communicated to neighboring layers of fluid, however, with
diminishing magnitude, the fluid motion will progressive decrease as further away from the
upper plate. In this system, the dynamic viscosity Ƞ of fluid can be determined using
Equation 2-1.
5
Figure 2.1 Laminar shear of fluid between two plates
Equation 2-1: Dynamic Viscosity Calculation Formula
Ƞ = τ𝑑𝑈𝑥
𝑑𝑈𝑧
Where τ is an applied shear force and dUx/dUz is the velocity decreasing gradient (also
called strain rate).
There are two major categories, Newtonian and Non-Newtonian fluid, which is differently in
the ratio of applied shear force and dUx/dUz [7]. The details of each category and example
were summarized in Table 2.1. It is known that the Newtonian fluid behavior linear
proportional relationship between shear stress and strain rate at a constant temperature, which
reported a fixed viscosity for that fluid as shown in Figure 2.2. Other fluids, called non-
Newtonian fluid, have a polynomial relation between shear stress and strain rate, which
indicated that the viscosity is a variable parameter based on the shear rate.
6
Figure 2.2 Shear stress vs strain rate of Newtonian liquid and non-Newtonian fluid
Table 2.1 Category of different types of fluids
Category Description Example
Newtonian Fluid Liquid whose viscosity keep
constants with the rate of the shear
strain
Molten slag
Water
Non-Newtonian
Fluid
Shear Thinning
Fluid
Liquids whose viscosity increase
with the rate of shear strain
Modern paints
Ketchup
Shear Thickening
Fluid
Liquids whose viscosity decreases
with the rate of shear strain
Corn starch
Silica nanoparticles in
polyethylene glycol
Bingham Plastics Behave as a solid at low stresses
but flow as a viscous fluid at high
stresses
Mayonnaise
Toothpaste
7
A fully liquid slag belongs to the Newtonian fluid at constant condition (pressure,
temperature and etc) [8]. This characteristic had been practically confirmed by researchers
through the calculation of viscosity at the different shear rate.
However, the solid containing slag was reported a different fluidic rheology. For silicate
melts, at high-temperature condition, Wu discovered that the slag will become shear thinning
fluid above 15% solid fraction [9]. The viscosity of suspension system will be reviewed in
Section 2.5.
2.1.2 Viscometer
The viscometer is an instrument for measuring liquid viscosity under steady flow condition.
At high temperatures, it is practically difficult to examine and observe the relevant rheology
property of slag/matte. In pyro-metallurgical field, generally, the velocity of liquid slag and
matte is slow and steady, which can be assumed as an ideal flow.
At high-temperature condition, a technique that could accurately measure the viscosity at
wide slag composition is still a challenging area in the pyro-metallurgy field. In this section,
the common methods of viscosity measurement technique of molten slag will be reviewed
and compared.
From the existing literature, the following viscometers are often used in viscosity
measurement of molten slag, which are:
Rotational Spindle Viscometer
Falling Viscometer
Oscillating Viscometer
Two extra viscometers were reviewed, which is specifically to the certain liquid system:
Capillary Viscometer
Ultrasonic Viscometer
The major features of above viscometer were summarized in Table 2.2.
8
Table 2.2 The Summary of Reviewed Viscometers
Viscometer Section Description Disadvantage
Rotational 2.1.2.1
A wide viscosity measurement ranges cover 10-4
-
107 Pa.s. It require high accuracy torque
measurements, hard to clean thick fluids
The major disadvantage is the interaction between rotational
cylinder and crucible wall, which will reduce the measured torque
accuracy [10].
Falling Body 2.1.2.2
A wide viscosity measurement ranges cover 10-3
-
107 Pa.s, simple, good for high temperature and
pressure, not good for viscoelastic fluids.
The major disadvantage is the thermal expansion of falling
ball. And it required a certain distance to achieve freefalling,
which is practically difficult at high-temperature condition [11].
Oscillating 2.1.2.3
A wide viscosity measurement ranges covers 10-5
-
10-2
Pa.s, good for low viscosity liquid, need constant
and steady instrument
The major disadvantage is similar as falling ball viscometer
shown above [11].
Capillary 2.1.2.4
Simple, very high shears and range, but very
inhomogeneous shear. The capillary viscometer is
often utilized for high viscous and non-Newtonian
fluid.
The capillary viscometer could not control the PO2 during
viscosity measurement, which is not suitable for high-temperature
condition [12].
Ultrasonic 2.1.2.4
Good for high viscosity fluids, small sample
volume, gives shear and volume viscosity, and elastic
property data.
The ultrasonic viscometer could not provide accurate and
precise measurements at high-temperature condition [18].
9
2.1.2.1 Rotational Viscometer
The rotational viscometer is the most widely used viscometer in nowadays research. The
basic schematic diagram is shown in Figure 2.3. The bob located in the central position of the
crucible and rotated at a constant rate. The resistance force from fluid was recorded as torque.
The torque at known rotation rate was measured to calculate liquid viscosity as Equation 2-2.
Equation 2-2: Viscosity calculation using data from rotational viscometer [13]
Ƞ =𝜏
𝛾 ∗ 𝐾
Where Ƞ is the slag viscosity, 𝜏 is the measured torque, 𝛾 is the rotational speed and 𝐾 is the
instrument parameter.
Figure 2.3 Schematic diagram of rotational cylinder viscometer
It has found that reactive force from the bob rotation, called edge effect, reduce the reliability
of the measured torque, which causes that the calculated viscosity data inconsistent with
shear rate [14]. Different shapes of bobs were designed to minimize the interaction, which
improve the measured torque for accurate viscosity measurements. The most common
cylinder shape includes the cylinder, disc, cone, spindle and etc., which were demonstrated in
Figure 2.4. Other shapes were developed, such as spindle and thin disc to minimize the wall
edge effect [13].
10
Figure 2.4 geometry for rotational bob, (a) cylinder, (b) cylinder, (c) cone, (d) cone, (e)
parallel plate (f) parallel plate
In summary, it is widely accepted that rotational viscometer is mostly used and reliable
viscometer, which covers a wide range from 10-4
to 107 Pa.s. The major physical uncertainty
of rotational viscometer is the edge effect causing by the settings of container and bob, which
has been considered and minimized from Chen’s research [13]. And the major chemical
uncertainty generally is from the reaction among molten slag, crucible, spindle, and
atmosphere. The post-experimental analysis is significantly necessary to ensure the viscosity
measurement reliability, such as examine the slag sample concentration and container/sensor
condition.
2.1.2.2 Falling-Body Viscometer
Falling-Ball viscometer
The falling-ball viscometer is one of the earliest developed methods to determine the
viscosity of a Newtonian fluid. In this method, as Figure 2.5 shown, a sphere is allowed to
fall freely a measured distance through a viscous liquid medium and its velocity is measured.
The viscosity can be measured directly through the falling velocity as Equation 2-3 shown.
Equation 2-3: Viscosity Formula of Falling Sphere Method [11]
Ƞ = 2𝑔𝑟2(𝜌𝑠 − 𝜌𝑙)
9𝑈
Where Ƞ is the slag viscosity, g is the specific gravity, r is the effective radius of the falling
sphere, 𝜌𝑠 is the density of sphere, 𝜌𝑙 is the density of liquid and U is the falling velocity.
11
Figure 2.5 Schematic diagram of the falling sphere viscometer
Counter-balanced Viscometer
The working mechanisms of counter-balance viscometer are similar as the falling-ball
viscometer. As Figure 2.6 shown, a standard weight is put on one arm of balance and crucible
containing liquid slag is set in another arm inside the furnace. The viscosity of liquid slag is
calculated from the movement of weight through a certain fixed distance. The improvement
from counter-balanced viscometer is that the flexible control of settling rate of falling items,
which improve the measurements reliability comparing to falling ball viscometer [15].
Figure 2.6 Counter balance viscometer [15]
12
There are several disadvantages involved using falling body viscometer at the high-
temperature condition. The falling item requires a certain distance to reach a constant speed,
called free falling velocity. However, the hot zone of the furnace is generally too short for
freefalling of the ball, which could not determine the reliable velocity. It practically increased
the difficulty of crucible settings to reach steady position and temperature. Another major
disadvantage is that the thermal expansion of the ball materials. Riebling determined that the
thermal expansion of the falling ball is able to cause 10-100 Pa.s uncertainty in viscosity
measurements, which is dependent on the ball material and settle length [11].
2.1.2.3 Oscillating Viscometer
The oscillating viscometer is another technique used to measure the slag viscosity of the
small sample. As Figure 2.7 shown, when the piston is contained within the fully liquid
vessel and oscillated about its vertical axis, the motion of piston will cause a gradual damping.
The damping effects arise as a result of the viscous coupling of the liquid to the piston. From
observations of the amplitudes and time periods of the oscillations, a viscosity of the liquid
can be calculated. The oscillating method is best suited for use with low values of viscosity
within the range of 10-5
Pa.s to 10-2
Pa.s [16]. The closed design has made this design popular
on measuring low viscosity liquid, such as pure metals.
Figure 2.7 Schematic diagram of the oscillating piston viscometer
13
2.1.2.4 Other Viscometers
Capillary Viscometer
The capillary viscometer is based on the fully developed laminar tube flow theory (Hagen-
Poiseuille flow) and is shown in Figure 2.8. The capillary tube length is much larger than its
diameter; therefore, the impact of entrance flow on viscosity measurement can be neglect.
The shear stress and strain rate can be measured from mathematical expression of tube
diameter and length, which used to calculate liquid viscosity as Equation 2-4. The main
advantage of capillary over rotational viscometers is low cost and the ability to achieve high
shear rates, even with high viscosity samples. The main disadvantage is high residence time
and variation of shear across the flow, which might change the structure of complex test
fluids. In addition, because of its long tubes, capillary viscometer does not suit viscosity
measurement of high-temperature melts [15].
Equation 2-4. Viscosity Formula of Capillary Viscometer [17]
𝑛 =𝜏
𝛾=
∆𝑃 ∗ 𝐷4𝜋
128𝑄𝐿
Where P, D, Q, and L are pressure, tube diameter, fluid volume flow and tube length
respectively.
Figure 2.8 Schematic diagram of the capillary viscometer
14
Ultrasonic viscometer
The ultrasonic viscometer is a newly developed technique to measure viscosity based on
wave absorption of liquid. Liquid viscosity plays an important role in the absorption of
energy of an acoustic wave traveling through a liquid. The mechanical vibrations in a
piezoelectric are generated and go through the liquid sample and will be received by another
similar transducer in the end. The decay rate and amplitude of wave will be analyzed to
calculate fluid viscosity. Ultrasonic methods have not been and are not likely to become the
mainstay of fluid viscosity determination because they are more technically complicated than
conventional viscometry techniques [18]. Ultrasonic absorption measurements play a unique
role in the study of volume viscosity as providing volume viscosity data.
2.1.3 Post-Experimental Analysis
The experimental method used to characterize the internal structures of silicate melts can be
classified in terms of a) Composition analysis, b) Surface morphology and c) internal
structure. Table 2.3 provides a summary of several experimental techniques that have been
used to study the complex silicate system (molten slag). The methods described in Chapter
2.1.3.1 are commonly used to determine the composition of silicate. Chapter 2.1.3.2 outline
the methods for surface morphology study. Chapter 2.1.3.3 introduce the techniques for
internal structure analysis of silicate.
Table 2.3 Summary of post-experiment techniques
Chapter Method Exciting
Radiation
Application
2.1.3.1 EDS Focus beam of
electron
Obtain the composition of metal
element
EPMA-WDS Focus beam of
electron
Obtain the composition of most
elements except [O]
ICP-MS Pulse from
magnetic field
Obtain the composition of most
elements after calibration of that
15
element
2.1.3.2 SEM Focus beam of
electron
Surface morphology
TEM Focus beam of
electron
Surface morphology
Crystal information
and etc.
2.1.3.3 Raman & FTIR Laser light Stretch and vibration of internal
structure
XRD X-ray Crystal structure determination
NMR Pulse from
magnetic field
Magnetic properties of atomic
nuclei. Order-disorder
2.1.3.1 Composition Analysis
The composition analysis of post-experimental sample confirmed the reliability of viscosity
data. Three techniques were widely used: a) EDS, b) EPMA and c) ICP.
Energy Dispersive X-ray Spectroscopy (EDS)
EDS is an analytical technique used for the elemental analysis of metals or chemical
characterization of a sample [19]. During operation, a high-energy beam of charged is
focused into the sample, which excites the ground state electrons. The excited electrons at
inner shell may eject from the shell while creating an electron-hole where the electron was.
An electron from an outer, higher energy shell then fills the hole, and the energy difference
between electrons may be released in the form of an X-ray. The number and energy of the X-
rays can be measured by an energy dispersive spectrometer and recorded. The quantitative
analysis can be performed by counting the x-rays at the characteristic energy levels for each
element.
The accuracy of EDS spectrum can be affected by various factors. There are several common
issues of X-ray techniques. These X-rays are emitted in any direction, and so they may not all
escape the sample. The likelihood of an X-ray escaping the specimen, and thus being
16
available to detect and measure, depends on the energy of X-ray and the amount and density
of material it has passed through, which reduced accuracy in inhomogeneous and rough
samples. For major elements, it is usually possible to obtain a statistical precision of 3%
relative error [20]. In the review of viscosity study of CaO-MgO-Al2O3-SiO2, 7 authors
reported the composition analysis utilizing EDS [21-27].
EPMA-WDS
The Electron Probe Micro Analyser (hereinafter, “EPMA”) is an instrument to for elemental
analysis, by irradiating electron beams onto the substance surface and measuring the
characteristic of X-ray [28]. In the operation, the electrons emitted from the electron source
are accelerated at a certain accelerating voltage and collimated through electron lenses. When
accelerated electrons hit a specimen, in addition to the X-rays, particles and electromagnetic
waves carrying various kinds of information are emitted, which is also called wavelength-
dispersive X-ray spectroscopy (WDS). With EPMA, signals such as the characteristic-X-rays,
secondary electrons, backscattered electrons, etc. are detected by the appropriate detectors
and that information is utilized to find the area of interest on a specimen, and for analysis.
Quantitatively, EPMA-WDS report more accuracy elemental analysis than EDS [20].
Comparing their energy resolution, a Si Ca X-ray line on an EDS system will typically be
between 160 eV wide. On a WDS system, this same X-ray line will only be about 15 eV wide.
This means that the amount of overlap between peaks of similar energies is much smaller on
the WDS system. Therefore, the reliability and accuracy of WDS are overwhelming the EDS
as from pure to multi-component system. Another major problem with EDS systems is their
low court rates. Typically, a WDS system will have a count rate that 10 times of an EDS
system. In the review of viscosity study of CaO-MgO-Al2O3-SiO2, only 2 authors reported
the composition analysis utilizing EPM--WDS technique [29, 30].
Inductively Coupled Plasma Mass Spectrometry (ICP)
The inductively coupled plasma mass spectrometry, known as ICP, is a type of mass
spectrometry which is capable of detecting metals and several non-metals at concentrations as
low as 10-15 (limited series) [31]. As Figure 2.9 shown, when plasma energy is given to an
analysis sample from outside, the component elements (atoms) are excited. When the excited
17
atoms return to low energy position, emission rays (spectrum rays) are released and the
emission rays that correspond to the photon wavelength are measured. The element type is
determined based on the position of the photon rays, and the content of each element is
determined based on the wave intensity. To generate plasma, first, argon gas is supplied to
torch coil, and high-frequency electric current is applied to the work coil at the tip of the
torch tube. Using the electromagnetic field created in the torch tube by the high-frequency
current, argon gas is ionized and plasma is generated. This plasma has high electron density
and temperature (10000K) and this energy is used in the excitation-emission of the sample.
Solution samples are introduced into the plasma in an atomized state through the narrow tube
in the center of the torch tube. In the review of viscosity study of CaO-MgO-Al2O3-SiO2,
only 4 authors reported the composition analysis utilizing ICP technique [32-35].
Figure 2.9 Schematic diagram of ICP [31]
2.1.3.2 Surface Morphology Study
The surface morphology provides a visible information on the structure of the silicates. Two
most common techniques are SEM and TEM.
Scanning Electron Microscope
A scanning electron microscope (SEM) is a type of electron microscope that produces images
of a sample by scanning it with a focused beam of electrons. The electrons interact with
atoms in the sample, producing various signals that contain information about the sample's
surface topography and composition. The electron beam is generally scanned in a raster
18
scan pattern, and the beam's position is combined with the detected signal to produce an
image. SEM can achieve resolution better than 1 nanometer.
The common application of SEM is to examine the surface of post-experiment sample. In the
viscosity study of fully liquid slag, it is expected that only one phase existing, which could be
confirmed by SEM image. Different phase can be observed with the application of different
light. In the study of alumina silicate melts, as an example, the application of polarized light
exposure the crystal part within samples as Figure 2.10 shown. The crystals appear as well-
rounded and homogeneously distributed, which have nearly the same size [36].
Figure 2.10 Spherulite of aluminous enstalite under (a) natural and (b) polarized light after
the viscosity measurements [36]
19
Transmission Electron Microscope
Transmission electron microscopy (TEM) is a microscopy technique in which a beam
of electrons is transmitted through an ultra-thin specimen, interacting with the specimen as it
passes through it. An image is formed from the interaction of the electrons transmitted
through the specimen. The image of TEM is formed as electrons went through the sample,
which can obtain many characteristics of the sample, such as morphology, crystallization, and
stress. On the other hand, SEM shows only the morphology of samples.
In Vail study, the microstructure of various polymer-organically modified layered silicate
hybrids, synthesized via static polymer melt intercalation, is examined with transmission
electron microscopy [37]. As Figure 2.11 shown, in these hybrids, individual silicate layers
are observed near the edge, whereas small coherent layer packets separated by polymer-filled
gaps are prevalent toward the interior of the primary particle. In general, the features of the
local microstructure from TEM give useful detail to the overall picture and enhance the
understanding of various thermodynamic and kinetic issues. However, few study was
constructed on the glass form of silicate melts.
Figure 2.11 Bright-field TEM image [37]
20
2.1.3.3 Internal Structure Study
In the past decades, abundant experimental and theoretical studies have been carried out so
far on the determination of silicate structure, thermodynamic and mechanical properties.
Many spectroscopic methods have been developed to determine the structure of slags and
distinctively identify the ionic structural units composing them. However, due to amorphous
properties, novel methods continue to evolve to elucidate the structure of the ionic slag
structure for metallurgical slag, many well-proven spectroscopic methods has been developed
and are now widely applied to correlate the viscous behavior with structure melts at high
temperature. These methods include Raman spectroscopy, NMR, and XRD, which will be
reviewed in the present section. Based on the spectroscopic results, the network structure
theory was proposed, developed and mostly accepted by present researchers to describe the
silicate slag structure.
Raman Spectroscopy
Raman spectroscopy is a spectroscopic technique used to observe vibrational, rotational, and
other low-frequency modes in a system. It relies on inelastic scattering, or Raman scattering,
of visible laser light near infrared range. The laser light interacts with molecular vibrations
other excitations in the system, resulting in the energy of the laser photons being shifted up or
down. The shift in energy gives information about the vibrational modes in the system.
Although, the silicate glass is an amorphous state; it is becoming popular to utilize Raman to
disclosure the structural information of molten slag of a multi-component system. The Raman
investigation had been constructed for pure silica glass, CaO-SiO2, CaO-Al2O3-SiO2 and
other multicomponent system by researchers. Several bands were detected by Raman
Spectrum in the fused silica glass (amorphous phase) in the shift range of 0-1500 cm-1
as
Figure 2.12 shown. The two major bands located in the region of 300-600 cm-1
and 800-900
cm-1
. Sharp peaks appear in the position of 390, 420, 510, 560 and 590 cm respectively. The
peaks in the 400-600 cm-1
was generally assigned to Si-O-Si bond-bending vibration and
formed the silicate network referring to its area.
Galeener and co-workers proposed another theory by applying the energy minimization
argument method [38]. The bond angle referring to peak D1 and D2 were calculated and
21
suggested that the 606 and 495 peak can be assigned to 3-fold and a 4-fold ring of tetrahedral
SiO4 respectively [38]. The ring structure were mentioned and discussed by later researchers
[39-41]. However, there is limited experimental evidence for this theory.
Figure 2.12 Raman spectrum of silica glass [38]
The Raman spectrum of CaO-SiO2 system was investigated to understand the impact of CaO
addition into amorphous SiO2 [42, 43]. Comparing the spectrum of pure SiO2 glass (Figure
2.12) and CaO-SiO2 system (Figure 2.13), the peaks located at 500 cm-1
shrinks and 800-
1200 cm-1
enlarged, which indicated the broken of silica tetrahedral network. The addition of
CaO would break SiO4 tetrahedral network and form different [Ca]2+
[44]- combinations,
which can be assigned to the peaks at 800-1200 cm-1
. For Raman spectrum region of 800 to
1200 cm-1
, the bands were deconvoluted to several peaks for analysis, which reflects different
silicate-oxide units [43]. As Figure 2.13 shown, with the decreasing of Ca/Si ratio from 1.4 to
0.5, the intensity of peak M shrinks and peak C significantly enlarged. Through analysis
multi-components, four peaks were assigned and summarized in the Table 2.4. After the peak
deconvolution, the structural can be qualitatively determined by the ratio of non-bridging
oxygen/Si (NBO/Si).
22
Figure 2.13 The Raman spectrum of SiO2-CaO system at different Ca/Si ratio [43]
The structure of silicate glasses was continually investigated utilizing Raman spectra [41, 43,
45-48]. Park proposed a research of quantitative structural information such as the relative
abundance of silicate discrete anions (Qn units) and the concentration of three types of
oxygens, viz. free-, bridging- and non-bridging oxygen can be obtained from micro-Raman
spectra of the quenched CaO-SiO2-MgO glass samples [41]. Various transport properties
such as viscosity, density, and electrical conductivity can be expected as a simple linear
function of ‘‘ln (Q3/Q2),’’ indicating that these physical properties are strongly dependent on
a degree of polymerization of silicate melts [41].
Table 2.4 the assigned peaks after peak deconvolution in the region 800-1200 cm-1
[41]
Peak Raman
Shift
(cm-1
)
Structural
Description
NBO/Si Structural
Units
23
Q1 850-880 SiO4 with zero
bridging oxygen
4 Monomer
Q2 900-930 Si2O5 with one
bridging oxygen
3 Dimer
Q3 950-980 Si2O6 with 2
bridging oxygen
2 Chain
Q4 1040-
1060
Si2O7 with three
bridging oxygen
1 Sheet
X-ray diffraction
X-ray crystallography is a technique used for determining the atomic and molecular structure
of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into
many specific directions. By measuring the angles and intensities of these diffracted beams,
a crystallographer can produce a three-dimensional picture of the density of electrons within
the crystal. From this electron density, the mean positions of the atoms in the crystal can be
determined, as well as their chemical bonds, their disorder, and various other information.
On 1968, Mozzi utilized x-ray diffraction to analysis the vitreous silica and reported that the
Si-O distance is around 1.62 A; while the Si-O-Si angle is approximately 144o [49]. As
Figure 2.14 shown, the calculated spectrum agreed with the experimental values for the first
three peaks.
24
Figure 2.14 The pair distribution for the pure SiO2. A is the experimental curve, B is the
calculated curve [49]
A high-temperature XRD technique has been carried by Waseda and Toguri for in-situ XRD
measurements, which confirm the similarity of the melts structure to the corresponding
glasses [50]. However, because of the amorphous materials, it is difficult to gather useful
information from CaO-MgO-Al2O3-SiO2 system. A limited study was performed in the fully
liquid system.
Nuclear Magnetic Resonance Spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is
a research technique that exploits the magnetic properties of certain atomic nuclei. This type
of spectroscopy determines the physical and chemical properties of atoms or the molecules in
which they are contained. It relies on the phenomenon of nuclear magnetic resonance and can
provide detailed information about the structure, dynamics, reaction state, and chemical
environment of molecules. The intramolecular magnetic field around an atom in a molecule
changes the resonance frequency, thus giving access to details of the electronic structure of a
molecule and its individual functional groups.
MMR spectroscopy has been used extensively, similar to Raman spectroscopy in the
identification of silicate melts structure. 29Si and 27 Al elements were selected for analysis
of silicate melt slag. Most of the binary silicate based slag were investigated using 29
Si NMR.
In the structural investigation of the SiO2-Na2O system by Maekawa, as shown, the peak
deconvolution was utilized to quantitatively analysis the correlation between structures and
composition, which theoretically determined that the modify ability decreased as Li+>Na
+>K
+
25
at the same basic oxide concentration [51]. As shown in Figure 2.15, this theoretical
discovery was confirmed from the experimental measurement by Kim in the CaO-MgO-
Al2O3-SiO2-Na2O/K2O system [52].
Figure 2.15 (a) left,
29Si NMR spectra of SiO2-Na2O glasses [52]
On 1970, Masson utilizes polymer theory to estimate the molecular size in binary silicate
melts [53]. As Figure 2.16 shown, the derived results were in good agreement with
experimental spectrum over the entire range of compositions up to the maximum degree of
poly utilized NMR to obtain the polymerization degree allowed by the theory in the SiO2-
SnO binary system.
26
Figure 2.16 Activity of SnO plotted against mole fraction of SiO2 for the SiO2-SnO system at
1100 oC. Kozuka experimental data and 1) Masson prediction, 2) Flory expression k11=2.55.
And 3) Flory expression with k11=1.443 [53]
2.2 The review of viscosity data of sub binary, ternary of CaO-MgO-Al2O3-SiO2 system
A critical review of viscosity data is important for industrial application and fundamental
research. In the present section, a careful review of experimental method and viscosity data
will be demonstrated first for the binary and ternary of SiO2-CaO-Al2O3-MgO system in
section 2.2.1 and 2.2.2 respectively. In Section 2.2.3, the viscosity study of the minor element
on blast furnace slag, which includes TiO2, CaF2, MnO, FeO and etc, were reviewed as well.
Please note, only the quaternary system viscosity data of CaO-MgO-Al2O3-SiO2 were
carefully reviewed and evaluated in the Section 2.3. The viscosity data of other systems were
collected and utilized as supporting information of the viscosity database, which improved
the understanding of the viscosity impact of oxide on silicate network.. In the Section 2.2.4,
the evaluation criteria will be introduced and utilized to select reliable data for the SiO2-CaO-
Al2O3-MgO system.
2.2.1 Binary System
2.2.1.1 SiO2-CaO
SiO2 and CaO are the two major components for CaO-MgO-Al2O3-SiO2 ironmaking slags,
which have been investigated by 5 researchers on a wide composition and temperature ranges,
which is summarized in Table 2.5.
27
Table 2.5 Summary of viscosity study at binary system SiO2-CaO
Composition
(wt%)
Viscosity
(Pa.s)
Temperature
oC
Methodology Description
Bockris [54] 45-75% SiO2
25-55% CaO
0.02-2.38 1400-2120 Rotational viscometer
Graphite crucible
Hofmaier [22] 45-75% SiO2
25-55% CaO
0.02-1.85 1560-2120 Rotational viscometer
Ar atmosphere
Kozakevitch [55] 55-75% SiO2
25-45% CaO
0.07-1.23 1500-2000 Rotational viscometer
Ar atmosphere
Licko [56] 56-63% SiO2
37-44% CaO
0.15-2.38 1400-1700 Falling ball viscometer
Urbain [57] 45-75% SiO2
25-55% CaO
0.02-1.7 1550-2120 Rotational viscometer
Mo crucible and bob
Ar atmosphere
2.2.2.2 SiO2-Al2O3
For SiO2-Al2O3 system, the addition of Al2O3 also reduced the viscosity compared to pure
SiO2.
However, the reduction ability of Al2O3 is lower than CaO and MgO content.
3 types of research of viscosity measurements on this system have been constructed. The
methodology and viscosity ranges are shown in Table 2.6.
Table 2.6 Summary of viscosity data of SiO2-Al2O3 system
Composition
(wt%)
Viscosity
(Pa.s)
Temperature
oC
Methodology Description
28
Elyutin [58] 93-68% SiO2
7-32% Al2O3
0.02-0.21 1900-2350 Rotational viscometer
Ar atmosphere
Kozakevitch
[59]
45-55% SiO2
45-55%
Al2O3
0.12-0.58 1850-2100 Rotational viscometer
Ar atmosphere
Urbain [57] 23-91% SiO2
9-77% Al2O3
0.04-
8000
1650-2200 Rotational viscometer
2.2.2.3 SiO2-MgO
In the SiO2-MgO system, similar to SiO2-CaO system, the addition of MgO significantly
reduced the slag viscosity compared to pure SiO2. In addition, by comparing of CaO and
MgO at same condition, it is found that CaO has stronger reduction ability than MgO. At
1800 oC, the viscosity of SiO2-MgO is slightly higher than SiO2-CaO system at various silica
concentration, which indicated that the modify ability of CaO is stronger than MgO at fixed
condition [60].
3 types of research of viscosity measurements on this system have been constructed. The
methodology and viscosity ranges are shown in Table 2.7.
Table 2.7 Summary of viscosity data of SiO2-MgO system
Composition
(wt%)
Viscosity
(Pa.s)
Temperature
oC
Methodology Description
Bockris [54] 55-62% SiO2
38-45% MgO
0.1-0.83 1550-1800 Rotational viscometer
Ar atmosphere
Hofmaier [61] 56% SiO2
44% MgO
0.04-0.33 1625-2280 Rotational viscometer
Ar atmosphere
29
Urbain [60] 55-65% SiO2
35-45% MgO
0.06-0.36 1700-1985 Rotational viscometer
Mo crucible
Ar atmosphere
Review of the viscosity measurements in SiO2-CaO-MgO ternary system by Licko shows that
the replacement of CaO by MgO will reduce the slag viscosity as shown in Figure 2.17 (a).
At 1500 °C, 40 and 50 wt% SiO2 condition, the replacement of MgO by CaO can cause
server viscosity reduction, which indicated the CaO has stronger network modify ability than
MgO. The viscosity measurements by Brokris of SiO2-CaO and SiO2-MgO binary system
support this conclusion as Figure 2.17 (b) shown. Under same basic oxide concentration, the
viscosity of SiO2-CaO system is larger than the SiO2-MgO system at 1850 oC. The viscosity
different between SiO2-CaO and SiO2-MgO system decreased above 50 wt% basic oxide
concentration; because the viscosity impact of CaO reduced at high concentration.
Figure 2.17 isovicosity data by Licko in SiO2-CaO-MgO system at 1500 °C at 40 wt.% and
50 wt.% SiO2 [56](b) The viscosity data of Bockris of SiO2-CaO and SiO2-MgO system at
1750 °C [54]
2.2.2 Ternary System
2.2.2.1 SiO2-CaO-Al2O3
SiO2-Al2O3-CaO ternary system is one of the pseudo-quaternary system; such as CaO-MgO-
Al2O3-SiO2 and SiO2-Al2O3-CaO-FeO. The study of this ternary system directly supports the
quaternary phase study of ironmaking slag.
30
The role of Al2O3 in silicate melts is amphoteric. From Saito, at SiO2/CaO=0.3, the addition
of Al2O3 has a negative impact on the slag viscosity at 1800 oC [62]. However, by Leiba’s
study, it has been found that at the low SiO2/CaO ratio, the addition of Al2O3 has a positive
impact on the viscosity and vice versa [63]. At different SiO2/CaO ratio, the amphoteric
behavior of Al2O3 was studied in terms of its structure unit [AlO4]. The silicate structure
details will be reviewed in the later section.
15 researchers of viscosity measurements on this system have been constructed. The
methodology and viscosity ranges are shown in Table 2.8.
Table 2.8 Summary of SiO2-Al2O3-CaO viscosity study
Composition
(wt%)
Viscosity
(Pa.s)
Temperature
oC
Bills [64] 40-50% SiO2
15-20% Al2O3
35-40% CaO
0.8-28.1 1250-1500
Hofmaier [61] 20-70% SiO2
20-50% Al2O3
10-30% CaO
0.04-357 1500-2080
Urbain [60] 20-70% SiO2
20-50% Al2O3
10-40% CaO
0.03-292 1300-2180
Gultyai [65] 30-55% SiO2
10-20% Al2O3
35-50% CaO
0.27-13.35 1250-1550
Johannsen [66] 50-70% SiO2
10-27% Al2O3
4-1520 1200-1450
31
10-30% CaO
Kato [67] 32-57% SiO2
10-35% Al2O3
30-47% CaO
0.24-6.9 1320-1500
Kita [27] 35-50% SiO2
15-30% Al2O3
30-35% CaO
1.3-25.6 1305-1500
Kozakevitch [59] 10-60% SiO2
10-65% Al2O3
10-60% CaO
0.04-4.24 1450-2000
Leiba [63] 30-32% SiO2
13-21% Al2O3
50-54% CaO
0.4-9.3 1450-1600
Machin [68] 30-70% SiO2
5-40% Al2O3
10-50% CaO
0.3-16300 1150-1500
Rossin [69] 27% SiO2
29% Al2O3
43% CaO
0.09-0.68 1550-1985
Saito [62] 30-70% SiO2
5-40% Al2O3
10-50% CaO
0.06-0.36 1400-1600
Scarfe [70] 43% SiO2
37% Al2O3
2.15-36.6 1375-1625
32
20% CaO
Solvang [71] 25-47% SiO2
13-36% Al2O3
30-43% CaO
0.3-2.75*1011
780-1550
Taniguchi [72] 43% SiO2
37% Al2O3
20% CaO
4.78-7.94*1012
845-1580
2.2.2.2 SiO2-Al2O3-MgO
Similar to Al2O3-CaO-SiO2 ternary system, SiO2-Al2O3-MgO is another important pseudo-
quaternary, which supports viscosity study of the quaternary system. The Al2O3 will
contribute a positive impact on the viscosity at the low SiO2/MgO ratio and vice versa.
8 researchers of viscosity measurements on this system have been constructed. The
methodology and viscosity ranges are shown in Table 2.9.
Table 2.9 Summary of viscosity study at SiO2-Al2O3-MgO system
Composition
(wt%)
Viscosity
(Pa.s)
Temperature
oC
Hofmaier [61] 20-70% SiO2
20-55% Al2O3
8-22% MgO
0.03-257 1500-2120
Johannsen [66] 65-68% SiO2
16-18% Al2O3
13-19% MgO
0.04-0.33 1300-1450
Lyutikov [73] 50-60% SiO2 0.17-11.6 1400-1800
33
10-35% Al2O3
9-40% MgO
Machin [74] 60-65% SiO2
10-25% Al2O3
10-30% MgO
2-1240 1250-1500
Mizoguchi [75] 50-65% SiO2
9-32% Al2O3
15-30% MgO
54-63 1500-1575
Riebling [76] 43-71% SiO2
11-40% Al2O3
8-32% MgO
0.33-148 1500-1720
Toplis [77] 45-73% SiO2
17-41% Al2O3
7-16% MgO
1.34-408 1400-1640
Urbain [60] 20-71% SiO2
20-55% Al2O3
9-22% MgO
0.039-169.5 1530-2115
Zhilo [78] 47-56% SiO2
12.5-39% Al2O3
19-32% MgO
0.038-6 1400-1675
2.2.2.3 Conclusion
The viscosity data of binary and ternary system were utilized as the supporting information
for the SiO2-CaO-Al2O3-MgO system. The role of metals oxide can be empirically
determined from the collected viscosity data at constant condition (temperature and pressure),
34
which is summarized in Table 2.10. The network theory would be demonstrated in the section
2.3.4, which explains the fundamental mechanisms of oxide impact on pure silica.
Table 2.10 Viscosity impact of oxide in their binary and ternary system with silica
Viscosity Impact
Binary Ternary
SiO2 Positive Positive
Al2O3 Positive Negative at low (CaO+MgO) content
Positive at high (CaO+MgO) content
CaO Negative Negative
MgO Negative Negative
2.3 Evaluation of Quaternary system CaO-MgO-Al2O3-SiO2
The CaO-MgO-Al2O3-SiO2 quaternary system is the four major components of blast furnace
final slag. 3135 viscosity data for 607 compositions in this system have been collected from
37 publications and critically reviewed in this section, which covers composition range of 10-
67 wt% SiO2, 0-40 wt% Al2O3, 0-60 wt% CaO, 0-38 wt% MgO and temperature between
1350 and 1550 °C [12, 21, 24-27, 30, 32, 34, 52, 65, 67, 68, 70, 72, 74, 79-99].
Techniques for the measurement of slag viscosity at high temperatures are difficult and have
the potential for large uncertainties in the results. The 37 publications of viscosity study were
published from 1940s to 2010s crossing 70 years. In present study, three sequential steps
were used to evaluate the data, which check:
the review experimental techniques
the data self-consistency
the cross reference comparison
35
In addition, the viscosity impacts of the minor element, including FeO, TiO2, Na2O and K2O,
were reviewed in the section 2.3.5.
2.3.1 Experimental Techniques in Viscosity Measurements
The proper selection and setting of viscometer will reduce measurement uncertainty. Three
types of viscometer were used: rotational viscometer (27 publications), oscillation plate
viscometer (7 publications) and falling-body viscometer (2 publications). It is widely
accepted that the rotational viscometer is a more reliable viscosity measurement technique
compared to other viscometers. For rotational viscometer, one uncertainty is the edge-effect
from the crucible wall at high rotational speed; limited researchers reported the setting
parameters of crucible/spindle: spindle weight, distances between the spindle and crucible,
and thermal expansion, which have studied and reported as uncertainty factor by Chen [13].
The oscillating plate viscometer suits better for low values of viscosity within the range of 10-
5 to 10
-2 Pa.s, such as pure liquid metal system. For falling-ball viscometer, it has been found
that the thermal expansion of the sensor (ball) significantly increases viscosity measurement
uncertainty, ranges from 1 to 100 Pa.s, which depends on the temperature and the falling ball
material. The falling-ball viscometer results were rejected because of potential uncertainty.
From 1997 to 1999, K.C Mills constructed the globe project “Round Robin”, which
determine the accuracy and reliability of various experimental techniques from different labs
using the referenced materials. Altogether 21 participants measured the referenced materials
and provide valuable information for the crucible and spindle materials. Mill et al reported
that the graphite container/sensor materials can cause significant uncertainty (>50%) in the
high temperature viscosity measurement. Under graphite crucible condition, Bockris et al
reported that graphite material may reduce the SiO2 and form SiC particles on the crucible
wall at high temperature, which may change slag composition and contribute to experimental
uncertainties [54]. Software Factsage 6.2 was used to estimate the reaction temperature
between SiO2 and graphite. The graphite container/sensor data were carefully reviewed, and
high-temperature sets were rejected (>1520 °C). In the contrast, the uncertainty of viscosity
measurements by Mo crucible is under 10%, which is confirmed as the reliable materials. At
high temperatures (1400 – 1550 °C) conditions, the aggressive molten slags may react with
the container and sensor materials leading to changes in slag composition or container/sensor
geometry [14]. Pt, Pt/Rh alloy, Fe, Mo, and graphite, are major materials for containers and
sensors utilized in the reviewed studies. Most of the researchers (18) use N2, CO or Ar gas to
36
prevent potential oxidation reaction between crucible/spindle. Air atmosphere was only
utilized in experiments with Pt sensor/container. Despite the chemical reactions, the geometry
of container/sensor can be physically changed at high temperatures due to thermal expansion
and softening. The hardness of metal keeps reducing when the temperature approaches the
melting point. The melting temperature of pure Fe and Pt is 1500 and 1700 °C respectively.
Therefore, these viscosity measurements, which are taken from improper container/sensor
materials and temperature, are not reliable and will not be accepted for model evaluation.
In 37 publications, three publications reported non-equilibrium viscosity measurements, in
which the viscosity data were recorded during the continuous cooling process. The viscosity
and internal structure of the molten slag do not correspond to the recorded temperature when
the furnace is continuous-cooling. For same composition slag sample, the viscosity measured
on continuous cooling is shown to be lower than the viscosity measured at the steady
condition at the same temperature. Therefore, non-equilibrium viscosity measurements are
not the actual slag viscosity at designed temperature and they will not be accepted in the
database.
Some of the viscosity measurements were constructed below the liquidus temperature with
the given composition. However, the slag compositions, the presence of solid and
container/sensor geometry changes can only be examined by post-experimental technology.
However, none of the slag samples was immediately quenched after viscosity measurements
in all 37 publications. Therefore, the viscosity measurements require further investigations
for removal or not.
In summary, the reported methodology is not sufficient to filter out the reliable results. The
self and cross consistency of viscosity data should be checked.
2.3.2 Data Consistency
Liquidus temperature is an important indicator to discover inappropriate measurements of the
viscosity. The phase diagram of CaO-MgO-Al2O3-SiO2 has been well studied. Software
Factsage 6.2 is utilized to predict the liquidus temperature of slag. The viscosity of bulk slag
with solid precipitated significantly increased. For example, in Figure 2.18, the viscosity
measurements were reported by Tang et al and Machin. Only the last points of two sets were
rejected because of dramatic increasing. The second last point of Tang’s was accepted. To
prevent the prediction error of liquidus temperature, the viscosities taken below liquidus
37
temperature have been critically reviewed and abnormal ones were removed from the
database.
Figure 2.18 Examples showing viscosity measured below liquidus by Machin [74] and Tang
[99]
It is accepted that the slag viscosity and temperature follow the Arrhenius-type equation.
According to the Equation 2-5, the natural logarithm of viscosity has a linear correlation to
reciprocal of absolute temperature. Figure 2.19 shows an example of viscosity measurements
with high and low consistency. Clearly, the data from Muratov and Yakushev et al have low
reliability and they are excluded from the database [98, 100]. In Yakushev’s data, the last
three points dramatically increased, which were taken under liquidus temperature[98]. Due to
insufficient information of post-experiment analysis from published paper, the reasons for
other non-linear results are not clear. Data linearity is a good indication to evaluate the
measurements reliability in the absence of enough experimental conditions.
Equation 2-5 Logarithm form of Arrhenius equation
ln(η) = ln(𝐴) +𝐸
𝑇
Where η is viscosity, A is the pre-exponential factor, E is the activation energy of system and
T is the absolute temperature (K)
38
Figure 2.19 Linearity comparison examples by Muratov [100], Machin[80], and Yakushev
[89]
2.3.3 Cross Reference Comparison
For CaO-MgO-Al2O3-SiO2 slag system, the experimental measurements and modelling focus
on the blast furnace composition range. The viscosities measured from different researchers
at close compositions were carefully compared to cross check the reliability of the data. As
shown in Figure 2.20, there were four sets of viscosity measurements in the same
composition and three sets of data are close. Data from Kita are excluded from the database
as they are significantly different from others.
Figure 2.20 Four sets viscosity measurement at 45 wt % SiO2, 15 wt% Al2O3, 30 wt% CaO
and 10 wt% MgO by Gul’tyai [83], Han [93], Kita [27] and Machin [27, 74, 83, 93]
39
In case the available viscosity data are not consistent and the information reported is not
enough for the evaluation, the viscosities at this composition were measured by the present
authors using a recently developed technique at the University of Queensland. Figure 2.21 is
an example, where it can be seen that the results of Park et al are confirmed by the author's
measurements and Kim et all’s data are not accepted. The methodology was detailed
discussed in a previous publication. The main feature of this technique is the possibility of
quenching the slag sample immediately after the viscosity measurement. Electron probe X-
ray microanalysis (EPMA) with wave spectrometers was used for microstructural and
elemental analyses of the quenched samples. In addition, the possible errors associated with
the high-temperature viscosity measurements have been analyzed and significantly
minimized, which include effects of bob weight, distances to the crucible and thermal
expansion during rotational viscometer measurements.
Figure 2.21 Comparison of viscosity data by the present authors (UQ), Kim et al [35] and
Park et al [101] at composition of 36.5% SiO2, 17% Al2O3, 36.5% CaO and 10% MgO
2.3.4 Summary of Experimental Data
3135 viscosity data for 607 compositions in this system have been collected from 37
publications, critically reviewed and summarized in Table 2.11. The viscosity measurements
taken at graphite crucibles, such as Gul’tyai and Gupta were mostly rejected [83, 87]. The
data of three authors, Kim, Sheludyakov, and Tsybulnikov, were fully rejected because
measurements were carried out at non-equilibrium condition [35, 86, 88]. The viscosity data
of Kato and Taniguchi were also fully rejected because of large uncertainty at the falling ball
40
viscometer. Over 50% of Machin’s data were rejected, due to most of measuring
temperatures were under liquidus temperature of slag for more than 50 oC.
The rejection reasons include:
Lower than liquidus temperature (436 data)
Use of graphite crucible at high temperature condition (273 data)
Non-equilibrium measurement (252 data)
Low linearity with unknown reasons (197 data)
Conflict with other authors’ results at same composition (82 data)
Extreme large or small viscosity data, >40 Pa.s or <0.01 Pa.s (68 data)
Only 2 viscosity points at one composition (36 data)
In summary, 1760 viscosity measurements were accepted and utilized for viscosity model
development in CaO-MgO-Al2O3-SiO2 system.
41
Table 2.11 The summary of existing viscosity study in CaO-MgO-Al2O3-SiO2 system
Sources Method Atmosphere Container Sensor Temperature (°C)
Post
Experiment
Techniques
Viscosity
(Pa.s) No of Data Accepted
Forsbacka [21] RB Ar+5%CO Mo Mo 1580-1750 EDS 0.08-0.6 50 50
Gao [30] RB CO C Mo 1450-1550 XRD
FT-IR 0.33-2.21 36 36
Gul'tyai [83] RB N2 C C 1250-1550 N/A 0.2-10 633 234
Gupta [87] RB Ar C C 1400-1550 N/A 0.28-3.24 493 245
Han [93] RB Ar C Pt-10Rh 1300-1500 N/A 0.3-0.8 5 3
Hofmann [82] RB Air Pt Pt 1450-1600 EDS 0.1-3 59 41
Hofmann [61] RB n/a C N/A 1400-1550 EDS 0.11-2.17 24 4
Johannsen [24] RB n/a Pt/20Rh Pt/20Rh 1250-1450 EDS 20-900 13 4
Kawai [79] RB n/a C C 1500-1600 N/A 0.09-90 69 19
42
Kim [102] RB Ar C N/A 1400-1550 XRF 0.136-2.41 13 8
Kim [103] RB Ar Pt-10Rh Pt-10Rh 1425-1500 N/A 0.04-5.1 79 61
Kim [35] RB Ar Pt/10Rh Pt/10Rh 1450-1500 ICP 0.3-0.5 122 0
Koshida [25] RB N/a N/a N/a 1360-1500 EDS 0.03-3.81 32 22
Li [104] RB Ar Mo Mo 1400-1550 FT-IR 0.1-1 104 104
Lee [91] RB Ar Pt/10Rh Fe 1400-1450 N/A 0.3-1 14 13
Lee [105] RB Ar Pt/10Rh Fe 1400-1450 XRF
FT-IR 0.3-0.9 12 9
Mishra [90] RB N2 C n/a 1350-1575 N/A 0.1-4.6 179 81
Muratov [100] RB n/a Mo Mo 1300-1650 N/A 0.2-5 57 20
Nakamoto [26] RB Ar Fe Fe 1250-1450 EDS 0.29-2.89 6 6
Park [106] RB Ar Pt-10Rh Pt-10Rh 1325-1500
XRD
FT-IR
Raman
0.15-0.8 16 16
43
Saito [95] RB Ar Pt-20Rh Pt-20Rh 1400-1600 N/A 0.1-1.3 20 20
Scarfe [70] RB Air Pt Pt/10Rh 1175-1600 N/A 0.4-100 64 49
Shankar [32] RB Ar Mo Mo 1400-1600 ICP 0.16-2.55 30 29
Song [107] RB Ar Mo Mo 1475-1630 SEM-EDS 0.12-0.56 63 56
Tang [99] RB Ar Mo Mo 1267-1525 N/A 0.31-10.03 105 101
Vyatkin [84] RB n/a C C 1300-1500 N/A 0.3-5 15 15
Yao [82] RB Ar C Mo 1400-1550 XRF 0.1-1 48 48
Kita [27] OP n/a Pt Pt 1250-1502 EDS 0.6-10 12 12
Machin [68] OP Air Pt Pt-alloy 1250-1500 X-ray 0.2-2.83
562 390 Machin [74] OP Air Pt Pt-alloy 1250-1500 X-ray 1-30
Machin [80] OP Air Pt Pt-alloy 1250-1500 X-ray 0.2-60
Sheludyakov
[108] OP n/a Pt Pt 1240-1410 N/A 1-40 18 0
Tsybulnikov [88] OP n/a Mo Mo 1500-1700 N/A 0.1-0.4 14 0
44
Yakushev [98] OP n/a Mo Mo 1461-1725 N/A 0.08-0.7 92 64
Kato [67] FB Air Pt Pt 1347-1476 N/A 0.3-2 10 0
Taniguchi [72] FB n/a Pt Pt 1100-1650 N/A 0.4-400 46 0
45
2.3.5 Random Network Structure
Zachariasen firstly proposed the ideas of the network structure of the binary system of
silicate slags [109]. The binary system was continuously developed and extended to
the multi-component system. In the CaO-MgO-Al2O3-SiO2 system, they can be
categorized into three groups, which are the acidic oxide (SiO2), basic oxide (CaO and
MgO) and amphoteric oxide (Al2O3). As Figure 2.22 shown, pure SiO2 forms a
network structure using (SiO4) tetrahedral units, which contribute for viscosity
ascending. When the basic oxides are added, the O2-
(free oxygen) from basic oxide
will bind with O0 (bridging oxygen) to break the silicate network and reduce the
viscosity [111].
Al2O3 can behaviour as either acidic or basic oxide. When there are sufficient basic
oxides, excess cations (Ca2+
and Mg2+
) balance the (AlO4)5-
charges, the Al2O3 acts as
an acidic oxide, Al3+
can form tetrahedron structure (AlO4)5-
as (SiO4)4-
and
incorporate into the silicate network. In the case of insufficient basic oxides, Al2O3
will behaviour as Ca2+
or Mg2+
to break the (SiO4)4-
network.
Figure 2.22 (a) Left, pure SiO2 structure. (b) Right, silicate mix with other basic oxide
solution
Although, the network model is widely accepted as the best structural model of the
silicate melts. The applicability to the multi-component alkali and alkaline is much
46
more questionable, such as TiO2 and CaF2. The random network model has been
optimized for certain alkaline glass system. However, limited literatures discussed the
possible structural units between silicate network and basic oxides; because the
present techniques could not determine the structural units at smelting temperature
conditions. Most of theories were the estimation based on the experimental
measurements and post sample analysis. For example, Bockris and co-workers
proposed a theory of the structure units of CaO-SiO2 system by assuming the co-
existing form of silicate with basic oxide for binary slag system. The summary of
structure description of silicates is given in Table 2.12 [111].
Table 2.12 Summary of Brokis study of expression of SiO2 unit at various
concentration [111]
SiO2 concentration (wt %) Type of silicate units
0-33 [SiO4]O2-
ions
33-45 Chains of general form SinO3n+1
45-66 Mixture of discrete polyamines based on
Si3O10 and Si6O15
66-90 Discrete silicate polyamines based upon a
six-membered ring Si6O15
90-100 Essentially SiO4 network with number of
broken bonds approximately equal to
number of added O atoms from MeO and
a fraction SiO2 molecules and radicals
containing Me
100 Continuous networks of SiO4 tetrahedral
with some thermal bonds
47
2.3.5 Minor Element Impact
In the ironmaking process, the four major components, SiO2, Al2O3, CaO, and MgO
occupied over 96% of the final slag. The rest 4% were contributed by the other metal
oxides, including “FeO”, F, S, and Cu2O, which is called minor elements. A limited
study was constructed on the viscosity impact of minor elements, which will be
reviewed in the present study.
2.3.5.1 “FeO”
There are two different slags on the CaO-MgO-Al2O3-SiO2-“FeO” system, one is
ironmaking final slag and another is copper-making slag. In the present study, only
the ironmaking final slag will be studied according to the scoping, as a summary in
Table 2.13. Only 2 researchers constructed the viscosity study of CaO-MgO-Al2O3-
SiO2-“FeO” system in the composition range of ironmaking slag, which report 30-40
wt% SiO2, 30-40 wt% CaO, 10-15 wt% Al2O3, 0-10 wt% MgO and 0-5 wt% FeO.
Iron saturation is always considered by researchers, which control the oxidation status
of Fe element. In conclusion, the “FeO” addition has a negative impact on the slag
viscosity.
Table 2.13 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-”FeO” system
Composition Viscosity
(Pa.s)
Temperature
(oC)
Methodology Description
Tang [112] 31-40 %SiO2
15-16 %Al2O3
30-40 %CaO
15-17 %MgO
0-1 %FeO
0.1-3.4 1300-1600 Rotational viscometer
Mo crucible and bob
Ar atmosphere
48
Kim [94] 28-34 %SiO2
10-18 %Al2O3
40-48 %CaO
3.5-10 %MgO
1-5 %FeO
0.1-1.54 1400-1550 Rotational viscometer
Mo crucible and bob
Ar atmosphere
It is confirmed that the addition of “FeO” content will reduce the slag viscosity [113].
In addition, the modify ability of “FeO” content could be determined from viscosity
measurement. Kim proposed that, if the SiO2 and Al2O3 content kept constant, the
replacement of either CaO or MgO by “FeO” content will increase the slag viscosity,
which indicated that the viscosity reduction ability of “FeO” is weaker than the CaO
and MgO [94]. As Figure 2.23 shown, the viscosity firstly decreased and then
increased with the replacement of both CaO and MgO by FeO at fixed temperature
condition.
Figure 2.23 FeO replaced the CaO and MgO oxide at 40 wt% SiO2, 1500 oC for
SiO2-CaO-FeO system, 40 wt% SiO2, 1550 oC for SiO2-MgO-FeO system, by Bockris
[94], Chen [115], Ji [114]and Urbain [13]
49
2.3.5.2 TiO2
TiO2 is a gangue mineral containing in the iron ore, which is removed in the slag
phase. In the ironmaking process, there are two types of slag containing TiO2; normal
blast furnace slag contain <1 wt% TiO2 and another in PanSteel could achieve 30 wt%
TiO2. The PanSteel from Panzhihua of China reported final slag containing large
amounts of TiO2 due to vanadium-titanium magnetite ore in that region, which would
achieve over 30% TiO2 in the slag. The viscosity study of slag is completed by
Chinese researchers. Also, extra TiO2 were added in the recent ironmaking process.
Because, the formation of Ti(C, N) fill the defect spot inside the furnace wall, which
can extend the usage life of blast furnace. The viscosity study of two types of TiO2
slag is summarized in Table 2.14.
Table 2.14 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-TiO2 system
Composition Viscosity
(Pa.s)
Temperature
(oC)
Methodology Description
Handfield
[116]
21-40 %SiO2
15-16 %Al2O3
20-30 %CaO
5.2-5.7 %MgO
5-26 %TiO2
0.03-
0.36
1550-1710 Rotational viscometer
Pt crucible and bob
Air atmosphere
Van
[117]
24-37 %SiO2
11-16 %Al2O3
19-26 %CaO
13-20 %MgO
24-37 %TiO2
0.01-0.2 1360-1640 Rotational viscometer
Mo crucible and bob
Ar atmosphere
50
Saito [62] 32-36 %SiO2
16-18 %Al2O3
32-36 %CaO
5-10 %MgO
10-20 %TiO2
0.109-
0.629
1400-1600 Rotational viscometer
Graphite crucible and bob
Ar atmosphere
Xie [118] 19-30 %SiO2
9-19 %Al2O3
19-30 %CaO
7-16 %MgO
17-33 %TiO2
0.01-
0.06
1350-1500
Rotational viscometer
Graphite crucible and bob
Ar atmosphere
Shankar
[32]
32-40 %SiO2
21-29 %Al2O3
28-40 %CaO
2-5 %MgO
0-2.17 %TiO2
0.16-
2.55
1400-1600 Rotational viscometer
Graphite crucible and bob
Ar atmosphere
Liao
[119]
26-44 %SiO2
12 %Al2O3
22-32 %CaO
7 %MgO
15-30 %TiO2
0.1-1.7 1350-1500 Rotational viscometer
Graphite crucible and bob
Ar atmosphere
Park
[120]
28-40 %SiO2
17 %Al2O3
30-40 %CaO
10 %MgO
0.14-
1.05
1325-1500 Rotational viscometer
Mo crucible and bob
Ar atmosphere
51
5-10 %TiO2
In terms of the viscosity impact of TiO2, there are two contradictive opinions. Liao
believed that the TiO2 has a similar structural unit as SiO2, which positively increase
the slag viscosity (TiO2>20wt%) [119]. When the TiO2 concentration decreased, in
Park’s viscosity measurement, it has been found the addition of TiO2 reduce the slag
viscosity of blast furnace type slag [121].
2.3.5.2 Na2O and K2O
The viscosity impact of Na2O and K2O is different, which is negative and positive
respectively. Most of the basic oxides were reported a negative impact on the slag
viscosity, such as CaO, MgO, FeO, CuO and etc. However, it is found that the
addition of K2O would increase the slag viscosity in CaO-MgO-Al2O3-SiO2 system.
The mechanism of viscosity increasing is not fully explained. Both Kim and Park
estimated that the K+ has a strong combination with AlO4 and form KAlO4 units, and
hence increase the slag viscosity by network formation. The reviewed publications
were summarized in Table 2.15.
Table 2.15 Summary of viscosity study at CaO-MgO-Al2O3-SiO2-Na2O and K2O
system
Composition Viscosity
(Pa.s)
Temperature
(oC)
Methodology Description
Na2O
Kim [122] 30-40 %SiO2
10-15 %Al2O3
0.1-0.4 1360-1600 Rotational viscometer
Pt crucible and bob
52
20-40 %CaO
5-10 %MgO
10-15 %Na2O
Ar atmosphere
Kim [123] 15-30 %SiO2
5-16 %Al2O3
10-40 %CaO
4-8 %MgO
1-10 %Na2O
0.1-0.5 1350-1550 Rotational viscometer
Pt crucible and bob
Air atmosphere
Takahira
[124]
25-45 % SiO2
10-15 %Al2O3
30-40 %CaO
5-10 %MgO
1-5 %Na2O
0.05-0.3 1400-1650 Rotational viscometer
Mo crucible and bob
Ar atmosphere
K2O
Kim [122] 30-40 %SiO2
1-15 %Al2O3
35-45 %CaO
3-15 %MgO
1-5 %K2O
0.1-0.55 1300-1550 Rotational viscometer
Pt crucible and bob
Ar atmosphere
Wu [125] 25-40 %SiO2
1-15 %Al2O3
30-45 %CaO
5-15 %MgO
3-10 %K2O
0.3-0.5 1350-1600 Rotational viscometer
Mo crucible and bob
Ar atmosphere
53
2.4 The review and evaluation of viscosity model for silicate melts of CaO-MgO-
Al2O3-SiO2 system
Abundant viscosity models were developed to predict the viscosity of molten slag at
various systems. In the present sections, the models, which covered CaO-MgO-Al2O3-
SiO2, will be reviewed. Some models only release the equations and did not include
parameters, which is not capable of calculating the slag viscosity. These models were
reviewed from section 2.4.1 to 2.4.6. The other models, suitable for CaO-MgO-Al2O3-
SiO2 system, were reviewed from section 2.4.6 to 2.4.18. In addition, the prediction
performance of each model will be shown in the section 2.4.22, which utilized the
evaluated viscosity database in the CaO-MgO-Al2O3-SiO2 system.
2.4.1 Bottinga Model
The Bottinga model has been developed for magmatic silicate liquid of geological
interest [126]. Authors used a total of 2440 observations, which span the temperature
range 1100 to 1800 oC and the composition range 35 to 91 mol% SiO2 for D
parameters optimization. The Equation 2-6 were proposed to calculate the viscosity
utilizing parameter D and slag composition.
Equation 2-6. Bottinga model Equation [126]
log(η) = ∑ 𝑋𝑖𝐷𝑖
Where η viscosity in Poise, Xi is the weight fraction of metal oxides and Di are the
model parameters, which are constant over restricted composition and temperature
range.
An example of parameter D value of CaO-MgO-Al2O3-SiO2system is shown in Table
2.16 below, it can be seen that the temperature gap between two values is large and
54
cause deviations on viscosity predictions. In addition, the four components CaO, MgO,
Al2O3 and SiO2 in different molar fractions has new sets parameters, which altogether
report 470 model parameters.
Table 2.16 the parameter D values of Bottinga model in CaO-MgO-Al2O3-SiO2
quaternary system [126]
When XSiO2 is from 0.45-0.51
Component 1400 oC 1450
oC 1500
oC 1550
oC
SiO2 10.5 9.8 9.2 8.56
CaAl2O4 1.74 2.84 4.09 4.84
MgAl2O4 4.82 6.04 6.63 7.91
CaO 3.61 3.47 5.17 4.5
MgO 2.23 2.05 2.62 2.7
2.4.2 Neural Network Model
Hanao used neural networks theory to describe viscosity of blast furnace-type slags
[127]. The neural network is a typical fully computer-based models without any
consideration of silicate structure. The neural network model did not report a set of
equations or parameters for viscosity calculation. The software will compare the input
variable with existing database and calculate the viscosity value. The input includes
molar fraction SiO2, Al2O3, CaO, MgO, Temperature, and basicity. This theory can
apply in any other fields with large quantity of database [127].
2.4.3 Giordano Model
The Giordano model is a purely empirical models, which is developed based on
Vogel-Fulcher-Tamman equation to describe slag viscosity [128]. The VFT equation
55
is shown below, where A, B, and C are model parameters. Model parameters were
fitted to each slag compositions as Equation 2-7 shown. Therefore, the model reports
an outstanding agreement with entire database (5% relative error) but is limited to use
for un-fitted composition.
Equation 2-7. VFT model equation [128]
log(η) = A +B
𝑇 − 𝐶
Where η is the viscosity of Poise, T is the temperature in K, A, B and C is the
parameters given by Giordano shown in Table 2.17.
Table 2.17 Model parameters for Giordano [128]
A B C Relative Error
Slag Sample 1 -7.38 27568.73 -24.48 0.05
Slag Sample 2 -4.77 9184.3 473.71 0.08
Slag Sample 3 -6.05 13653.62 165.01 0.03
Slag Sample 4 -3.82 9055.89 362.25 0.08
2.4.4 CSIRO Model
Zhang proposed a structurally-based model to predicate the viscosity of a large
silicate melts system, including, pure oxides SiO2, Al2O3, CaO, MgO, Na2O K2O and
binary systems SiO2–Al2O3, SiO2–CaO, SiO2–MgO, SiO2–Na2O, SiO2–K2O, Al2O3–
CaO, Al2O3–MgO, Al2O3–Na2O, Al2O3–K2O, as a fundamental study for the system
SiO2–Al2O3–CaO–MgO [129]. The completed model reported a good agreement
between experimental data and calculated viscosity using only one set of model
parameters. The critical model parameters were calculated using the concentration of
different oxygen species, which were obtained by the cell model formalism. However,
56
the model parameters were not published. Only the equation can be reviewed, as
shown in Equation 2-8.
Equation 2-8 CSIRO model equation [129]
η = AW ∗ T ∗ exp (Ew
η
RT)
Where η is the viscosity, T is the temperature in (K), R is the gas constant, AW
and
Ew
n are the pre-exponential term and the activation energy, respectively.
Ewη = a + b(N𝑂0)3 + 𝑐(𝑁𝑂0)2 + 𝑑(𝑁𝑂−2)
Where a, b, c and d are fitting parameters optimized against experimental data. The
values of NO and NO2- were obtained by the Cell model formalism.
ln(AW) = a′ + b′ ∗ Ewη
Where a’ and b’ are fitting parameters in the publications [129]
2.4.5 KTH Model
The KTH viscosity model was developed on the basis of the Erying equation, which
is based on the absolute reaction rate theory for the description of flow processes
[130]. The completed model reported a good agreement between experimental data
and calculated viscosity using as a function of temperature and composition. However,
the model parameters were not published. Only the equation can be reviewed, as
shown in Equation 2-9.
Equation 2-9 Model equation of KTH model [130]
η =ℎ𝑁ρ
𝑀exp (
∆𝐺∗
RT)
57
Where η is the viscosity, T is temperature in (K), R is the gas constant, h is Planck’s
constant, N is Avogadro's number, ρ is average density and ∆𝐺∗ is the gibbs energy of
activation per mole.
2.4.6 Urbain Model
Urbain’s model is one of the most widely used slag viscosity models and based on the
Weymann-Frenkel liquid viscosity model [131]. Urbain proposed two versions
models on 1981 and 1987 respectively. The application range of Urbain model
include the oxide CaO, MgO, SiO2, S and F containing slag, which covers most of
slag system. Although, the Urbain model covers wide range of slag system; the
prediction deviations is large in the particular slag system. Another disadvantage of
Urbain model is the consideration of amphoteric oxide, which regarded Al2O3 as
positive terms to slag viscosity without correlation with basic oxide concentration.
Therefore, in the conditions of low abundance of basic oxide slag, Urbain model
reported a high variance of viscosity prediction. For the Urbain model 1981 and 1987
version, the mathematical equations and parameters were similar except the
calculation of individual B parameters.
The development Urbain model was based on the CaO-Al2O3-SiO2 system and
classified the slag components into three categories: glass former; modifier and
amphoteric [132]. In the CaO-MgO-Al2O3-SiO2 system, the XG, XM and XA were
calculated as follows. The XG* was obtained by division of
(1+XCaF2+0.5XFeO1.5+XZrO2). For example, the XG*=XG/ (1+XCaF2+0.5XFeO1.5+XZrO2).
Equation 2-10 Urbain Model Equation [132]
X𝐺 = X𝑆𝑖𝑂2+ ⋯
X𝑀 = X𝐶𝑎𝑂 + X𝑀𝑔𝑂 + ⋯
X𝐴 = X𝐴𝑙2𝑂3+ ⋯ X𝐹𝑒2𝑂3
+ X𝐵2𝑂3
58
𝑋𝐺∗ =𝑋𝐺
1 + XCaF2 + 0.5XFeO1.5+ XZrO2
η = 𝐴 ∗ 𝑇 ∗ exp (1000𝐵
𝑇)
ln(𝐴) = 0.29 ∗ 𝐵 + 11.57
Where XA is the molar composition of that component, η is the viscosity in poise, T is
the temperature in K, A and B are model parameters.
The XA were fitted into a third order polynomial equation to calculate the parameter B.
Parameter B in Urbain model equalled to the role of activation energy of Arrhenius
equation. The parameters B were expressed by third order polynomial equation of 4
model terms B0-3 as equation shown.
Equation 2-11 Urbain Model Equation [132]
𝐵0 = 13.8 + 39.9355 ∗ α + 44.049 ∗ α2
𝐵1 = 30.481 − 117.1505 ∗ α + 139.9978 ∗ α2
𝐵2 = −40.9429 + 234.0486 ∗ α − 300.04 ∗ α2
𝐵3 = 60.7619 − 153.9276 ∗ α + 211.1616 ∗ α2
B = 𝐵0 + 𝐵1 ∗ (𝑋∗𝐺)3 + 𝐵2 ∗ (𝑋∗
𝐺)2 + 𝐵3 ∗ (𝑋∗𝐺)3
α =X𝑀
X𝐴+X𝑀
Where XA and XM is the molar composition of that component
On 1987, Urbain suggested a different method to determine the individual parameter
B of BCa and BMg; and then determined the mean B as Equation 2-12 shown. The
modified equations of B improve the prediction accuracy CaO, MgO and MnO
including system, especially CaO-MgO-Al2O3-SiO2. The B of Ca, Mg and Mn (if
necessary) was calculated individually, which combine to the final B. The required
model equations and parameters were shown in Table 2.18.
59
Equation 2-13. Urbain model equation [131]
𝐵 =𝑀𝐶𝑎 ∗ 𝐵𝐶𝑎 + 𝑀𝑀𝑔 ∗ 𝐵𝑀𝑔 + 𝑀𝑀𝑛 ∗ 𝐵𝑀𝑛
𝑀𝐶𝑎 + 𝑀𝑀𝑔 + 𝑀𝑀𝑛
𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔) = 𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔)0 + 𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔)
1 + 𝐵𝑖(𝑖=𝐶𝑎,𝑀𝑔)2
𝐵𝑖 (𝑖=𝐶𝑎,𝑀𝑔)0,1,2 = 𝐵0,𝐶𝑎 + 𝐵1,𝐶𝑎 ∗ 𝑅 + 𝐵2,𝐶𝑎 ∗ 𝑅2
Basicity index (R) =𝑀𝐶𝑎 + 𝑀𝑀𝑔
𝑀𝐶𝑎 + 𝑀𝑀𝑔 + 𝑀𝐴𝑙
Table 2.18 Model parameters of Urbain Model [131]
Constant B1* α B2* α2
CaO
MgO
MnO
CaO MgO MnO CaO MgO MnO
0 13.2 41.5 -45 20 15.9 -18.6 -25.6
1 30.5 -117.2 130 26 -54.1 33 -56
2 -40.4 232.1 -298.6 -110.3 138 -112 186.2
3 60.8 -156.4 213.6 64.3 -99.8 97.6 -104.6
The Urbain model of 1987 version is more suitable for the viscosity prediction of
CaO-MgO-Al2O3-SiO2 system. As Figure 2.24 shown, the 1987 Urbain models
reported smaller prediction deviation comparing to the 1981 version, due to Urbain
optimization on the parameter calculations. Please note, the quantity of viscosity
measurements of before-evaluation group is 3105, which was the original viscosity
data without evaluation process in Section 2.3. The quantity of viscosity
measurements of after-evaluation group is 1760.
60
Figure 2.24 The comparison between Urbain model of 1981 [132] and 1987 version
[131] using the viscosity database of before-evaluation, after-evaluation and BF
composition
2.4.6.1 Riboud Model
Riboud optimized the Urbain model to estimate the viscosity in mould fluxes [133].
Riboud simplified the Urbain’s expression of B term, the model term A is not
dependent on B, which was calculated using slag composition. As Equation 2-14
shown, the network modifiers parameter, CaO, and MgO have the same contribution
(value=1.73) to the viscosity, which did not obey their network modify ability. It is
accepted that different basic oxide has various ability to break silicate network.
Equation 2-14. Riboud model equation [133]
η = 𝐴 ∗ 𝑇 ∗ exp (1000𝐵
𝑇)
𝑙𝑛𝐴 = −19.81 + 1.73(𝑋𝐶𝑎𝑂 + 𝑋𝑀𝑔𝑂) − 35.76𝑋𝐴𝑙2𝑂3
𝐵 = 31140 − 23896(𝑋𝐶𝑎𝑂 + 𝑋𝑀𝑔𝑂) + 68833𝑋𝐴𝑙2𝑂3
Where η is the viscosity of Poise, A and B is the parameters, T is the temperature in K,
XCa and XMg are the molar composition of slag system
61
2.4.6.2 Kondratiev and Forsbacka Model
The modified-Urbain viscosity model was also constructed at the University of
Queensland by Kondratiev and Forsbacka for the viscosity prediction of coal ash slag
[134, 135]. Kondratieve first proposed the model for viscosity prediction of coal ash
slag of CaO-FeO-Al2O3-SiO2 system [134]. Later, Forsbacka optimized the
parameters using excel-solver and extend the prediction range to MgO, CrO and
Cr2O3 containing system [135]. The proposed model reported similar mathematical
structure as Urbain model, which changed the equations and parameters of B
calculation. The model was able to describe the viscosity of complex slags reasonably
well in most experimental cases, which agreed well with experimental measurements
in the ‘Round Robin’ project [135].
2.4.7 Iida Model
Iida proposed the mathematical model to estimate the slag viscosity, which is based
on Arrhenius type of equation and slag basicity property [136, 137]. The core
parameters A,𝜇0 E are determined based on temperature as Equation 2-15 shown.
Bi was defined as slag basicity. In the CaO-MgO-Al2O3-SiO2 system, it is accepted
that (wt% CaO/SiO2) slag basicity is an indication of the ironmaking operation
performance. Referring to the viscosity, a high basicity slag would report a low
viscosity. Iida considered and encountered the amphoteric oxide Al2O3 and regarded it
as a network former, which will reduce the slag basicity. Iida reported that the
viscosity predictions closely fit with the experimental data for a large number of blast
furnace type slags. The relevant equations and parameters are shown in 错误!未找到
引用源。 and Table 2.19 respectively.
Equation 2-15. Iida Model Equations [136, 137]
η = 𝐴 ∗ 𝜇0 ∗ exp (𝐸
𝐵𝑖∗)
62
A = 1.745 − 1.962 ∗ 10−3𝑇 + 7 ∗ 10−7𝑇2
𝐵𝑖∗ =𝑎𝐶𝑎𝑂 ∗ 𝑊𝐶𝑎𝑂 + 𝑎𝑀𝑔𝑂 ∗ 𝑊𝑀𝑔𝑂
𝑎𝐴𝑙2𝑂3 ∗ 𝑊𝐴𝑙2𝑂3 + 𝑎𝑆𝑖𝑂2 ∗ 𝑊𝑆𝑖𝑂2
𝜇0 = ∑ 𝜇0𝑖𝑋𝑖
𝜇0𝑖 = 1.8 ∗ 10−7(𝑀𝑖 ∗ (𝑇𝑚)0.5
𝑖
(𝑉𝑚)𝑖2/3
exp (𝐻𝑖
𝑅 ∗ (𝑇𝑚)0.5𝑖
) )
𝐻𝑖 = 5.1 ∗ (𝑇𝑚)1.2𝑖
E = 11.11 − 3.65 ∗ 10−3𝑇
Where Mi is the formula weight of i component, Tmi is the melting temperature, R is
gas constant, Hi melting enthalpy of i component, Bi is the slag basicity, W is the wt%
of each oxide, aoxide is the model parameters, E is the enthalpy of slag.
Table 2.19 Equation parameters for Iida model [136, 137]
SiO2 Al2O3 CaO MgO
A 1.48 0.1 1.53 1.51
Temperature Μ
oC SiO2 Al2O3 CaO MgO
1400 3.76 7.95 23.82 39.66
1450 3.43 7.12 20.67 34.01
1500 3.11 6.36 17.83 28/96
1550 2.92 5.89 16.15 26.03
63
2.4.8 NPL (Mills) Model
Mills’ viscosity model (also called NPL) is based on optical basicity parameter, which
is firstly determined and named by Duffy J.A [138, 139]. The metal oxides were
reported various peak intensity under UV light. Assume CaO is 1, the other oxides
basicity were determined and demonstrated by Duffy [139, 140].
The NPL model was developed based on the Arrhenius-type equation. As Equation
2-16 shown, the AOP
, Mills calculated the slag basicity with insertion of oxide
composition*optical basicity. The AOP
term were directly linked to the parameter A
and B for viscosity calculation. The predictions of NPL model were in reasonable
agreement with experimental data for reported multicomponent system.
Equation 2-16. NPL (Mills) model equation [138]
η = 𝐴 ∗ exp (𝐵
𝑇)
B = Exp (−1.77 ∗2.88
𝐴𝑜𝑝) ∗ 1000
ln(A) = −144.17 + 357.32 ∗ A𝑜𝑝 − 232.69 ∗ (A𝑜𝑝)2
A𝑜𝑝 =𝛾𝑆𝑖𝑂2 ∗ 𝑀𝑆𝑖𝑂2 + 𝛾𝐴𝑙2𝑂3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝛾𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + 𝛾𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂
2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂
Where η is the viscosity in Pa.s, T is the temperature in K, Mi is the molar
composition of slag system and all other parameters are shown in Table 2.20.
Table 2.20 Model parameters of NPL model [138]
SiO2 Al2O3 CaO MgO
Optical Basicity 0.48 0.6 1 0.78
64
2.4.9 Shankar Model
Based on Mills work on the optical basicity, Shankar did a doctoral thesis work on the
studies on high alumina blast furnace slags, which investigate the viscosities data and
improve the model prediction accuracy on blast furnace slag system [141]. The model
equations were shown as Equation 2-17. Shankar has different calculations on the AOP
comparing to the NPL model. The basicity of basic oxide and acid oxide were
normalized first; then calculated the slag basicity. The model predictions report
satisfactory agreement with experimental data.
Equation 2-17. Shankar model equations [141]
η = 𝐴 ∗ exp (1000 ∗ 𝐸
𝑇)
ln(A) = −0.3068 ∗ A𝑜𝑝 − 6.7374
B = −9.897 ∗ A𝑜𝑝 + 31.347
A𝑜𝑝 = (𝛾𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + 𝛾𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂
𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂)/ (
𝛾𝑆𝑖𝑂2 ∗ 𝑀𝑆𝑖𝑂2 + 𝛾𝐴𝑙2𝑂3 ∗ 𝑀𝐴𝑙2𝑂3
2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3)
Where η is the viscosity of poise, T is the temperature in K, Mi is the molar
composition of slag system and all other optical basicity parameters are the same as
Table 2.20 shown.
2.4.10 Hu Model
Hu did a similar work as Shankar that optimized the Mill’s model towards the blast
furnace slag field [142]. Comparing the model from Mills and Shankar, Hu consider
the alumina charge compensation effect by the CaO, which is noted from his equation.
However, the equation structure can only apply on the MCaO>MAl2O3 condition, which
is a typical blast furnace composition range. The model prediction fits well with
experiment data in the SiO2-Al2O3-CaO, CaO-MgO-Al2O3-SiO2 and CaO-MgO-
65
Al2O3-SiO2-TiO2 system, with the mean deviation less than 25%. The model
equations were shown as Equation 2-18.
Equation 2-18. Hu model equations [142]
η = 𝐴 ∗ exp (1000 ∗ 𝐸
𝑇)
ln(A) = −0.3068 ∗ A𝑜𝑝 − 6.7374
B = −9.897 ∗ A𝑜𝑝 + 31.347
A𝑐𝑜𝑟𝑟 =0.48 ∗ 2 ∗ 𝑀𝑆𝑖𝑂2 + 0.6 ∗ 3 ∗ 𝑀𝐴𝑙2𝑂3 + (𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3) + 0.78 ∗ 𝑀𝑀𝑔𝑂
2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3 + (𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3) + 𝑀𝑀𝑔𝑂
Where η is the viscosity of poise, T is the temperature in K, Mi is the molar
composition of slag system and all other optical basicity parameters are the same as
Table 2.20 shown.
2.4.11 Shu Model
There are two versions of Shu’s viscosity model, which published at 2009 and 2015
[143, 144]. In the present study, only the latest version (2015) were reviewed and
evaluated. Shu pointed that viscosity of CaO-MgO-Al2O3-SiO2 quaternary system is
composed of two sub ternary systems ideal mixing, which is SiO2-Al2O3-CaO and
SiO2-Al2O3-MgO. This assumption has benefits that ternary system involved
parameters and consideration are less than the quaternary system. For example, Ca
and Mg cations are required to charge compensate (AlO4)5-
structure. This assumption
avoids the consideration of the priority of Ca and Mg cations with AlO4. The
normalized molar fraction formula is used to combine two sub-ternary systems to a
quaternary variable, and then use Arrhenius equation to calculate the final viscosity.
Shu’s model considers the equilibrium between three types oxygen: O (bridging
oxygen), O- (non-bridging oxygen) and O
2- (free oxygen). Shu utilizes the Ottonello’s
66
work on the equilibrium constant K, which established a link between the optical
basicity and silicate polymerization [144]. A good agreement between calculated and
measured viscosity with a mean deviation of less than 25% was achieved.
Equation 2-19. Shu model equations [143, 144]
lnη = 𝑙𝑛𝐴 + 𝐸/𝑅𝑇
ln(𝐴) = 𝑚 ∗𝐸
𝑅+ 𝑛
E = 𝑋𝐴𝑙𝐸𝐴𝑙 + (1 − 𝑋𝐴𝑙)(𝑋𝑂2−𝐸𝑂2−𝑋𝑂−(𝑦𝑆𝑖𝐸𝑂− − (𝑆𝑖 − 𝑂−) + 𝑦𝐴𝑙𝐸𝑂− − (𝐴𝑙 − 𝑂−))
+ 𝑋𝑂0 ∗ (𝑦𝑆𝑖𝐸𝑂0(𝑆𝑖 − 𝑂0) + 𝑦𝐴𝑙𝐸𝑂0(𝐴𝑙 − 𝑂0)))
Where η is the viscosity of poise, T is the temperature in K, Xi is the molar
composition of slag system and E parameters shown in publication [143, 144].
2.4.12 Zhang Model
Zhang proposed a mathematical model to describe the viscosity behavior of the
multicomponent system, which is based on different oxygen ions present in molten
slag [145]. The three oxygen ions are bridging oxygen [O], non-bridging oxygen [O-],
and free oxygen [O2-
]. With the consideration of possible structural units, Zhang
specifies the oxygen ions between Al, Ca and Mg cations. For example, the charge
compensated oxygen between Ca and Al etc. The concentrations of these different
oxygen ions are calculated on the basis of Zhang’s assumptions, then, Zhang uses
Arrhenius type equation to calculate the slag viscosity and reported an outstanding
agreement with experimental data. The utilized equation and model parameters were
included in the Equation 2-20 and Table 2.21 respectively. As shown in Table 2.21
and Table 2.22, the major features of Zhang’s model are the assumptions based
calculations. The calculated structural units would be utilized to determine the
67
activation energy of that composition slag, and hence determine the viscosity at fixed
temperature.
Equation 2-20. Zhang model equations [145]
lnη = 𝑙𝑛𝐴 + 𝐸/𝑅𝑇
Where η is the viscosity of poise, E is the activation energy term, T is the temperature
in K, R is the gas constant
lnA = k(E − 572516) − 17.47
k = ∑ (𝑥𝑖𝑘𝑖)/ ∑ (𝑥𝑖)
𝑖,𝑖≠𝑆𝑖𝑂2𝑖,𝑖≠𝑆𝑖𝑂2
E =572516 ∗ 2
𝑛𝑂𝑆𝑖+ ∑ 𝑎2 ∗ 𝑛𝑂−
Where 𝑛𝑂𝑆𝑖 is the number of oxygens bridging with silicate, the 𝑛𝑂− is the number of
other types of oxygen except bridging oxygens 𝑛𝑂𝑆𝑖. The calculation of these
parameters were shown in the Table 2.22
Table 2.21 The model parameters used to calculate E [145]
kMg aMg aSiMg
aAl,Mg aMg
Al,Mg
-2.106*10-5
15.54 6.908 5.606 3.975
kCa aCa aSiCa
aAl,Ca aMg
Al,Mg
-2.088*10-5
17.34 7.422 4.996 7.115
kAl aAl
aMg
Al,Ca
-2.594*10-5
5.671 8.334
68
Table 2.22 All possible condition in the CaO-MgO-Al2O3-SiO2 system, only the
condition 1 equations were included. The equations for other conditions is not
included due to text limitation [145].
Condition
I. x𝐶𝑎𝑂 + x𝑀𝑔𝑂 < x𝐴𝑙2𝑂3 η𝑂𝑆𝑖= 2𝑥𝑆𝑖𝑂2
η𝑂𝐴𝑙= 3(𝑥𝐴𝑙2𝑂3
− x𝐶𝑎𝑂 − x𝑀𝑔𝑂)
η𝑂𝐴𝑙,𝐶𝑎= 4𝑥𝐶𝑎𝑂
η𝑂𝑆𝑖,𝑀𝑔= 4𝑥𝑀𝑔𝑂
II. x𝐶𝑎𝑂 < x𝐴𝑙2𝑂3, x𝐶𝑎𝑂 + x𝑀𝑔𝑂 < x𝐴𝑙2𝑂3
and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 − x𝐴𝑙2𝑂3< 2(x𝑆𝑖𝑂2
+
2x𝐴𝑙2𝑂3)
[145, 146]
III. x𝐶𝑎𝑂 > x𝐴𝑙2𝑂3and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 −
x𝐴𝑙2𝑂3< 2(x𝑆𝑖𝑂2
+ 2x𝐴𝑙2𝑂3)
[145, 146]
IV. x𝐶𝑎𝑂 > x𝐴𝑙2𝑂3and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 −
x𝐴𝑙2𝑂3> 2(x𝑆𝑖𝑂2
+ 2x𝐴𝑙2𝑂3)
[145, 146]
V. x𝐶𝑎𝑂 < x𝐴𝑙2𝑂3and x𝐶𝑎𝑂 + x𝑀𝑔𝑂 −
x𝐴𝑙2𝑂3> 2(x𝑆𝑖𝑂2
+ 2x𝐴𝑙2𝑂3)
[145, 146]
2.4.13 Gan Model
Gan developed blast furnace viscosity model based on Vogel-Fulcher-Tammann
Equation 2-21, which has successfully applied to magmatic liquids before [147]. It is
a linear relation between the slag composition and model parameter (B, C). Gan
reported that model can accurately predict the viscosity of blast furnace slag with a
relative average error of 0.211. A slight modification of this model can also predict
the glass transition temperature of blast furnace slag satisfactorily.
Equation 2-21. Gan model equations, A is -3.1, the parameters of bi and ci were
shown in Table 2.23 [147]
η = 𝐴 +𝐵
𝑇 − 𝐶
69
B = ∑ 𝑏𝑖𝑥𝑖
C = ∑ 𝑐𝑖𝑥𝑖
Where η is the viscosity in Pa.s, T is the temperature in K, Xi are the molar
composition of slag system
Table 2.23 Model parameters of Gan model [147]
bi ci
SiO2 3308.42 1019.48
Al2O3 5490.72 725.95
CaO 751.19 985.23
MgO 1944.87 556.66
2.4.14 Tang Model
Tang proposed viscosity model utilizing a ratio of non-bridging oxygen to tetrahedral
metal (NBO/T) [148] as Equation 2-22 shown. Tang’s expression is similar to Iida’s
basicity equation with additional concerning of alumina-silicate structure. In “round
robin project”, the model predictions have an outstanding agreement with
experimental data, which reported smaller deviations than Iida model in CaO-MgO-
Al2O3-SiO2-R2O (K2O or Na2O) system.
Equation 2-22. Tang model equations [148]
η = exp (−9.4 −43.63
(3.75 +𝑁𝐵𝑂
𝑇 )+
150450
(3.75 +𝑁𝐵𝑂
𝑇 ) ∗ 𝑇)
𝑁𝐵𝑂
𝑇=
2 ∗ (𝑎𝑀𝑔𝑂 ∗ 𝑋𝑀𝑔𝑂 + 𝑎𝐶𝑎𝑂 ∗ (𝑋𝐶𝑎𝑂 − 𝑋𝐴𝑙2𝑂3))
2 ∗ 0.427 ∗ 𝑏𝐴𝑙2𝑂3 ∗ 𝑋𝐴𝑙2𝑂3 + 𝑋𝑆𝑖𝑂2
70
Where η is the viscosity in Pa.s, T is the temperature in K, Xi are the molar
composition of slag system and all other parameters are given by Shankar, other
model parameters are shown in Table 2.24
Table 2.24 Model parameters of Tang model [148]
ai bi
Ca 1 1
Mg 0.86 0.47
2.4.15 Ray Model
Based on the Urbain model, Ray proposed a new mathematical model, which is
capable of calculating the viscosity based on slag composition, temperature and
optical basicity [149] as Equation 2-23 shown. The model proposed is applicable to
homogeneous fluid melts only. The mathematical equations of Ray model are similar
to Mill model, which were shown as below:
Equation 2-23. Ray model equations [149]
η = 𝐴 ∗ exp (𝐵
𝑇)
B = 297.14 ∗ (A𝑜𝑝)2 − 466.69 ∗ A𝑜𝑝 + 196.22
ln(A) = −0.2056 ∗ B − 12.492
A𝑜𝑝 =𝛾𝑆𝑖𝑂2 ∗ 𝑀𝑆𝑖𝑂2 + 𝛾𝐴𝑙2𝑂3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝛾𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + 𝛾𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂
2 ∗ 𝑀𝑆𝑖𝑂2 + 3 ∗ 𝑀𝐴𝑙2𝑂3 + 𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂
Where η is the viscosity of Poise, T is the temperature in K, Mi is the molar
composition of slag system and all other optical basicity parameters are the same as
Table 2.20 shown.
71
2.4.16 Li Model
Li proposed a novel viscosity model based on the flow mechanism involving the
concept of “cut-off” points proposed by Nakamoto [150]. The non-bridging oxygen
and free oxygen have large mobility because there are “cut-off” points near non-
bridging oxygen linkage Si-O-Ca and free oxygen. These “cut-off” points constantly
move and break the networks to produce new “cut-off” points when shear stress is
applied to the silicate melts. Thus, the movement of “cut-off” points results in viscous
flow. The concept of “cut-off” from Li and Nakamoto is similar to the “hole” theory
in the other silicate melts structure.
The model equations and parameters have been summarized in the Equation 2-24 and
Table 2.25.
Equation 2-24 Li model equations [150]
η = 𝐴𝑊 ∗ exp (𝐸
𝑅𝑇)
ln(𝐴𝑊) = 𝑎 + 𝑏 ∗ 𝐸
a =∑ 𝑎𝑖𝑥𝑖
∑ 𝑥𝑖
b =∑ 𝑏𝑖𝑥𝑖
∑ 𝑥𝑖
Where η is the viscosity of Poise, A and B is the parameters calculating from equation,
T is the temperature in K
Table 2.25 Model parameters of Li model [150]
A b
CaO-SiO2 -5.5781 -0.0000196
MgO-SiO2 -5.4658 -0.0000198
Al2O3-SiO2 -2.6592 -0.0000248
72
2.4.17 Quasi-Chemical Viscosity Model
Alex, Suzuki and Jak developed multicomponent slag viscosity model, which is called
quasi-chemical viscosity model (QCV) [151], as Equation 2-25 shown. QCV is based
on Erying liquid viscosity model, which assumes molten slag has quasi-crystalline
structure. In molten slag, the molecules oscillate from equilibrium position to a
neighboring one when their energy momentarily is equal or larger than the height of
the potential barrier. Therefore, QCV model links the oscillation molecules (also
called bond fraction) to slag viscosity. The potential oscillated molecules are
subdivided into cationic molecular structures (also called bond fraction). For example,
bond fraction parameters of alumina include Al-O-Al, Al-O-Si, Al-O-Mg and Al-O-
Ca. These bond fractions of each metal oxide can only be calculated from FactSage
software. In addition, second nearest neighbor bond (SNNB), which defines as the
impact from neighboring structure, is introduced to improve the model prediction
accuracy. As shown, QCV model includes calculations of each minor structure of four
aspects, which are mass, volume, and activation and vaporization energy term.
Equation 2-25. QCV model equations [151]
η = 2 ∗𝑅𝑇
∆𝐸𝑉∗
(2𝜋𝑘𝑚𝑆𝑈𝑇)0.5
𝑣𝑆𝑈
23
exp (𝐸𝑎
𝑅𝑇)
Factsage model links the viscosities of silicate melts to their thermodynamic
properties, which is described by the quasi-chemical theory. It utilized Q-pairs
(similar as a bond fraction in QCV model) to determine the E parameters and hence
viscosity. Therefore, the QCV models highly rely on the FactSage software to
calculate the critical parameters Q-pair. When FactSage updated from 6.2 to 6.4, the
model parameters require optimization to suit the changes of Q-pair.
73
2.4.18 Factsage 7.0
Factsage is one of the largest fully integrated database computing systems in the
chemical thermodynamics field of pyro-metallurgy study, which focus on the study of
thermodynamic prediction, such as equilibrium, viscosity, and chemical reaction.
Viscosity is one of the features of Factsage and the latest version is 7.0. Although the
mathematical formulas for Factsage are uncertain, it is still a useful and convenient
tool for viscosity prediction with input of temperature and slag composition as
Equation 2-26, which covered most of the slag system and temperature ranges.
Equation 2-26. Factsage model requirements
η = 𝑖𝑛𝑝𝑢𝑡 (𝑠𝑙𝑎𝑔 𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛, 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒)
Where η is the slag viscosity, the input is the required information from user
2.4.19 Summary
Abundant mathematical models were developed to predict the viscosity of the molten
slag. In the present study, altogether 20 models, which is capable of predicting the
CaO-MgO-Al2O3-SiO2 system, were critically reviewed.
In summary, there are several common features within 18 models:
1. Most of the model utilize Arrhenius type equation to express and calculated slag
viscosity. Arrhenius equation is a formula for the temperature dependence of reaction
rates. Viscosity, as physical properties, was reported an outstanding agreement using
Arrhenius-type equation (Equation 2-27).
Equation 2-27. Arrhenius equation
η = 𝐴 ∗ exp (𝐸
𝑇)
74
Where η is the viscosity of Poise, A is the pre-exponential factor and B is the
activation energy of reaction, T is the temperature in K
2. Another interesting feature is the linear correlation between pre-exponential factor
A and activation energy B. From the publications different authors in various systems,
there is a strong linear relationship between A and B, which was utilized in the model
development. Fundamentally, in the Arrhenius equation, the A was regarded as a
frequency factor, which indicated the rate of collision between reactants. B is
activation energy the energy gap required to initial chemical reaction. The linear
relationship was never reported between A and B in reaction kinetics field. As
Equation 2-28 shown, the linear relationship between A and B was widely utilized
and demonstrate a linear relationship at existing viscosity data, including Hu, Shankar,
Urbain and Shu model [131, 142, 143].
Equation 2-28 the linear correlation between ln(A) and b
ln(A) = m ∗ b + n
Where A and B are the parameters required for Arrhenius model calculation, m and b
is generally given by authors
It is widely accepted that molten slag viscosity is determined by its internal structure.
In CaO-MgO-Al2O3-SiO2 system, (SiO4) tetrahedral forms the slag network, hence
increases viscosity. The CaO and MgO perform as network modifiers, which reduce
the slag viscosity. Al3+
can form (AlO4)-
tetrahedral structure similar to SiO4 (network
former). However, AlO45-
requires Mg and Ca cations to balance the electrical charge.
With an insufficient amount of Ca and Mg cations, AlO45-
tetrahedral structure will
break and behavior as network modifier (same as Mg2+
and Ca2+
).
75
The reviewed models can be categorized based on model structure, parameters, and
consideration of the silicate structures. In different stages of the viscosity
development, understanding of alumina-silicate structure was different:
(I) Al2O3 as an amorphous oxide was not considered in model development,
including Gan models.
(II) Consider Al2O3 as network former and introduce into the viscosity model. This
includes Urbain, Riboud, Iida, Mill, Shankar, Hu, Ray, Tang, Li, Suzuki and
Factsage, models.
(III) If basic oxides e.g. CaO are insufficient, the excess Al2O3 will behavior as basic
oxides. This was considered by Shu and Zhang models.
In the pyro-metallurgy field, the fundmental equation from other field were often
utilzed for the viscosity model development. The most popular equation was the
Arrhenius-type equation and its modified equations, which was utilized by Urban,
Mill, Shankar, Hu, Li, Zhang, Li, Ray, Riboud, and Shu (10 authors, Equation 2-29).
Equation 2-29 General form of Arrhenius-type equation
η = A ∗ T𝑋 ∗ 𝑒𝐸𝐴𝑅𝑇
Where η is viscosity in (Pa.s), T is temperature in K; and A is pre-exponential factor,
R is gas constant, X can be 0 (Ray, Shu, Mills, Shankar, Zhang, and Li), 0.5 (Suzuki)
and 1 (Riboud, Hu, and Urbain) from different researchers.
Vogel-Fulcher-Tammann (VFT) is an equation for glass-forming liquid (Equation
2-30), which was firstly proposed by Gan to predict slag viscosity of molten slag of
the CaO-MgO-Al2O3-SiO2 system.
Equation 2-30 VFT equation
log(η) = A +𝐵
𝑇 − 𝐶
76
Where η is viscosity in (Pa.s), T is the temperature in K; and A, B, C are model
parameters.
Another general equation is the basicity calculation of slag, which is the ratio of basic
oxide to acidic oxide. Researchers proposed different mathematical formulas to
correlate the slag structures with compositions. Urbain uses a weight ratio of
(WCaO+WMgO)/ (WAl2O3) to describe the basicity of slag and predict viscosity.
Afterward, Iida and Mills proposed viscosity models using the ratio of (WCaO+WMgO)/
(WSiO2+WAl2O3), with the multiplication of basicity of each oxide. Based on optical
basicity and Mills model, Shankar Ray and Hu revised the model structures and
parameters to improve the precision and accuracy on blast furnace slags containing
minor elements. Shu and Zhang's models established viscosity model with
consideration of three type’s oxygen O, O- and O
-2. However, the calculation of
oxygen concentration is a lack of theory support and relies on assumption. The
features of the existing viscosity models are summarized in Table 2.26 and Table 2.27.
14 structural models were reviewed are evaluated in the present study using the
accepted viscosity database of CaO-MgO-Al2O3-SiO2 slag system. Equation 2-31 is
used to calculate the difference between the measured and the calculated viscosity
values. The evaluation results have been summarized in Table 2.26 and Table 2.27.
Equation 2-31 Error deviation calculation
Δ =1
𝑛∗ ∑ |
𝜂𝐶𝑎𝑙𝑐 − 𝜂𝐸𝑥𝑝
𝜂𝐸𝑥𝑝| ∗ 100%
Where Δthe mean deviation, n is is the total number of simulations, ηCalc is the model
viscosity and ηExp is the experimental viscosity.
77
Table 2.26 Summary of reviewed viscosity model in CaO-MgO-Al2O3-SiO2 system
Sources Structure Related Equation Model Features
Error
Deviation
(%)
Urbain [131] 𝑊𝐶𝑎𝑂 + 𝑊𝑀𝑔𝑂
𝑊𝐴𝑙2𝑂3
Based on Frenkel-Weymann liquid viscosity model, Urbain
theoretically approved the linear correlation between A and B in
the Arrhenius-type equation.
30.2
Riboud [133] A = e(𝑎∗(𝑀𝐶𝑎𝑂+𝑀𝑀𝑔𝑂)−𝑏∗𝑀𝐴𝑙2𝑂3+𝑐)
B = 𝑎 ∗ (𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂) − 𝑏 ∗ 𝑀𝐴𝑙2𝑂3 + 𝑐
Based on Urbain model, Riboud simplify the model equations and
optimize the model parameters using viscosity data of blast
furnace slag
61.0
Iida [136,
137]
𝑊𝐶𝑎𝑂 ∗ 𝑎 + 𝑊𝑀𝑔𝑂 ∗ 𝑏
𝑊𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑊𝑆𝑖𝑂2 ∗ 𝑑
Iida’s model was developed based on slag basicity and own
optimized parameters. 68.6
Mill [138] 𝑀𝐶𝑎𝑂 ∗ 𝑎 + 𝑀𝑀𝑔𝑂 ∗ 𝑏
𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑀𝑆𝑖𝑂2 ∗ 𝑑
Mill’s model was developed based on the oxides’ optical basicity,
which was reported by Duffy and Ingram 70.4
Shankar
[141]
𝑊𝐶𝑎𝑂 ∗ 𝑎 + 𝑊𝑀𝑔𝑂 ∗ 𝑏𝑊𝐶𝑎𝑂 + 𝑊𝑀𝑔𝑂
𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑀𝑆𝑖𝑂2 ∗ 𝑑𝑀𝐴𝑙2𝑂3 + 𝑀𝑆𝑖𝑂2
Shankar optimized the model parameters and equation based on
Mill’s work. 55.2
78
Ray [149] 𝑀𝐶𝑎𝑂 ∗ 𝑎 + 𝑀𝑀𝑔𝑂 ∗ 𝑏
𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 𝑀𝑆𝑖𝑂2 ∗ 𝑑 Ray optimized the model parameters based on Mill’s work. 51.5
Hu [142] 𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3 + 𝑀𝑀𝑔𝑂 ∗ 𝑏 + 2𝑀𝑆𝑖𝑂2 ∗ 𝑐
𝑀𝑀𝑔𝑂 + 𝑀𝐶𝑎𝑂 − 𝑀𝐴𝑙2𝑂3 + 𝑀𝐴𝑙2𝑂3 ∗ 𝑐 + 2𝑀𝑆𝑖𝑂2
Hu also optimized the model parameters and equations based on
Mill’s work 44.3
Gan [147]
B = ∑ 𝑏𝑀𝑂𝑀𝑀𝑂
C = ∑ 𝑐𝑀𝑂𝑀𝑀𝑂
Gan first proposed Vogel-Fulcher-Tammann-type equation in
CaO-MgO-Al2O3-SiO2 field, which can also predict the glass
transition temperature the blast furnace slag with slight
modification.
54.1
Tang [148] 𝑁𝑜𝑛 − 𝑏𝑟𝑑𝑔𝑖𝑛𝑔 𝑜𝑥𝑦𝑔𝑒𝑛
𝑆𝑖𝑂4
Tang proposed the viscosity model using the ratio of non-bridging
oxygen to silica content. 63.9
QCV [151]
E𝑎 = E𝑎,𝑆𝑖−𝑆𝑖𝑀𝑆𝑖−𝑆𝑖 + E𝑎,𝑆𝑖−𝑀𝑒𝑀𝑆𝑖−𝑀𝑒
+ E𝑎,𝑀𝑒−𝑀𝑒𝑀𝑀𝑒−𝑀𝑒
Suzuki developed the viscosity model based on a bond fraction,
which was calculated by Factsage software. Suzuki’s model
contains large number of equations and parameters (>50 equations
and parameters for CaO-MgO-Al2O3-SiO2 quaternary system,
more for higher order system)
35.1
FactSage N/A N/A 37.7
Shu [143, E = E𝑆𝑖𝑂2𝑀𝑆𝑖𝑂2 + E𝑀2𝑆𝑖𝑂4𝑀𝑀2𝑆𝑖𝑂4 + E𝑀𝑜𝑀𝑀𝑜 Shu developed the viscosity models based on compositions of 42.4
79
144] three types of oxygen, which was calculated from optical basicity
values.
Zhang [145]
E𝑎 = E𝑎,𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔𝑀𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔 + E𝑎,𝑛𝑜𝑛−𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔
𝑀𝑛𝑜𝑛−𝑏𝑟𝑖𝑑𝑔𝑖𝑛𝑔 + E𝑎,𝑓𝑟𝑒𝑒𝑀𝑓𝑟𝑒𝑒
Zhang developed the viscosity models based on compositions of
three types of oxygen, which was calculated from assumptions of
[AlO4] binding with Ca2+
and Mg2+
in CaO-MgO-Al2O3-SiO2
system.
28.5
Table 2.27 Summary of applicable oxides of existing viscosity model
Sources Application
Bottinga [126]
SiO2, Al2O3, CaO, MgO, TiO2, FeO, MnO, SrO, BaO,
Li2O, Na2O and K2O
Giordano [128]
SiO2, Al2O3, CaO, MgO, Na2O and K2O
Gupta
SiO2, Al2O3, CaO, MgO, Na2O, K2O, MnO and FeO
Neutral Network
[127]
SiO2, Al2O3, CaO and MgO
Urbain [131] SiO2, Al2O3, CaO, MgO, B2O3, MnO, FeO and PbO
80
Riboud [133] SiO2, Al2O3, CaO and MgO
Iida [136, 137] SiO2, Al2O3, CaO and MgO
Mill [138] SiO2, Al2O3, CaO, MgO, Na2O, TiO2, B2O3, MnO,
FeO, PbO and CaF2
Shankar [141] SiO2, Al2O3, CaO, MgO and TiO2
Ray [149] SiO2, Al2O3, CaO, MgO and TiO2
Hu [142] SiO2, Al2O3, CaO and MgO
Gan [147] SiO2, Al2O3, CaO, MgO, N2O and K2O
Tang [148] SiO2, Al2O3, CaO, MgO, N2O, K2O, FeO and Fe2O3
QCV [151] SiO2, Al2O3, B2O3, MgO, CaO, MnO, FeO, ZnO and
CuO
FactSage All oxides
Shu [143, 144] SiO2, Al2O3, CaO and MgO
81
2.5 The viscosity study review of suspension system
The viscosity of suspensions is of interest in many disciplines of engineering, for example,
food science, wastewater treatment and etc. The suspension viscosity ηsus primarily depends
on (1) the solid fraction, (2) shape and size of particles, and (3) the suspending Newtonian
liquid, which will be reviewed in the section 2.5.1 and 2.5.2 respectively.
A large number of studies have been carried experimentally and theoretically at room
temperature condition. There is a research gap that the solid impact on suspension was rarely
studied in a high-temperature region. It is known that the precipitation of solid particles in
molten slag was commonly observed in iron, steel, copper and other pyrometallurgy
processes. It is necessary to explore and compare the suspension viscosity by the systematic
variation of the parameters at both room and smelting temperature conditions. Table 2.28
summarized the experiment measurements of suspension viscosity at different systems.
Table 2.28 The brief review of viscosity study of suspension system at different system,
viscosity and temperature range, note: the relative viscosity means the ratio of suspension
viscosity to liquid viscosity
Author Solid/Liquid System Viscosity Range
(Pa.s)
Temperature Range
(oC)
Bibbo [152] Fiber
Water
Relative Viscosity
0.5-10
25
Chong [153] Glass beads
Polyisobutylene (PIB)
10-500 25
Darton [154] Silica sand
Water
0.1-3 20
Fan [155] Fiber
Water
Relative Viscosity
0.4-2
25
82
Joung [156] Fiber
Water
Relative Viscosity
0.5-3.7
25
Kwon [157] Magnetic particle
Ethylene glycol
0.02-0.6 25
Konjin [158] Glycerine
polymethylmethacrylate
0.1-2.3 25
Marshall [159] Silica sols
Cis/trans-
decahydronaphthalene,
(Decalin)
2-3.5 200
Namburu [160] SiO2 nanoparticle
60% ethyleneglycol 40%
water
0.004-0.3 -35-50
Tsuchiya [161] Glass beads
Water
0.5-10 20
Wu [9] Paraffin
Oil
0.09-0.47 25
CaO-MgO-Al2O3-SiO2 0.2-0.5 1300-1400
Lejeune [162] CaO-MgO-Al2O3-SiO2 1.4-5 830-950
Wright [163] CaO-MgO-Al2O3-SiO2 2-7.5 1400-1500
2.5.1 Effects of liquid viscosity & Solid Fraction
Liquid viscosity and solid fraction are the two most critical factors in the experimental study
of suspension viscosity, which was also approved in the model simulation work. Einstein first
83
proposed a mathematical expression to predict the suspension viscosity ηsus using liquid
viscosity ηLiq and solid fraction f. The mathematical expression was accepted and optimized
by other researchers to improve the prediction accuracy of Einstein Model [164]. From the
model view, the mathematical expression η𝑠𝑢𝑠 = η𝑙𝑖𝑞 ∗ η𝑟𝑒𝑙𝑎 were utilized for the model
development of suspension viscosity prediction, where nrela is expressed by solid fraction as
shown in Equation 2-32.
Equation 2-32 Definition of relative viscosity
η𝑠𝑢𝑠
η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = f(𝑓)
Where η𝑠𝑢𝑠 is suspension viscosity, η𝑙𝑖𝑞 is the liquid viscosity. f (f) is a mathematical
function of solid fraction.
From the existing viscosity results, it is accepted that both liquid viscosity and solid fraction
has a positive proportional impact on the suspension viscosity at a temperature ranging from -
40 to 1500 oC. When a force applied, the shear stress of liquid is enlarged when the solid
exist within liquid comparing to the pure liquid condition. As
Figure 2.25 shown, with the appearance of the solid particle, the smooth molecular
distribution of fully liquid was converted to the rigid distribution of solid/liquid system;
hence increased the gradient (viscosity). Also, the increase in viscosity with solids
concentrations was attributed to the increased frequency of particle-particle interactions.
Figure 2.25 The shear stress enlarged from fully liquid system to solid/liquid system
84
For the solid fraction ranging from 0-1, the solid proportion and liquid viscosity have a
positive proportional impact on the suspension viscosity. In the low melt fraction regime, the
solid particles have a predominant role until the solid-like behavior is exhibited as solid
fraction achieving 1. As Figure 2.26 shown, with the increasing of solid particles, the
viscosity moderately increases but when a critical solid content is reached, the viscosity
increases so rapidly that over a short range. Upon critical point, the viscosity slowly increased,
which is known as solid-like behavior.
Figure 2.26 Viscosity deduced from data of van der Molten and Paterson (1979) [165]at high
solid fraction (circles) and from data of Mg3Al2Si3O12 by Lejeune (triangles) [162] and other
values at low solid fraction (squares) by Thomas [166]
2.5.2 Effects of Particle Size
There is a contradiction discussion about the impact of particle size on the suspension
viscosity. As Figure 2.27 shown, Wu construct a series study of paraffin/silicon oil system
under room temperature condition. The particle size ranges from 150 um to 450 um reported
similar results, which is only slightly derivate 1.2% [9]. Konijn constructs viscosity
measurement of glycerine/polymethylmethacrylate system and also reported that the particle
size did not impact on the suspension viscosity [167].
85
Figure 2.27 Experiment data of different particle size vs model prediction [167]
However, in Gust’s study, utilizing silica sand/water system, he proposed that the apparent
viscosity increased with particle size at the different pseudo shear rate [168]. The particles of
greater size possess more inertia such that on interaction with rotational bob, which will
momently stop and accelerate during rotation. In both these stages, their inertia affects the
amount of energy required. This dissipation of energy appears as “extra viscosity”.
In Bruijn's study of glycerine and polymethylmethacrylate system, for particles with
diameters less than 1 to 10 microns, colloid-chemical forces become important causing that
the relative viscosity increase as particle size decreasing [169]. For particles larger than 1 to
10 microns, de Bruijn believes that inertial effects due to the restoration of particle rotation
after collision result in an additional energy dissipation and consequent that viscosity
increased with increasing particle diameter, which reports similar conclusion as Gust study
[169].
Most of the viscosity models assumed that the particle shape is sphere for the estimation of
volume impact of solid particle. However, the experimental results demonstrated that
different particle shape could have significantly impact on the suspension viscosity. Nawab
observed experimentally that Nylon fibre suspensions could produce a measured viscosity
three times of the theoretical predictions [170]. This difference might be a result of fibre
curvature. By comparison of suspension viscosity of different particle shapes, at same
condition, it can be ranked that spherical particle reported the smallest suspension viscosity
[170].
86
2.5.3 The review of viscosity model of suspension system
On 1905, Einstein proposed the mathematical equations to estimate the viscosity of the
suspension system, which related the viscosity of the two-phase mixture to the volume
fraction of solid particles and liquid viscosity [173]. The Einstein model was developed using
Stoke law under the assumption of no interaction between the solid particles. Also, he
assumed that at very low particle fraction, the energy dissipation during laminar shear flow
increase due to the perturbation of the streamline by particles. Because the interactions
between solid particles are not considered, the equation can only be applied to the dilute
solution system [173].
Although Einstein model has a limited prediction range, the basic mathematical expression of
viscosity model of suspension system was accepted and utilized by other researchers, which
the suspension viscosity dependent on a constant liquid viscosity and solid volume fraction.
Other researchers accepted the basic expression of relative viscosity [η𝑠𝑢𝑠
η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 ] and
developed own mathematical models to express the relative viscosity with high particle
fractions. There are two major branches of model development: 1) Extension of Einstein
model and 2) Cell model theory.
It is known that Einstein model assumed that no interaction occurred between solid particles.
Part of researchers focuses on the study by considering the possible interaction between two
or more particles interactions and derives the mathematical equations to predict the
suspension viscosity with a high solid fraction. For example, KD assume three flow pattern of
nearby particles including rotating independently, rotate as dumb-bell and rigid flow pattern;
hence derive the equation.
The development of Cell model based on the assumption that solid sphere of radius of Ro is
surrounded by liquid out to a radius R as shown in Figure 2.28. Suitable boundary conditions
and Stoke equation were applied at this outer boundary layer. For example, Brady assumed
that the velocity field on the outer sphere is precisely that of externally imposed flow [171].
Happel assumes that the shear stresses on the outer sphere are those of the imposed flow
[172].
87
Figure 2.28. The description of interaction between solid sphere and fluid particle
In the present study, altogether 11 models were collected and evaluated using experimental
data. The model features and its equations were summarized in Table 2.29 below.
88
Table 2.29. Summary of 10 different viscosity model, f is the solid fraction within suspension
Model Features Model Equation
Einstein [173] Einstein model is suitable for diluted sphere particles suspension under the assumption of
no interaction between solid particles.
η𝑠𝑢𝑠
η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = (1 +
5
2𝑓)
Kunitz [174] Kunitz modifies Einstein model in one of the deviation steps and empirical optimal the
parameters from (1-f)2 to (1-f)
4.
η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓
(1 − 𝑓)4
Krieger-Dougherty
[175]
Assume three flow pattern of nearby particles including rotate independently, rotate as
dumb-bell and rigid flow pattern; hence derive the equation. η𝑟𝑒𝑙𝑎 = (1 −
𝑓
0.62)
−2.5∗0.62
Probstein [176]
A polydisperse suspension with a particle size distribution from submicrometer to
hundreds of micrometers is simulated and treated as bimodal. η𝑟𝑒𝑙𝑎 = (
1 − 1.351𝑓
1 − 0.39𝑓)
−2.493
Toda [177]
Based on Einstein theory, Toda model further derives the equation on the calculation of
dissipation of mechanical energy into heat in the dispersion. η𝑟𝑒𝑙𝑎 =
1 + 0.5𝑓 ∗ (1 + 0.6𝑓) − 𝑓
(1 − (1 + 0.6𝑓) ∗ 𝑓)2(1 − 𝑓)
Happel [178]
Based on the cell model theory, Happel assumes that the shear stresses on the outer sphere
are those of the imposed flow; then derive the equations on the steady-state Stokes-Navier
equations of motion omitting inertia terms.
η𝑟𝑒𝑙𝑎
= (1
+𝑓 (22 ∗ 𝑓
73 + 55 − 42 ∗ 𝑓
23)
10 ∗ (1 − 𝑓103 − 25 ∗ 𝑓 ∗ (1 − 𝑓
43))
Thomas [179]
Thomas model largely concerned with the transport characteristics of non-Newtonian
suspensions (sphere particle) by consideration of inertial force and measuring instrument
wall effects.
Thomas model reported an average 25% deviations for sets of existing viscosity data
η𝑟𝑒𝑙𝑎 = 1 + 2.5 ∗ f + 10.05 ∗ f 2
+ 0.00273 ∗ e16.6𝑓
89
using different size sphere particles and containers.
Roscoe [180]
Einstein expression is re-evaluated and optimized to improve the prediction of existing
viscosity data.
Roscoe model reported a good agreement with different sizes of sphere particles
suspension, which ranges from 10-40 solid%.
η𝑟𝑒𝑙𝑎 = (1 − 𝑓)−2.5
Mooney [181]
Mooney developed a model based on Einstein approach and reported a good agreement
with experimental data. η𝑟𝑒𝑙𝑎 = e
2.5𝑓1−0.75𝑓
Batchelor [182]
Cell model theory η𝑟𝑒𝑙𝑎 = (1 +
5
2𝑓 + 7.6 ∗ 𝑓2)
Bergenholtz [183]
Cell model theory η𝑟𝑒𝑙𝑎 = (1 +
5
2𝑓 + 5.92 ∗ 𝑓2)
90
Chapter 3 : Experiment Methodology
This chapter describes the experimental methodology utilized in the present study, which
include:
1. High-temperature viscosity measurements for fully liquid slag, which is established
by the Dr. Chen
2. Room temperature viscosity measurements for suspension, which ranges from 0-30
wt% solid.
3. The Raman spectroscopy study
3.1 High-Temperature Viscosity Measurement
The viscosity measurement techniques of high-temperature viscosity measurements have
been detailed studied by Dr. Chen in his Ph.D. Thesis [184]. A digital rotational rheometer
(model LVDV III Ultra; Brookfield Engineering Laboratories, Middle-boro, MA) controlled
by a personal computer was used in the current study. The acquisition of the torque measured
by the rheometer was simultaneously collected by Rheocalc software provided by Brookfield
Engineering Laboratories. A Pyrox furnace with lanthanum chromite heating elements
(maximum temperature 1923 K (1650 oC) was employed. The rheometer placed on a
movable platform was enclosed in a gas-tight steel chamber. There were two independent gas
flow circuits (one through the chamber, and another through the furnace) to suppress heat to
the chamber and protect the rheometer from high temperature. The rheometer rotated co-
axially the alumina driving shaft with the cylindrical spindle. The schematic diagram of
experimental set up is shown in the Figure 3.1.
91
Figure 3.1 Schematic diagram of furnace for viscosity measurement at high temperature
Figure 3.2 provide dimensional details of the cylindrical crucible and spindle used during
viscosity measurements. The viscosity measurements included 3 major steps: 1. the
calibration of one set of equipment under room temperature, including Al2O3 rod, crucible
and spindles, 2. High temperature viscosity measurement using the calibrated equipment and
3: elemental analysis of quenched sample using EPMA.
Figure 3.2 Schematic diagram of crucible and spindle
92
3.2 Room Temperature Viscosity Measurement
The viscosity of suspension was measured using rotational viscometer as Figure 3.3. The
viscosities of solid-containing liquid at room temperature are measured by A Brookfield
digital rotational rheometer (model LVDV III Ultra) controlled by a PC with the standard
spindle provided by the same company. The acquisition of the torque measured by the
rheometer can be simultaneously collected by Rheocalc software provided by Brookfield
Company. A thermostatic water bath will be used to control and maintain the temperatures at
low-temperature ranges from 10 – 40 oC. A transparent crucible will be submerged in the
water
Figure 3.3 Schematic diagram of viscosity study at room temperature
3.3 Raman Spectroscopy Study
The Raman spectroscopy study was carried into two steps, the first step is to obtain the
quenched sample, which is completed using phase equilibrium experiment. The phase
equilibrium experiments were carried out in the vertical tube furnace by stabilizing the
synthetic sample in the hot zone for a period of time at Ar gas atmosphere. After the sample
achieves equilibrium, it will be quenched directly into the water bucket, which maintains the
high-temperature structure for Ramen analysis. The quenched sample will be crashed and
mounted to stabilize in the resin for Raman analysis.
93
The photograph of the furnace below is vertical tube furnace. The schematic diagram is
shown in Figure 3.4. The detailed description of the experimental procedures and conditions
were demonstrated in the “Chapter 6: Structural studies of Silicate using Raman
Spectroscopy”.
Figure 3.4 (a) left, a photograph of phase equilibrium experiment. (b) Right, a schematic
diagram of a vertical tube furnace
94
Chapter 4 : Viscosity Model Development in CaO-MgO-Al2O3-SiO2 System Based
on Urbain Model
The Urbain model was optimized in the present study by introducing the concept of optical
basicity to describe the correlation between slag composition and viscosity. The optimized
version significantly improves the prediction accuracy of CaO-MgO-Al2O3-SiO2 system of
blast furnace slag; also the parameters in the present model are 14 comparing to 22
parameters in the Urbain model (1987 version).
In chapter 4, the optimized Urbain model was presented in section 4.1. In addition, the
optimized model can be extended to calculate the viscosity of blast furnace slag including 8
common minor elements, including Fe, Ti, F, S, Na, K, B and Mn, which was reported in
section 4.2.
4.1 CaO-MgO-Al2O3-SiO2 system in blast furnace composition range
4.1.1 Introduction
Development of a reliable viscosity model for the CaO-MgO-Al2O3-SiO2 systems over a
wide range of compositions and temperatures is important for iron and steel making
processes. A blast furnace (BF) slag with proper viscosity leads to (a) fluent flowing in the
tapping process, (b) easy separation from hot metal and coke, (c) efficient desulphurisation
process and (d) less accretion formation on the BF wall [1]. High-temperature viscosity
measurement is practically difficult and, costing considerable time and money. Therefore, it
is necessary to establish a reliable model to predict slag viscosity to provide accurate
information for efficient blast furnace operation.
A number of viscosity models have been developed to predict the viscosity in the CaO-MgO-
Al2O3-SiO2 (typical BF slag components) system over the last decades as reviewed in Section
2.4. These viscosity models can be generally classified into two groups, empirical models,
and structural models. The empirical models correlate slag viscosity as a function of
temperatures and bulk compositions directly using experimental data. The structural models
consider the profound internal structure of silicate melts, which are more accurate and
flexible than empirical models. Urbain model is one of the structural viscosity models for
viscosity prediction covering a wide range of multi-component system. Several authors
95
chosen Urbain model for optimization due to its flexibility. Riboud and Forsbacka optimized
the Urbain model for mould fluxes and coal ash slag respectively, which both reported an
outstanding agreement with that slag system [134, 135]. Urbain proposed the model on 1981
for viscosity prediction of complex slag system, including CaO, MgO, FeO, SiO2, K2O and
etc [132]. From 1981-1990, Urbain focus on the viscosity experiment study of CaO-MgO-
Al2O3-SiO2 slag system and published the outcomes [60, 185]. Later on 1987, Urbain modify
the model equations and parameters for CaO-MgO-Al2O3-SiO2 system, which were
demonstrated in Section 2.4.7 [131]. The 1987 version of Urbain model demonstrated
superior performance on the CaO-MgO-Al2O3-SiO2 slag system. In the present study, due to
high flexibility, the Urbain model (1987 version) was selected as basement to developed a
new viscosity model for the CaO-MgO-Al2O3-SiO2 system in the blast furnace slag
composition range [131].
4.1.2 Experimental Data Used for Model Development
Accurate viscosity data are essential for successful development of a reliable viscosity model.
The viscosity measurements in the CaO-MgO-Al2O3-SiO2 system have been collected from
37 publications and critically reviewed in the Section 2.3. These data covers the composition
ranges of 10-67 wt% SiO2, 1-40 wt% Al2O3, 1-60 wt% CaO and 1-38 wt% MgO. The
reliability of viscosity data directly impacts on the model prediction performance. The quality
of data was carefully examined. Three sequential steps were undertaken to evaluate the data:
a) Review experimental techniques, b) Check data self-consistency, and c) Cross reference
comparisons. The evaluation details and examples have been demonstrated in the Section 2.3.
1760 out of 3125 viscosity data in the CaO-MgO-Al2O3-SiO2 system were accepted for
model development in the present study.
4.1.3 Silicate Melt Structure
The viscosity of molten slag is closely related to its structure, which is dependent on its
composition and temperature. The final blast furnace slag has four major components, SiO2,
Al2O3, CaO and MgO that can be categorized into three groups, acidic oxide (SiO2), basic
oxide (CaO and MgO) and amphoteric oxide (Al2O3). SiO2 forms a network structure through
(SiO4)4-
tetrahedral units to increase viscosity. The basic oxides Ca2+
and Mg2+
tend to break
the network and reduce slag viscosity.
Al2O3 can behave as either an acidic oxide or basic oxide depending on the concentrations of
other components. If sufficient basic oxides Ca2+
and Mg2+
are present to balance the (AlO4)5-
96
charges, the Al2O3 acts as an acidic oxide, which is incorporated into the silicate network as
(AlO4)5-
form. In the case of insufficient basic oxides, Al2O3 will behave the same as Ca2+
or
Mg2+
to break the (SiO4)4-
network. In typical BF composition ranges, where
(CaO+MgO)/SiO2 is high, the Al2O3 component is considered to act as an acidic oxide and
requires charge compensation of CaO and MgO.
4.1.4 Description of Model
The Urbain model is a structure-based model for the slag viscosity prediction, which has been
optimized for other multi-component systems by various researchers. Urbain firstly proposed
the model on 1981 and modified it to improve the performance in CaO-MgO-Al2O3-SiO2
system on 1987. As comparison in the literature review, the Urbain model (1987) version is
more suitable for the viscosity prediction of CaO-MgO-Al2O3-SiO2 system. Present study
select the Urbain model (1987 version) as a basement for the model development due to its
high flexibility. The comparisons of two Urbain models were introduced in the Section 2.4.7.
Viscosity is generally a function of temperature and chemical composition of molten slag.
Urbain considered Weymann’s expression of the temperature dependence of viscosity, which
is the modified Arrhenius-type equation [186] (Equation 4-1).
Equation 4-1 Arrhenius-type equation
η = A ∗ T ∗ exp (1000𝐵
𝑇)
Where η is viscosity in Pa.s, T is the absolute temperature (K), A is the pre-exponent factor
and B represents the integral activation energy.
In the modelling study by Urbain, the pre-exponent factor A and activation energy B was
reported to have a relationship as Equation 4-2 shown. The linear correlation were accepted
and utilized in other researchers’ viscosity models, such as the Shankar [32], Shu [187] and
Hu [142]. In the current study, a similar relationship between ln(A) and B is confirmed for
the CaO-MgO-Al2O3-SiO2 system using the accepted viscosity data. ln(A) and B has a strong
linear correlation (R2=0.948) and is used in the construction of current viscosity model. The
values of m and n in the present model are determined to be 0.501 and 7.681 respectively
optimized from the evaluated measurements in the CaO-MgO-Al2O3-SiO2 system (Section
2.3).
97
Equation 4-2 the linear relationship between A and B
𝑙𝑛𝐴 = −𝑚𝐵 − 𝑛
Where A the pre-exponential factor and B is the activation energy from Equation 4-3. m and
n is the model parameters are 0.501 and 7.681 respectively.
They are close to that reported by Hu (0.508 and 7.28) but different from that reported by
Urbain (0.29 and 11.57) [142]. Because, both Urbain and present study utilized the equation
ln(n/T)=ln(A)+1000B/T to determine the value of B; however Hu model utilized the
ln(n)=ln(A)+1000B/T. Both equations reported the linear relationship as Figure 4.1 shown.
𝑙𝑛𝐴 = −𝑚𝐵 − 𝑛
Figure 4.1 The linear relationship between EA and ln(A)
4.1.5 Expressions of Activation Energy
In the tradition Arrhenius equation, B is defined as the term “activation energy”. It is known
that the viscous flow is driven by thermally activated process. According to the network
theory, there are silicate network, broken network and free-moving components in the molten
slag. The activation energy term described the sum of required energy for these components
movement, which overcome the potential barrier to reach another equilibrium positions. In
the present study, the integral activation energy can be expressed as Equation 4-3 shown. The
contribution of the broken and free-moving components were individually calculated and
98
normalized based on molar composition. The contribution of silicate network is constant,
which is derived from the pure silica.
Equation 4-3 Parameter B calculation
𝐵 =𝑀𝐶𝑎𝑂 ∗ 𝐵𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂 ∗ 𝐵𝑀𝑔𝑂 + 𝑀𝐴𝑙2𝑂3
∗ 𝐵𝐴𝑙2𝑂3
𝑀𝐶𝑎𝑂 + 𝑀𝑀𝑔𝑂 + 𝑀𝐴𝑙2𝑂3
+ 𝐵𝑆𝑖0
Where M is a molar fraction of oxide, Bi is partial activation energy calculated by Equation
4-4 to Equation 4-6. A constant value of 63.98 is used for𝐵𝑆𝑖0 , which is derived from the pure
SiO2.
The partial activation energy Bi of each oxide is expressed as the third order polynomial
equation Equation 4-4 shown.
Equation 4-4 Partial activation energy Bi calculation, for Equation 4-3
𝐵𝐶𝑎 = 𝐵𝐶𝑎1 + 𝐵𝐶𝑎
2 ∗ 𝑁 + 𝐵𝐶𝑎3 ∗ 𝑁2
𝐵𝑀𝑔 = 𝐵𝑀𝑔1 + 𝐵𝑀𝑔
2 ∗ 𝑁 + 𝐵𝑀𝑔3 ∗ 𝑁2
𝐵𝐴𝑙 = 𝐵𝐴𝑙1 + 𝐵𝐴𝑙
2 ∗ 𝑁 + 𝐵𝐴𝑙3 ∗ 𝑁2
Where N represents the effective optical basicity of the slag and Bi1, Bi
2 and Bi
3 are model
parameters of each metal oxide.
The parameters B1, B
2 and B
3 for the present model were optimized from the viscosity
measurements as shown in Table 4.1. The parameter optimizations were constructed from
calculated activation energy and molar composition of oxides. The activation energy B and
pre-exponential factor A can be determined from plotting ln (η
𝑇) = ln(A) +
1000B
T. With
known B and Equation 4-3, the range of BCaO, BMgO, BAl2O3 and BSiO2 can be estimated within
a certain range for all compositions, which are BCaO= (-30)~ (-250), BMgO= (-45)~(-180),
BAl2O3= (-15)~(+10) and BSiO2= around 60. It can be noted that at low basic oxide conditions,
the Al2O3 has a negative contribution on the silicate network due to its amphoteric property.
The parameters of B1, B
2 and B
3 were \optimized based on the oxide contribution ranges.
99
The experiment measurements confirmed that CaO and MgO negatively contributed to the
activation energies, which represent the network breaking and reduce the slag viscosity. In
contrast, the Al2O3 and SiO2 positively contributed to the activation energy, which represents
the network-forming effect and improve the slag viscosity.
Table 4.1 Parameters B used in Equation 4-4
B CaO MgO Al2O3
1 -35.7 -46.9 0.5
2 6.76 20.16 2.32
3 -70.2 -60.1 -3.32
The effective optical basicity of the slag N can be calculated by Equation 4-5 using the
optical basicity of CaO, MgO, Al2O3, (SiO4)4-
and (AlO4)5-
. The optical basicity of each
component represents their ability for network-breaking or network-forming. The values of
optical basicity of CaO, MgO, and Al2O3 are adopted from Duffy. The new parameters ΛiOpt
,
which represent the optical basicity of (SiO4)4-
and (AlO4)5-
were derived from the viscosity
data. The optical basicity values were shown in Table 4.2.
Equation 4-5 Slag basicity N calculation, for Equation 4-4
𝑁 =Λ𝐶𝑎𝑂 ∗ 𝑀𝐶𝑎𝑂 + Λ𝑀𝑔𝑂 ∗ 𝑀𝑀𝑔𝑂 − Λ𝐴𝑙2𝑂3
∗ 𝑀𝐴𝑙2𝑂3
Λ(𝐴𝑙𝑂4)5−𝑂𝑝𝑡 ∗ 𝑀(𝐴𝑙𝑂4)5− + Λ
(𝑆𝑖𝑂4)4−𝑂𝑝𝑡 ∗ 𝑀(𝑆𝑖𝑂4)4−
Where M is a molar fraction of metal oxide, Λi is the effectiveness of basic oxides and ΛiOpt
is the effectiveness of acidic oxide. Note: MAlO4 = 2*MAl2O3.
Table 4.2 Model parameters N
CaO MgO Al2O3
100
Λ 1 0.78 0.6
(SiO4)4-
(AlO4)5-
ΛOpt
2.789
0.295
4.1.6 Model Performances
The revised Urbain model has been constructed in the present study to predict the viscosity
for BF slags. This optimized model has a reduced number of equations (from 14 to 7) and
parameters (from 22 to 14) compared to the Urbain model (1987 version). The prediction
performance was evaluated by comparison of other models using the accepted viscosity
measurements in the CaO-MgO-Al2O3-SiO2 slag system.
In order to provide a full view of the comparison, the evaluation of the model performance
was carried out for two different composition ranges: a) all data in the CaO-MgO-Al2O3-SiO2
system; b) data in the typical BF slag composition range 30-40 wt% SiO2, 10-20 wt% Al2O3,
30-45 wt% CaO and 5-10 wt% MgO. Each viscosity model was examined and compared
using the above data classifications to test its accuracy.
The mean deviation Δ is calculated using Equation 4-6 described as follows.
Equation 4-6 the viscosity prediction deviation calculation
Δ =1
𝑛∗ ∑ |
𝜂𝐶𝑎𝑙𝑐 − 𝜂𝐸𝑥𝑝
𝜂𝐸𝑥𝑝| ∗ 100%
Where Δ the mean deviation, n is is the total number of simulations, ηCalc is the model
viscosity and ηExp is the experimental viscosity.
The results for model comparison are shown in
Figure 4.2. It can be seen that the present model has the lowest deviation in both composition
ranges, with 29.5% in the full composition range and 13.5% in the BF slag composition range.
The relative deviations reported by other models are all above 30% in the full composition
range and 20% in the BF slag composition range.
101
Figure 4.2 Comparison of the current viscosity model with others
A detailed comparison of the viscosity model performance is constructed using the three most
accurate models: present model, Zhang model [188] and Urbain model [131] in the viscosity
range 0 - 1 Pa.s, which is typical for BF slags. As Figure 4.3 shown, the present model has
superior performance than both Zhang and Urbain models. The mean deviation is an average
of the absolute deviation which may underestimate the model prediction accuracy. For the
viscosity measurements between 0-1 Pa.s, as Figure 4.3 shown, the mean deviation is 12.5%,
16.4% and 16.3% for the present model, Zhang model, and Urbain model respectively.
However, for a given experimental viscosity, the maximum predicted deviations can be 0.3
Pa.s for Urbain model, 0.37 Pa.s for Zhang model that are much higher than the present
model (0.06 Pa.s).
102
Figure 4.3 Three model performance for 0 - 1 Pa.s, mean deviation for three models: present
model 12.5%, Zhang model 16.4% and Urbain model (1987 version) 16.3% [131, 188]
4.1.7 Industrial Applications
Examples of the applications in the prediction of BF slag viscosity are shown in this section
using the present viscosity model. Figure 4.4 shows the effect of MgO on the viscosity of BF
slag at 15 wt% Al2O3 and 1500 °C. It can be seen that the calculated viscosities by the present
model agree very well with Machin’s measurements. At a given CaO/SiO2 ratio and Al2O3
concentration, replace of (CaO+SiO2) by MgO decreases the slag viscosity. On the other
hand, the BF slag viscosity increases with decreasing MgO. In the ironmaking process,
sulphur removal of hot metal directly related to the slag viscosity. The higher viscosity of the
slag could increase the sulphur content in the hot metal. To balance the viscosity raised by
decreasing MgO, the CaO/SiO2 ratio in the slag can increase according to the predictions
shown in Figure 4.4. It also can be seen that at CaO/SiO2 ratio of 1.30, 15 wt% Al2O3 and
1500 °C, the viscosities of the BF slag are below 0.5 Pa.s even the MgO concentration in the
slag is as low as 2 wt%. This indicates that low MgO in slag does not have a significant effect
on slag tapping.
103
Figure 4.4 Effect of MgO on viscosity of BF slag at 15 wt% Al2O3 and 1500 °C predicted by
the present model with comparisons to the experimental data [74]
Figure 4.5 shows the effects of Al2O3 concentration and temperature on slag viscosity at 40
wt% SiO2 and 10 wt% MgO. It can be seen that the calculated viscosities by the present
model agree very well with the reported measurements. At fixed SiO2 concentration and
temperature, the viscosity increases with increasing Al2O3 concentration and the increment is
more significant at lower temperatures. For example, the viscosity is increased by
approximately 0.4 Pa.s at 1500 oC and 0.65 Pa.s at 1450
oC when the Al2O3 concentration in
the slag is increased from 10 to 20 wt%. On the other hand, the viscosity is more sensitive to
temperature for the slag containing higher Al2O3. Decrease of temperature from 1500 to
1450oC increases the viscosity by 0.1 Pa.s for 10 wt% Al2O3 slag and 0.35 Pa.s for 20 wt%
Al2O3 slag. This indicates that increased Al2O3 concentration in BF slag not only increases
viscosity directly but also decreases the thermal stability of the slag.
104
Figure 4.5 Effects of Al2O3 concentration and temperature on slag viscosity at 40 wt% SiO2
and 10 wt% MgO predicted by the present model with comparisons to the experimental data
of Gultyai [83], Hofmann [22] and Machin [68]
4.1.8 Conclusions
A novel viscosity model has been developed based on Urbain model (1987 version) in the
CaO-MgO-Al2O3-SiO2 system. The present model improved the viscosity prediction for the
blast furnace slag. The present model shows superior performance to the existing viscosity
models, which reduce the prediction deviation from 22% (Urbain model) to 14% (present
model). Also, the parameters in the present model are 14 compared to 22 in the original
Urbain model. Present model can provide accurate viscosity prediction of CaO-MgO-Al2O3-
SiO2 system, which occupied 97% of blast furnace slag. In recent study, the impact of minor
element was addressed, which report the significant impact on the final slag viscosity. The
present model was further investigated and developed for the viscosity prediction of minor
element within the blast furnace slag, which would be demonstrated in the Section 4.2.4.2
CaO-MgO-Al2O3-SiO2 system containing 8 minor elements
4.2.1 Introduction
Slag viscosity is one of the important properties in ironmaking process, which significantly
influences operation and fuel efficiency. Viscosities of the CaO-MgO-Al2O3-SiO2 system (97
wt% of slag) have been well studied in last decades. Because of gradual consumption of high-
grade iron ore, in view of operation cost and energy efficiency, the low-grade materials and
pulverized coal injection were used in the blast furnace (BF) operation. This results in
105
increases of impurities, such as Na2O, K2O, MnO and TiO2 in the slags. CaF2 and B2O3 are
fluxes used in BF maintenance stage to remove the accretion formed inside the furnace wall,
which will also affect the final slag composition. A typical blast furnace slag compositions
including minor elements are summarized in Table 4.3.
Table 4.3 Summary of typical BF composition range
In the present study, the impacts of 8 minor elements on slag viscosity were individually and
systemically studied. Previous viscosity data relevant to the BF slag with minor elements
were also collected and reviewed. A series of viscosity measurements of 6 minor elements
(Na2O, K2O, S, MnO, FeO, TiO2, CaF2 and B2O3) was conducted at the University Of
Queensland (UQ). The viscosity model was developed for the prediction of CaO-MgO-
Al2O3-SiO2 slag system containing minor elements.
4.2.2 Experimental Methodology
A series of high-temperature viscosity measurements were carried out to investigate the
effects of TiO2, MnO, FeO, B2O3, CaS, CaF2 on the BF slag. The apparatus and
methodologies of the viscosity measurements have been reported in previous studies [13] and
section 3.1. The viscosity measurements were carried out from high temperature to low
temperature in 50 °C interval. The sample was kept for long enough time after temperature
decreasing to achieve the equilibrium. The lowest measuring temperatures of the slags were
predicted by FactSage 6.2 to ensure the molten slag status. After measurements have been
Component Composition (wt%)
SiO2 30-40
Al2O3 15-20
CaO 35-45
MgO 5-10
CaO/SiO2 1-1.2
F, S, MnO, FeO, B2O3, Na2O, K2O, TiO2 0-3
106
completed, the sample was directly quenched into the water to convert the liquid into the
glass. The quenched samples were sectioned, mounted, polished and elementally analyzed by
electron probe X-ray micro-analysis (EPMA). In the present study, S is recalculated to CaS,
and F is recalculated to CaF2 for presentation purpose. The samples containing B2O3 and CaS
were also sent for Inductively Coupled Plasma (ICP) analysis. The compositions of B2O3 and
CaS measured by ICP were very close to those measured by EPMA.
4.2.3 Viscosity Database
4.2.3.1 Collected Reference
The viscosity database was established by collecting reliable viscosity measurements from
literature and present measurements. After a critical literature review, very limited viscosity
data in systems of CaO-MgO-Al2O3-SiO2-B2O3 and CaO-MgO-Al2O3-SiO2-Na2O (K2O)
were found, which were reviewed in the Section 2.3.5. More researchers studied the impact
of FeO and TiO2 additives on BF slag viscosity, which were reported in the section 2.4.5.
Only one publication in each system was collected for MnO, Na2O, and K2O containing BF
slag system. According to the measurement techniques and conditions, the viscosity data
were carefully examined and evaluated. For example, the data obtained at a temperature
significantly below the liquidus temperature (e.g. 50 °C), which is not accepted in the present
study.
4.2.3.2 Minor Element Impact
In the CaO-MgO-Al2O3-SiO2 slag system, the role of four major components CaO, MgO,
Al2O3 and SiO2 had been explained before in the Section 4.1.3. The viscosity of molten slag
is closely related to its structure, which is dependent on its composition and temperature. The
final BF slag has four major components, SiO2, Al2O3, CaO and MgO that can be categorized
into three groups, acidic oxide (SiO2), basic oxide (CaO and MgO) and amphoteric oxide
(Al2O3). SiO2 forms a network structure through (SiO4)4-
tetrahedral units to increase
viscosity. The basic oxides Ca2+
and Mg2+
tend to break the network and reduce slag
viscosity.
The silicate structure is composed of connected silicate, broken network and free-moving
component. According to the network theory, the minor elements can be classified into 3
categories: network former, network modifier and amphoteric oxide. The elements of F, S,
Na, Fe, Mn belong to the network modify group, which reduce the slag viscosity. According
to Kim’s viscosity study of K2O containing system, K2O is the network former, which
107
increased the slag viscosity within composition range 1-10 wt%. In terms of the viscosity
impact of TiO2, there are two contradictive opinions. Liao believed that the TiO2 has a similar
structural unit as SiO2, which positively increase the slag viscosity (TiO2>20wt%) [119].
When the TiO2 concentration decreased, in Park’s viscosity measurement, it has been found
the addition of TiO2 reduce the slag viscosity of blast furnace type slag [121].
4.2.4 Result & Discussion
4.2.4.1 Comparisons of viscosities
The viscosities of 8 synthetic slags with minor elements (B2O3, F, S, MnO, FeO, Na2O, K2O,
and TiO2) were measured. The viscosity data from both present study and literatures
indicated that the additions of minor elements B2O3, F, S, MnO, FeO, TiO2 and Na2O reduce
the viscosity. In addition, the viscosity reduction effect of CaF2 additive is stronger than other
minor elements. Kim et al reported that addition of K2O in CaO-MgO-Al2O3-SiO2 system
increased the viscosity.
Figure 4.6 shows the comparison between the present viscosity measurements and data from
Liao et al [119] and Park [120] in the close composition in the CaO-MgO-Al2O3-SiO2-TiO2
system. It can be seen that the present measurements generally agree with Park’s data. The
comparison of viscosity data at a different TiO2 concentration in close CaO/SiO2 ratio, Al2O3
content, and MgO content shows that the addition of TiO2 into the system keeps decreasing
the viscosity.
Figure 4.6 Comparison of viscosities for CaO-MgO-Al2O3-SiO2-TiO2 slag by Park [120] and
Liao [119]
108
4.2.4.2 Viscosity Model Description
A viscosity model on CaO-MgO-Al2O3-SiO2 system has been proposed by the present
authors in the Section 4.1. In the present study, the model is extended to predict the effects of
Na2O, K2O, MnO, FeO, TiO2, B2O3, CaF2 and CaS additions on the viscosity of blast furnace
slags.
The details of model developments had been introduced in the Section 4.1. The following
section will focus on the extension part of addition of minor element. The temperature
dependence of viscosity can be described by the Arrhenius-like equation as shown in
Equation 4-7.
Equation 4-7 the modified equation from Frenkel-Weymann equation (Equation 4-1)
η = A ∗ T ∗ exp (EA
𝑇)
Where η is viscosity in Pa.s, T is the temperature in K, EA is viscous activation energy in
kJ/mol, and A is the pre-exponential factor.
𝑙𝑛𝐴 = −𝑚 ∗ EA − 𝑛
Where A the pre-exponential factor and B is the activation energy from Equation 4-3. m and
n is the model parameters are 0.501 and 7.681 respectively.
This correlation has been widely used by many researchers in the development of viscosity
models, such as the Shankar, Shu, and Hu. The values of m and n in the present model are
determined to be 0.501 and 7.681 respectively, which is the same as shown in section 4.1.4.
As shown in Equation 4-8, the activation energy B in the present model is expressed by the
sum of all metal oxides multiplied with their partial activation energies Ei (i =SiO2, FeO, CaO,
MgO, Al2O3, CaF2, B2O3, TiO2, Na2O, K2O, MnO, and CaS).
Equation 4-8 Activation energy equation
EA = ∑(Mi *Ei)
Where Mi and Ei are molar fractions and partial energy of each metals oxides respectively.
109
Please note, the equation and parameters of SiO2, CaO, MgO, and Al2O3 were reported in the
section 4.1.4 before. In Equation 4-9, the partial activation energy Ei of each metallic oxide
can be expressed using the following polynomial equation. The model parameters were
reported in Table 4.4.
Equation 4-9 Partial activation energy Ei calculation, for Equation 4-8
Ei = Ei0 + Ei
1*B + Ei2*B2
Where B is optical basicity ratio, Bi0, Bi
1 and Bi
2 are model parameters of each metal oxide.
From the experiment measurements, the contributions of minor elements could be estimated
within a range using the calculated activation energy and its molar composition. And Bi1-3
can
be determined, which is summarized in the Table 4-4. A large negative numbers were
reported for the model parameters of CaF2 and B2O3, which significantly reduce the slag
viscosity. In contrast, the K2O positively contributed to the activation energy, which
represents the network-forming effect and improve the slag viscosity.
Table 4.4 Model parameters to calculate Ei of each minor element, the parameters of SiO2,
CaO, MgO, and Al2O3 were reported in the section 4.1.4 before
E CaF2 FeO TiO2 B2O3
CaS MnO Na2O K2O
1 -832.48 -279.62 -94.56 -263.07 -80.65 -43.77 -29.66 34.94
2 1752.92 1224.44 142.54 10.01 1.75 4.22 2.50 -1.10
3 -14.06 59.91 117.53 10.00 43.24 1.03 1.64 -6.52
As Equation 4-10 shown, the structural of different silica composition is indicated by
parameter basicity B, which was calculated using optical basicity and molar composition of
oxide.
Equation 4-10 Slag basicity B calculation, for Equation 4-9
B =∑ Bi*Mi-BAl2O3MAl2O3i=Ca,Mg,andetc
∑ Ai*Mii=Si&Al
110
Where M is molar fraction of cations and anions, Bi is optical basicity of basic oxides (CaO,
MgO, Na2O, K2O, MnO, CaS, CaF2, MnO, B2O3, FeO, and TiO2) and Ai is optical basicity of
acidic oxide (SiO2 and Al2O3) from the optical basicity of Duffy as shown in Table 4.5.
Table 4.5 Optical basicity of oxide from Duffy
Optical
Basicity CaF2 FeO TiO2 B2O3
CaS MnO Na2O K2O
1.2 1 1 0.42 1 1 1.15 1.4
The present model performance is evaluated using Equation 4-6 by comparison between the
predicted viscosity and experimental data. In the present study, only the measurements
ranging within blast furnace slag composition were selected for evaluation, which is
CaO/SiO2=1-1.3, 1-10 wt.% MgO, 10-20 wt.% Al2O3 and 1-5 wt.% minor element. In
addition, the Urbain model (1981 version) was utilized as the comparison with present model.
The outcomes were summarized in Table 4.6. Present model reported a low deviation within
BF slag composition ranges comparing to the Urbain model (1981 version). From the
equations and parameters of the Urbain model, it did not encounter the CaF2 and B2O3 as a
strong network modify, which report a large deviations for these two components. Also,
Urbain model regarded the K2O as a network modify in the CaO-MgO-Al2O3-SiO2 system,
which did not obey the experimental measurements. In contrast, the Urbain model reported
the lowest deviation for MnO containing system, because Urbain modified its models for
CaO-MgO-Al2O3-SiO2-MnO system on 1987.
Table 4.6 Summary of model performance in BF slag composition range
BF slag with different minor
elements
Deviation (%)
Present Model Urbain Model
TiO2 14.5 25.8
B2O3 4.9 40.6
111
CaF2 8.6 50.4
CaS 4.2 38.2
MnO 6.8 15.5
FeO 12.6 23.4
Na2O 14.6 32
K2O 13 30
The performance of present model (Figure 4.7A) and Urbain (Figure 4.7B) model were
further investigated in the CaO-MgO-Al2O3-SiO2-“TiO2” system of the Shankar, Park and
present study measurements [41]. As Figure 4.7 shown, present retained consistent
performance from low to high viscosity regions. Urbain model reported the accurate
prediction and under-estimate the high viscosity slag.
Figure 4.7 the model prediction vs experimental results of CaO-MgO-Al2O3-SiO2-TiO2 slag
system of Park [120], Shankar [32] and present (A) left, present model and (B) right, Urbain
Model (1981 version) [132]
At the current stage, the present model could not provide accurate predictions beyond BF slag
composition range. Figure 4.8 demonstrates that the deviation of the predictions increases
with increasing FeO concentration. As shown in Figure 4.8, when FeO concentration is lower
than 10 wt%, the average predict deviation is around 15%. If the FeO content is increased to
112
30 wt% (copper slag composition range), the prediction deviation will be increased to 30%. It
indicated that the present model can only provide accurate viscosity information for BF slag
composition ranges.
Figure 4.8 Increase of prediction deviation in CaO-MgO-Al2O3-SiO2-FeO system with
increasing FeO concentration by Bills [64] , Gorbachev [189], Higgins [190] and present
study
4.2.4.3 Industrial Application
The viscosity reduction ability of 8 minor elements was compared through model prediction
at 1500 °C. The base composition is 35 wt% SiO2, 17.4 wt% Al2O3, 38.6 wt% CaO and MgO
9 wt%. The concentrations of SiO2, Al2O3, CaO and MgO proportionally decrease when the
concentration of additive increases. Except for K2O, other additives decrease the slag
viscosity. It can be seen from Figure 4.9 that, the ability of viscosity decrement by different
minor elements in BF slag systems can be ranked as: CaF2> B2O3 > CaS > Na2O > TiO2 >
MnO > FeO. Because of strong viscosity reduction ability, CaF2 and B2O3 minor element
were often used to remove accretions on the BF wall.
113
Figure 4.9 The comparison of viscosity reduction ability of 8 minor elements on BF slag
viscosity
There are two major routes to reduce the operation cost of BF ironmaking process: 1) reduce
MgO flux addition, 2) increase using high Al2O3 content iron ore. Both routes will tend to
increase the slag viscosity at current operation condition. The minor elements from low-grade
iron ore can effectively reduce BF slag viscosity. For example, due to abundant Ti-bearing
iron ore resources in western part of China, Ti-bearing iron ores were used and CaO-MgO-
Al2O3-SiO2-TiO2 slag was generated. The concentration of TiO2 in final slag can be 21-23 wt%
in Panzhihua Iron and Steel and 15-18 wt% in Hebei Iron & Steel Group. As Figure 4.10
shown, present model can provide an accurate prediction for typical slag compositions
containing TiO2 above 1450 oC and 0-20 wt% TiO2 containing slag. The TiO2 addition into
slag can reduce slag viscosity however due to inevitable precipitation of Ti(C, N) at high
temperature; the viscosity significantly increases and blast furnace operation with high TiO2
slag is still challenging.
114
Figure 4.10 Comparison of model prediction and Liao’s measurements [119]
4.2.5 Conclusions
In the present study, the impacts of 8 minor elements on BF slag viscosity were systemically
studied, which includes Na2O, K2O, FeO, B2O3, CaF2, CaS, TiO2, and MnO. It was found that
CaF2 has the most significant effect of BF slag viscosity reduction. Except for K2O, the other
7 additives decrease the slag viscosity.
An existing CaO-MgO-Al2O3-SiO2 viscosity model has been extended to predict the effects
of minor elements on the viscosity of BF slags using present and collected viscosity data. The
model reported the good agreements with the available experimental data within BF slag
composition range. For the slag of CaO-MgO-Al2O3-SiO2-“FeO” system (copper smelting
slag), the prediction deviation would increase at high concentration of “FeO” content. Further
experimental work will be required to improve the model performance.
115
Chapter 5 : Viscosity Model Development Based on Probability Theorem
In the existing viscosity models of the CaO-MgO-Al2O3-SiO2 system, few researchers
discussed the distribution of cations (Ca2+
or Mg2+
) in SiO4 and AlO4 network
structure. A new term probability was proposed to describe the probability of Ca2+
(or
Mg2+
) cations to connect with SiO4 and AlO4 tetrahedra unit by considering the ionic
electronegativity and radius.
The proposed model demonstrated superior performance in the viscosity prediction of
full composition range of CaO-MgO-Al2O3-SiO2 system; as well as its sub binary,
ternary system, blast furnace composition and ladle furnace range. In chapter 5, the
novel developed model was presented in Section 5.1. In addition, the present model
can be extended to calculate the viscosity of CaO-MgO-Al2O3-SiO2-“FeO”, which
was reported in Section 5.2.
5.1 CaO-MgO-Al2O3-SiO2 system in full composition range
5.1.1 Introduction
Slag viscosity is critically important to various pyrometallurgical operations, which is
necessary for process optimization and reducing the operating costs.
Critical data evaluation and model assessments have been carried out in Section 2.3.
3115 viscosity data in the CaO-MgO-Al2O3-SiO2 system, which covers wide
composition and temperature ranges, were collected and examined based on
experimental techniques, data consistency, and cross-reference comparisons. The data
related to the compositions of ironmaking and steelmaking slags were also selected
for evaluation.
Using the accepted data above, a new viscosity model is proposed for the CaO-MgO-
Al2O3-SiO2 system and the performance of this model is compared with other existing
models. In addition, the present model can also be used to predict the low orders
silicate systems containing CaO, MgO, and Al2O3.
5.1.2 Silicate melt structure
The viscosity of molten slag closely related to its structure, which is dependent on
composition and temperature. The components of the quaternary system CaO-MgO-
Al2O3-SiO2 can be categorized into three groups: acidic oxide (SiO2), basic oxide
116
(CaO and MgO) and amphoteric oxide (Al2O3). SiO2 forms a network structure
through (SiO4) tetrahedral units. The addition of basic oxide, either CaO or MgO, will
break the [SiO4] network. It is widely accepted that O2-
from basic oxides tends to
break the Si-O-Si bond in silicate network and forms Si-O- intermediate, which
require cations (Ca2+
or Mg2+
) charge compensation. Also, amphoteric oxide Al2O3
can form AlO4 unit to connect with the [SiO4] network, which requires cations (Ca2+
or Mg2+)
charge compensation as well. As shown in Figure 5.1, the insertion of O2-
into SiO4 network tends to break covalent bond between Si and [O] and Ca2+
will
compensate the O- charge. This intermediate Ca(Mg)-SiO4 structure unit has one free
positive charge, which is able to break another SiO4 or compensate the AlO4 charges.
Figure 5.1 Interaction among Ca2+
cations, silica and alumina
Al2O3 can behave as either acidic oxide or basic oxide depending on the
concentrations of basic oxides. If sufficient Ca2+
and Mg2+
cations are present to
balance the (AlO4)- charges, the Al2O3 acts as an acidic oxide which is incorporated
into the silicate network in tetrahedron coordination. In the case of insufficient basic
oxides, Al3+
will behave the same as Ca2+
or Mg2+
to break the (SiO4) network.
In CaO-MgO-Al2O3-SiO2 system, the major roles of Ca2+
/Mg2+
are to compensate the
Si-[O]- charge and [AlO4]
5-. Due to electrical force between charges, it is accepted
that when the Ca2+
/Mg2+
concentration is low, they have higher priority to balance the
AlO4 charges than breaking the Si-O covalent bond.
5.1.3 Pre-Exponential Factor A
The temperature dependence of viscosity can be described by the Arrhenius-type
equation (Equation 5-1).
117
Equation 5-1 Arrhenius type equation
η = A ∗ exp (1000 ∗ 𝐸𝐴
𝑇)
Where η is viscosity in Pa.s, T is the absolute temperature (K), A is the pre-
exponential factor, EA represents the integral activation energy in J/mol.
As shown in Equation 5-2, a linear relationship between pre-exponent factor A and
activation energy EA was proposed by Urbain [131]. The activation energy EA and
pre-exponential factor A can be determined by plotting ln(η) against 1/T under the
same composition.
Equation 5-2 the linear relationship between A and B
𝑙𝑛𝐴 = −𝑚 ∗ 𝐸𝐴 − 𝑛
Where A the pre-exponential factor and EA is the activation energy from Equation 4-3.
m and n is the model parameters are 0.4144 and 4.1485 respectively.
This linear correlation has been widely applied in different viscosity models, such as
the Shankar’s and Hu‘s model [141, 142]. In the present study, from 604
compositions of accepted viscosity data, the linear correlation is confirmed as shown
in Figure 5.2, ln(A) and EA has a linear relationship with R2=0.948, which will be
used in the construction of the present viscosity model. m and n values in Equation
5-2 are 0.4144 and 4.1485 respectively.
118
Figure 5.2 The linear relationship between EA and ln(A)
5.1.4 Network Modifier Probability
In the existing viscosity models of the CaO-MgO-Al2O3-SiO2 system, few researchers
discussed the distribution of cations (Ca2+
or Mg2+
) in SiO4 and AlO4 network
structure except Zhang model [188]. Zhang et al calculated the concentration of three
types oxygen (O2-
, O- and O
0) by several assumptions; for example, the full amount of
CaO first compensate the Al2O3 then break silicate network; then MgO will break the
rest of silicate network, which did not consider equilibrium condition within the
quaternary system.
With the study of silicate based mineralogy, Ramberg suggests that the silicate
structure (polymerized level of the SiO4 network) is dependent on basic oxide
concentrations, atomic radius and electronegativity [191]. In the present study, a new
term “probability (P)” is introduced to describe the probability of Ca2+
(or Mg2+
)
cations to connect with SiO4 and AlO4 tetrahedral unit. PCa and PMg. The Equation 5-3
are proposed to be the probability of Ca2+
or Mg2+
connecting to the Si-O network
respectively. Ca2+
and Mg2+
cations were also required for (AlO4)- charge
compensation. Therefore, the (1-PCa) are the probability of cations to connect with
AlO4. It is known that Ca2+
and Mg2+
have a higher priority to compensate the AlO4
charges. At low concentration of CaO/MgO, there is a high probability of
compensating the (AlO4)- charges. When the concentration of CaO/MgO increases,
the probability of breaking Si-O will raise.
119
Equation 5-3 the probability calculation of cations Ca and Mg for Equation 5-6
𝑃𝐶𝑎 =χ𝐶𝑎2+𝑀𝐶𝑎2+
χ(𝑆𝑖𝑂4)4− ∗ 𝑀(𝑆𝑖𝑂4)4− + χ(𝐴𝑙𝑂4)5− ∗ 𝑀(𝐴𝑙𝑂4)5−
𝑃𝑀𝑔 =χMg2+𝑀𝑀𝑔2+
χ(𝑆𝑖𝑂4)4− ∗ 𝑀(𝑆𝑖𝑂4)4− + χ(𝐴𝑙𝑂4)5− ∗ 𝑀(𝐴𝑙𝑂4)5−
Where M is a molar fraction of a metal oxide; X is electronegativity of structure units
in slag system.
The electronegativity of Ca2+
, Mg2+
, AlO4 and SiO4 units are determined using
Mulliken equation, as shown in Equation 5-4, which is derived from 1st ionization
energy and electron affinity of the atom. The values of electronegativity are shown in
Table 5.1.
Equation 5-4 Mulliken equation
χ =𝐼 + E
2
Where I is the ionization energy (kJ/mol) and E is electron affinity (kJ/mol)
Table 5.1 Electronegativity χ of basic oxide cations and network former units
Ca2+
Mg2+
(AlO4)
(SiO4)
Χ 3.07 3.82 6.674 6.985
5.1.5 Activation Energy EA
In Arrhenius equation, EA is defined as the integral activation energy of silicate slag,
which is composed of four metal oxides and can be expressed as Equation 5-5.
120
Equation 5-5 Activation energy calculation
𝐸𝐴 = 𝐸𝐶𝑎𝑂 + 𝐸𝑀𝑔𝑂 + 𝐸𝐴𝑙2𝑂3+ 𝐸𝑆𝑖𝑂2
Where Ei is activation energy of i component (i = SiO2, Al2O3, CaO, and MgO),
which is calculated from Equation 5-6.
In CaO-MgO-Al2O3-SiO2 system, as a network modifier, three structure units are
relevant to CaO including free oxygen O2-
, SiO4-Ca-SiO4, and SiO4-Ca-AlO4. As PCa
defined before, one Ca2+
cation has probability PCa to connect with one SiO4
tetrahedron. Therefore, the probability of SiO4-Ca-SiO4 and SiO4-Ca-AlO4 can be
assumed as PCa2 and PCa*(1-Pca) respectively. As Equation 5-5 shown, the integral
activation energy of CaO is calculated by the sum of energy contributions of each
structural unit multiplied by its probability. The 𝐸𝐶𝑎0 is the constant representing O
2-
from CaO. Because of similar properties, the calculation of MgO integral energy is
expressed in Equation 5-6.
As an amphoteric oxide, Al2O3 shows both negative and positive impacts on
activation energy. There are four possible structure units for aluminum cations, those
are, network modifies unit: O2-
, 3(SiO4)-Al and network former unit: AlO4-Ca-AlO4
and AlO4-Mg-AlO4. The charge balanced AlO4-Ca/Mg structure units give a positive
contribution to the integral activation energy. The (1-PCa) and (1-PCa) are used to
describe the probability of Ca2+
/Mg2+
participating on alumina network. One
Ca2+
/Mg2+
cation is able to balance two (AlO4) structure units; therefore the
probability order is assumed to be 2. 3(SiO4)-Al represents the network breaking the
effect of Al3+
cation; so it gives a negative contribution to the activation energy. The
probability of one alumina cation which is not charge compensated is (1-(1-PCa)*(1-
PMg)). The probability order is assumed to be 3, because of 3 SiO4 structure units. The
EAl0 is the constant representing free O
2- from Al2O3. However, due to charge
compensation, most of the O2-
contributes into AlO4 network, which reflects small
activation energy in Table 5.2.
Silica has only one structure unit SiO4. It has a positive impact on viscosity and
activation energy and the parameter related is a constant shown in Table 5.2.
121
The overall activation energy of all structure units is optimized from collected
viscosity data in the CaO-MgO-Al2O3-SiO2 system. From the parameters in Table 5.2,
it can be seen that the major structural unit in network breaking is Si-Ca(Mg)-Si. The
free O2-
and Si-Ca(Mg)-Al have less significant impacts on the activation energy. The
Al2O3 behaves almost the same as SiO2 in CaO-MgO-Al2O3-SiO2, which has strong
positive impact on activation energy. In addition, the CaO has higher priority to
compensate the AlO4 charges and lower priority for SiO4 charges, which is
demonstrated by the optimized parameters.
Equation 5-6 Partial activation energy calculation
𝐸𝐶𝑎 = 𝐸𝐶𝑎0 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝑆𝑖𝑂4
∗ 𝑃𝐶𝑎2 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝐴𝑙𝑂4
∗ 𝑃𝐶𝑎 ∗ (1 − 𝑃𝐶𝑎)
𝐸𝑀𝑔 = 𝐸0𝑀𝑔 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝑆𝑖𝑂4
∗ 𝑃𝑀𝑔2 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝐴𝑙𝑂4
∗ 𝑃𝑀𝑔 ∗ (1 − 𝑃𝑀𝑔)
𝐸𝐴𝑙 = 𝐸0𝐴𝑙 + 𝐸𝐴𝑙−3𝑆𝑖𝑂4
∗ [1 − (1 − 𝑃𝐶𝑎) ∗ (1 − 𝑃𝑀𝑔)]3
+ 𝐸𝐴𝑙𝑂4−𝐶𝑎−𝐴𝑙𝑂4
∗ (1 − 𝑃𝐶𝑎)2 + 𝐸𝐴𝑙𝑂4−𝑀𝑔−𝐴𝑙𝑂4∗ (1 − 𝑃𝑀𝑔)
2
𝐸𝑆𝑖2= 𝐸𝑆iO4
Where P represents the probability of Ca/Mg molecules breaking silicate network
defined in Equation 5-3, and E is parameters of structure units from Table 5.2
Table 5.2 Activation energy parameters of all involved structural units in CaO-MgO-
Al2O3-SiO2 system
Basic Oxide Acidic Oxide
Ca2+
Mg2+
SiO4 Al3+
-0.24
ECa0 -0.31 E0
Mg -0.24 ESiO4 7.21 E0
Al -0.53
ESiO4−Ca−SiO4 -7.38 ESiO4−Mg−SiO4
-9.09 EAlO4−Ca−AlO4 23.78
ESiO4−Ca−AlO4 -0.71 ESiO4−Mg−AlO4
-0.51 EAlO4−Mg−AlO4 15.83
122
5.1.6 Model Performance
The performance of the current model is evaluated by comparison with other models
using the viscosity data in the CaO-MgO-Al2O3-SiO2 system.
The mean deviation Δ is calculated using Equation 5-7.
Equation 5-7 Error deviation calculation
Δ =1
n∗ ∑ |
ηCalc − ηExp
ηExp| ∗ 100%
Where Δ is the mean deviation, n is the total number of data, ηCalc is the model
viscosity and ηExp is the experimental viscosity.
5.1.6.1 CaO-MgO-Al2O3-SiO2 system
The evaluation of the model performance was carried out for three different
composition ranges: (i) all viscosity data in the CaO-MgO-Al2O3-SiO2 system; (ii)
data in the blast furnace slag composition range 30-40 wt.% SiO2, 10-20 wt.% Al2O3,
30-45 wt.% CaO and 5-10 wt.% MgO and (iii) data in the ladle slag composition
range 10-25 wt.% SiO2, 20-30 wt.% Al2O3, 40-50 wt.% CaO and 5-10 wt.% MgO.
The results for model comparison are shown in Figure 5.3. It can be seen that the
present model performance very well in all composition ranges, with the mean
deviation 21.4% in the full composition, 12.5% in the BF slag composition and 15.5
in the ladle slag composition range.
123
Figure 5.3 The performance summary of viscosity models in, (i) full CaO-MgO-
Al2O3-SiO2 composition, (ii) BF slag composition and (iii): ladle slag composition
A detailed comparison is conducted using three most accurate models: present model,
Zhang model and Urbain model at the viscosity range of 0 - 5 Pa.s [131, 145]. It can
be seen from Figure 5.4, the present model has overall superior performance than both
Zhang and Urbain models. The mean deviation is 12.5%, 19.4% and 19.3% for the
present model, Zhang model, and Urbain model respectively. At high-value ranges
(>2 Pa.s), the present model prediction distributed on both sides of the experiment
viscosity; in contrast, the Urbain and Zhang model tend to underestimate the
experimental data. On the other hand, it is clear that all models shown in Figure 5.4
can predict viscosity more accurately at viscosity range below 2 Pa.s which is usually
enough for BF and steelmaking ladle slags.
124
Figure 5.4 Comparison between experimental viscosity and calculated viscosity by
present model (12.5% deviation), Zhang model (19.4 deviations) [145] and Urbain
model (19.3 % deviation) [131]
5.1.6.2 Viscosity Trend Prediction
The impacts of CaO and MgO on viscosity are investigated using model prediction
and experimental data. At fixed SiO2, Al2O3 and temperature (1500 °C), as shown in
Figure 5.5, the replacement of MgO by CaO content was evaluated under two
compositions: 1) high acidic oxide (44 wt.% SiO2, 15 wt.% Al2O3) and 2) low acidic
oxide (33 wt.% SiO2 and 5 wt.% Al2O3). In both conditions, through CaO
replacement, the slag viscosities decrease and decrement slope continuously reduced.
Because of charge compensation impact of SiO4 and AlO4 units, the viscosity
decrement is more sensitive at low acidic oxide concentrations. It is noted that at 44
wt% SiO2 and 15 wt% Al2O3, replacement of MgO by CaO first decreases and then
increase viscosity. The model predictions agree well with experimental data by
Gul’tyai and Hofmann [22, 65].
125
Figure 5.5 Comparisons between model predictions and Gul’tyai [65] and Hofmann
[22] results, 1500 °C in the system CaO-MgO-Al2O3-SiO2
5.1.6.3 Sub-Ternary & Sub-Binary System
The present model can also be used to predict the low-order silicate systems
containing CaO, MgO, and Al2O3. As shown in Figure 5.6, the linear relationship
between activation energy EA and pre-exponential factor B can also be applied for
lower-order systems with different m and n values (Equation 5-2). For each binary
and ternary system, the individual m and n values were used to minimize the
prediction deviation. The values of m, n and prediction deviation for each system are
summarized in Table 5.3 below. In the lower-order system, modifications were
required in Equation 5-5 to suit the actual system. For example, in SiO2-CaO system,
both EMg and EAl equals to 0 in SiO2-CaO system.
Table 5.3 The summary of model parameters in binary and ternary silicate system
containing CaO, MgO, and Al2O3.
m n Error
Deviation (%)
Database
SiO2-Al2O3-CaO 0.5953
2.668 24.2 Hofmann, Bills, Johannsen
Machin and Urbain
SiO2-Al2O3-MgO 0.3831
1.442 28.4 Johannse and Lyutikov
126
SiO2-CaO 0.5741
2.311 20.2 Bockris and Urbain
SiO2-MgO 0.4468
1.532 13.1 Bockris, Hofmann, and
Urbain
SiO2-Al2O3 0.5359
2.371 9 Bockris and Urbain
Figure 5.6 The linear relationship between EA and ln(A) for (A): SiO2-Al2O3-CaO and
SiO2-Al2O3-MgO system and
The experimental viscosity data for the systems of SiO2-Al2O3-CaO, SiO2-Al2O3-
MgO, SiO2-CaO, SiO2-MgO and SiO2-Al2O3 are compared with calculated values by
the present model. As shown in Figure 5.7 (A~E), the predicted viscosities by the
present model agree well with reported data. Higher error deviations are reported in
two ternary systems indicating that current model needs to be improved to better
describe the amphoteric behavior of Al2O3 in extreme conditions (very high Al2O3
concentration). Note that all available viscosity data in the ternary and binary systems
have been used without evaluation. Evaluated data would give a better performance of
the present model.
127
(A)
(B)
128
(C)
(D)
(E)
Figure 5.7 Comparisons between experiment viscosity and model prediction in the
systems (A) SiO2-Al2O3-CaO, (B) SiO2-Al2O3-MgO, (C) SiO2-CaO, (D) SiO2-MgO
and (E) SiO2-Al2O3
5.1.7 Industrial Application
5.1.7.1 Blast Furnace Slag
Examples of the industrial applications using the developed viscosity model are
demonstrated in this section. Figure 5.8 shows the effect of (WCaO/WSiO2) on the
viscosity of blast furnace slag at 15 wt% Al2O3 and various MgO concentrations at
129
1500 oC. It can be seen that predictions agree well with Kim, Machin and Gul’tyai’s
data. At a given Al2O3 and MgO concentration, the addition of CaO continuously
decreases the slag viscosity. Also, it indicates that at a given WCaO/WSiO2, the slag
viscosities decrease with increasing MgO concentration. The effect of MgO seems to
be more significant at low WCaO/WSiO2. MgO is usually added in the BF operation as
flux. Reduction of MgO can decrease the direct cost in material and also fuel
consumptions. It can be seen from Figure 5.8 that reduced MgO will increase the slag
viscosity. To keep the slag viscosity at a low-level, WCaO/WSiO2 needs to be increased.
However, liquidus temperature has to be controlled to avoid the formation of solid
phase at operating temperature.
Figure 5.8 Effects of WCaO/WSiO2 and MgO on slag viscosity at 1500 °C and 15 Al2O3
by the present model in comparisons with the data from Kim [122], Gul’tyai [83] and
Machin’s [74]
The present viscosity model can only predict viscosities for single liquid phase. It is
essential to make sure the slag is liquid before the viscosity is calculated by the
viscosity model. It is necessary to present iso-viscosity lines on the phase diagram. As
an example, the iso-viscosity lines are calculated using the present viscosity model for
blast furnace slags at 1500 °C and 15 wt% Al2O3. In Figure 5.9, all viscosities are
presented within the full-liquid region. From the Figure 5.9, the viscosity is mainly
dependent on SiO2 concentration. The iso-viscosity lines are almost parallel to the
130
CaO-MgO axis, which has bias down to the MgO direction. It indicated that the
replacement of CaO by MgO will slightly decrease the slag viscosity at fixed SiO2
concentration. This behaviour is consistent with the fact that the viscosity parameters
of EMg are higher than ECa as a network modifier, which also matches the conclusion
from a review of binary viscosity data of SiO2-CaO and SiO2-MgO systems.
Figure 5.9 The model prediction of the iso-viscosity diagram at 1500 °C and 15 wt.%
Al2O3 and experiment data of Gultyai [83], Li [150], and Machin [68, 74]
5.1.7.2 Ladle Slag in Steelmaking Process
In steelmaking process, the desired viscosity of ladle slag (0.2-0.4 Pa.s) is lower than
BF final slag (0.4-0.6 Pa.s). Figure 5.10 shows effects of temperature and slag basicity
on viscosity at 30 wt% Al2O3 and 5 wt% MgO. The present model can well predict
Song’s data with average deviation 15%. At fixed Al2O3 and MgO concentrations,
the viscosities decrease significantly with increasing WCaO/WSiO2 ratio and the
decrement is more significant at low temperatures. For example, the viscosity is
decreased by approximately 0.13 Pa.s at 1450 °C when the WCaO/WSiO2 is increased
131
from 3 to 5.5. At 1550 °C, the decrement of the viscosity is only approximately 0.05
Pa.s when the WCaO/WSiO2 is increased from 3 to 5.5.
Figure 5.10 Effects of WCaO/WSiO2 and temperature on slag viscosity at 5 wt.% MgO
and 30 wt.% Al2O3 by present model in comparisons with Song’s data [107]
5.1.8 Conclusions
In conclusion, an accurate viscosity model has been developed in the system CaO-
MgO-Al2O3-SiO2 using a large number of critically reviewed experimental data. A
new term ‘probability’ based on composition and electronegativity was introduced to
describe the distribution of cations within the acidic oxide. The new model can
accurately predict viscosities for blast furnace slags and steel refining slags in the
system CaO-MgO-Al2O3-SiO2. The model developed also has good performance for
the sub-systems SiO2-Al2O3-CaO, SiO2-Al2O3-MgO, SiO2-Al2O3, SiO2-CaO, and
SiO2-MgO.
132
5.2 CaO-MgO-Al2O3-SiO2-“FeO” system in full composition range
5.2.1 Introduction
As one of the important physical properties of molten slag, viscosity performs an
important role in metallurgical processes. Abundant studies have been constructed by
researchers to investigate the correlation among slag composition, temperature, and
viscosity. There is a considerable demand for accurate viscosity data in mathematical
modeling for metallurgical processes, and although viscosity of slag can be measured
using the rotating cylinder method, reliable data for industrial application are limited
due to the difficulty and uncertainty of viscosity measurement at high temperature.
In the ironmaking process, the Blast furnace (BF) is the principal technology to
produce iron. The chemistries of these slags can be described by the system SiO2-
CaO-MgO-Al2O3-“FeO”. These slags have significant impacts on the gas
permeability and accretion formation in a blast furnace. In addition, the five
components are the major components of another smelting process, including
steelmaking, mould fluxes and copper-making process. A clear understanding of
viscosity changes during slag formation will help to improve the technical and
economic efficiency. High-temperature viscosity measurement is practically difficult,
time- and money-consuming. Therefore, it is necessary to use reliable viscosity data
to develop an accurate model to predict slag viscosity for CaO-MgO-Al2O3-SiO2-
“FeO” system.
5.2.2. Model Description
5.2.2.1 Silicate structure of SiO2-CaO-Al2O3-MgO-“FeO” system
The slag composition and temperature determined its momentary structures and
viscosity. According to the experimental data and network theory, the components of
the CaO-MgO-Al2O3-SiO2-“FeO” can be categorized into three groups: acidic oxide
(SiO2), basic oxide (CaO, MgO and “FeO”) and amphoteric oxide (Al2O3).
It is widely accepted the SiO2 forms a network structure through (SiO4) tetrahedral
units, which positively impact on the slag viscosity. In contrast, the basic oxide, either
“FeO”, CaO or MgO, will break the [SiO4] network, which negatively impacts on slag
viscosity. The insertion of O2-
will break the covalent bond between Si-O within the
133
(SiO4) tetrahedral unit and then balance the negative charge. This intermediate [Ca
(Mg)-SiO4]+ structure unit has one free positive charge, which is able to break another
SiO4 or compensate the AlO4 charges. The basic oxide “FeO” reported two possible
cations, Fe2+
and Fe3+
, which reported different modify ability in Wright’s viscosity
measurements of iron silicate slags with vary Fe3+
/Fe2+
ratio [192]. It concluded that
the modify ability of Fe3+
is 10-15% stronger than Fe2+
; because the Fe3+
is able to
compensate with 3 SiO4 units. However, it is difficult to form Fe-3[SiO4] structural
units because of the space limitation.
The Al2O3 can behave as either acidic or basic oxide depending on the concentrations
of other basic oxides. If sufficient Ca2+
, Mg2+,
and Fe2+
cations are present to balance
the (AlO4)- charges, the Al2O3 acts as an acidic oxide which is incorporated into the
silicate network in tetrahedron coordination. In the case of insufficient basic oxides,
Al3+
will behave the same as Ca2+
or Mg2+
to break the (SiO4) network.
In summary, in molten slag, the major roles network modifies, including Ca2+
, Mg2+
and Fe2+
is to compensate the Si-[O]- charge and [AlO4]
5-. Due to electrical force
between charges, it is accepted that when cations (Ca2+
, Mg2+,
and Fe2+
) concentration
is low, they have higher priority to balance the AlO4 charges than breaking the Si-O
covalent bond.
5.2.2.2 Temperature dependence
The temperature dependence of viscosity can be described by the Arrhenius-type
equation as Equation 5-8 shown.
Equation 5-8 Arrhenius type equation
1000*η A*exp AE
T
Where η is the viscosity in Pa.s, T is the absolute temperature in K, A is the pre-
exponential factor, EA represents the integral activation energy in J/mol.
134
5.2.2.3 Pre-exponential Factor A
A linear relationship between pre-exponent factor A and activation energy EA was
proposed by Urbain. The activation energy EA and pre-exponential factor A can be
determined by plotting ln(η) against 1/T under the same composition. This linear
correlation has been widely applied in different viscosity models, such as the
Shankar’s and Hu et al.’s model.
Equation 5-9 linear correlation between EA and pre-exponential factor A
* AlnA m E n
Where A the pre-exponential factor and EA is the activation energy from Equation
5-11. m and n are the model parameters are 0.4144 and 4.1485 respectively.
5.2.2.4 Fe2+
and Fe3+
Determination
The modify ability of Fe3+
is stronger than Fe2+
. Also, with abundant “FeO” existence
in silicate melts, the Fe2+
may convert to Fe3+
through breaking SiO4 unit. In the
present study, it is necessary to calculate the concentration of Fe3+
/Fe2+
for the model
establishment.
One of the most widely used methods to estimate Fe3+
/Fe2+
involves the use of
empirical equation relating to oxygen partial pressure to the iron redox state in
quenched silicate liquid. Computer based software, FactSage, was often utilized to
calculate the concentration of Fe3+
/Fe2+
[194].
5.2.2.5 Network Modify probability
With the study of silicate based mineralogy, Ramberg suggests that the silicate
structure (polymerized level of the SiO4 network) is dependent on basic oxide
concentrations, atomic radius and electronegativity [191]. The electronegativity of
Ca2+
, Mg2+
, Fe2+
, Fe3+
, AlO4 and SiO4 units are determined using Mulliken equation
as Equation 5-4, which is derived from 1st ionization energy and electron affinity of
the atom. The values of electronegativity are shown in Table 5.4.
135
Table 5.4 Electronegativity χ of basic oxide cations and network former units
Ca2+
Fe2+
Fe3+
Mg2+
(AlO4)
(SiO4)
Χ 3.07 3.2 3.3 3.82 6.674 6.985
The term “probability (P)” is introduced to describe the probability of Ca2+
(or Mg2+
,
Fe2+,
and Fe3+
) cations to connect with SiO4 and AlO4 tetrahedral unit as introduced in
Section 5.1. The PFe, as shown in Equation 5-10, are proposed to be the probability of
Fe2+
or Fe3+
connecting to the Si-O network respectively. Fe2+
and Fe3+
cations were
also required for (AlO4)- charge compensation. Therefore, the (1-PFe) are the
probability of cations to connect with AlO4.
Equation 5-10 probability calculation for Fe3+
and Fe2+
𝑃𝐹𝑒3+ =χ𝐹𝑒3+𝑀𝐹𝑒3+
χ(𝑆𝑖𝑂4)4− ∗ 𝑀(𝑆𝑖𝑂4)4− + χ(𝐴𝑙𝑂4)5− ∗ 𝑀(𝐴𝑙𝑂4)5−
𝑃𝐹𝑒2+ =χ𝐹𝑒2+𝑀𝐹𝑒2+
χ(𝑆𝑖𝑂4)4− ∗ 𝑀(𝑆𝑖𝑂4)4− + χ(𝐴𝑙𝑂4)5− ∗ 𝑀(𝐴𝑙𝑂4)5−
Where M is a molar fraction of a metal oxide; X is electronegativity of structure units
in slag system.
5.2.2.6 Activation Energy
In Arrhenius equation, EA is defined as the integral activation energy of silicate slag,
which is composed of metal oxides and can be expressed as Equation 5-11 shown:
Equation 5-11 Activation energy calculation
𝐸𝐴 = 𝐸𝐶𝑎𝑂 + 𝐸𝑀𝑔𝑂 + 𝐸𝐹𝑒𝑂 + 𝐸𝐹𝑒2𝑂3+ 𝐸𝐴𝑙2𝑂3
+ 𝐸𝑆𝑖𝑂2
Where Ei is the partial activation energy of i component (i = SiO2, Al2O3, CaO, MgO,
and FeO) calculating from Equation 5-12.
136
In CaO-MgO-Al2O3-SiO2-“FeO” system, as a network modifier, there is three
possible structure units combination with Fe2+
, including free oxygen O2-
, SiO4-Fe-
SiO4, and SiO4-Fe-AlO4. As PFe defined before, one Fe2+
cation has the probability of
PFe to connect with one SiO4 tetrahedron. Therefore, the probability of SiO4-Fe-SiO4
and SiO4-Fe-AlO4 can be assumed as PFe2 and PFe*(1-PFe) respectively. As Equation
5-11 shown, the integral activation energy of FeO is calculated by the sum of
activation energy of each structural unit multiplied by its probability. The EFe0 is the
constant representing O2-
from FeO. Because of similar properties, the calculation of
CaO and MgO integral energy is expressed in Equation 5-12. Unlike Fe2+
, the Fe3+
is
able to compensate three negative charges, which should consider 4 types of structure
units as Equation 5-12 shown.
The impact of cations Ca, Mg, Al and Si were detailed discussed and introduced in
Section 5.1.
Equation 5-12 the partial activation energy calculation
𝐸𝐶𝑎 = 𝐸𝐶𝑎0 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝑆𝑖𝑂4
∗ 𝑃𝐶𝑎2 + 𝐸𝑆𝑖𝑂4−𝐶𝑎−𝐴𝑙𝑂4
∗ 𝑃𝐶𝑎 ∗ (1 − 𝑃𝐶𝑎)
𝐸𝑀𝑔 = 𝐸0𝑀𝑔 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝑆𝑖𝑂4
∗ 𝑃𝑀𝑔2 + 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝐴𝑙𝑂4
∗ 𝑃𝑀𝑔 ∗ (1 − 𝑃𝑀𝑔)
𝐸𝐴𝑙 = 𝐸0𝐴𝑙 + 𝐸𝐴𝑙−3𝑆𝑖𝑂4
∗ [1 − (1 − 𝑃𝐶𝑎) ∗ (1 − 𝑃𝑀𝑔)]3
+ 𝐸𝐴𝑙𝑂4−𝐶𝑎−𝐴𝑙𝑂4∗
(1 − 𝑃𝐶𝑎)2 + 𝐸𝐴𝑙𝑂4−𝑀𝑔−𝐴𝑙𝑂4∗ (1 − 𝑃𝑀𝑔)
2+ 𝐸2𝐴𝑙𝑂4−𝐹𝑒2+ ∗ (1 − 𝑃𝐹𝑒2+)2 +
𝐸3𝐴𝑙𝑂4−𝐹𝑒3+ ∗ (1 − 𝑃𝐹𝑒3+)2
𝐸𝐹𝑒2+ = 𝐸0𝐹𝑒2+ + 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝑆𝑖𝑂4
∗ 𝑃𝐹𝑒2+2 + 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝐴𝑙𝑂4
∗ 𝑃𝐹𝑒2+ ∗ (1 − 𝑃𝐹𝑒2+)
𝐸𝐹𝑒3+ = 𝐸0𝐹𝑒3+ + 𝐸3𝑆𝑖𝑂4−𝐹𝑒3+ ∗ 𝑃𝐹𝑒3+
3 + 𝐸2𝑆𝑖𝑂4−𝐹𝑒3+−𝐴𝑙𝑂4∗ 𝑃𝐹𝑒3+
2 ∗ (1 − 𝑃𝐹𝑒3+) +
𝐸𝑆𝑖𝑂4−𝐹𝑒3+−2𝐴𝑙𝑂4∗ 𝑃𝐹𝑒3+ ∗ (1 − 𝑃𝐹𝑒3+)
2
𝐸𝑆𝑖2= 𝐸𝑆iO4
where P represents the probability of cations, Ca2+
, Mg2+
, Fe2+
and Fe3+
breaking
silicate network and Ei is parameters of structure units from Table 5.5.
137
Table 5.5 Activation energy parameters of all involved structural units in CaO-MgO-Al2O3-SiO2 system
Basic Oxide Acidic
Oxide
Amphoteric Oxide
Ca2+
Mg2+
Fe2+
Fe3+
SiO4 Al3+
𝐸𝐶𝑎0 -0.314 𝐸0
𝑀𝑔 -0.24 𝐸0𝐹𝑒2+ -0.11 𝐸0
𝐹𝑒3+ -0.14 𝐸𝑆iO4 7.21 𝐸0
𝐴𝑙 -0.53
𝐸𝑆𝑖𝑂4−𝐶𝑎−𝑆𝑖𝑂4 -7.38 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝑆𝑖𝑂4
-9.09 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝑆𝑖𝑂4 -5.32 𝐸3𝑆𝑖𝑂4−𝐹𝑒3+ -6.33 𝐸𝐴𝑙𝑂4−𝐶𝑎−𝐴𝑙𝑂4
23.78
𝐸𝑆𝑖𝑂4−𝐶𝑎−𝐴𝑙𝑂4 -0.71 𝐸𝑆𝑖𝑂4−𝑀𝑔−𝐴𝑙𝑂4
-0.51 𝐸𝑆𝑖𝑂4−𝐹𝑒2+−𝐴𝑙𝑂4 -0.22 𝐸2𝑆𝑖𝑂4−𝐹𝑒3+−𝐴𝑙𝑂4
-0.31 𝐸𝐴𝑙𝑂4−𝑀𝑔−𝐴𝑙𝑂4 15.83
𝐸𝑆𝑖𝑂4−𝐹𝑒3+−2𝐴𝑙𝑂4 -0.15 𝐸2𝐴𝑙𝑂4−𝐹𝑒2+ 13.45
𝐸3𝐴𝑙𝑂4−𝐹𝑒3+ 11.2
138
5.2.3 Model Performance
As Table 5.6 shown, the new model developed reported an overall 17% deviation
with the viscosity data comparing with other existing models for CaO-MgO-Al2O3-
SiO2-‘FeO’ system. As Figure 5.11 shown, the viscosity prediction accuracy was
significantly improved using present model; considering the two closest Urbain and
Zhang model reported 25% prediction deviations [131, 188].
Table 5.6 The prediction deviation of viscosity models for CaO-MgO-Al2O3-SiO2-
“FeO” system
Model Deviation (%)
Present 17.1
Zhang 24.9
Urbain 25.6
Factsage 34.2
QCV 36.8
Li 42.6
Iida 50.6
Mills 64.1
A detailed comparison of the viscosity model performance is carried out using the
three most accurate models: present model, Zhang model and Urbain model in the
viscosity range 0-2 Pa.s. As Figure 5.11 shown, the present model has superior
performance than both Zhang and Urbain models. It can be seen from Figure 5.11, the
calculated viscosity from Urbain and Zhang model was an under-estimation at large
viscosity region (>1 Pa.s). The experiment measurements (>1 Pa.s) was reported from
“Fe2O3” containing slags. Because both Urbain and Zhang model assumed only FeO
139
existence in the molten slag and did not consider the modify ability of Fe3+
is stronger
than Fe2+
, which is included in the present model development.
Figure 5.11 The comparison between experimental viscosity and calculated viscosity
using Current, Urbain [131] and Zhang model [145].
Sub-ternary and quaternary system
In addition, the present model can predict the viscosity of sub-ternary system of “FeO”
containing slags. In ternary system, the network modify ability of different basic
oxide can be determined. Figure 5.12 compared the viscosity of two ternary system,
CaO-SiO2-‘FeO’ and MgO-SiO2-‘FeO’. With the increasing of ‘FeO’ content, at 1500
oC and CaO (MgO)/SiO2=1.2 conditions, the measured viscosity steadily increased
for both ternary system. In addition, the viscosity of MgO-SiO2-‘FeO’ system is
higher than the CaO-SiO2-‘FeO’ system at 50 oC higher temperature. The trend
indicated that the modify ability of 3 basic oxides can be ranked as
CaO>MgO> ’FeO’.
140
Figure 5.12 40 wt% SiO2, 1500 oC for SiO2-CaO-“FeO” system by Chen [193],
Bockris [194] and Ji [114], 40 wt% SiO2, 1550 oC for SiO2-MgO-“FeO” system by
Chen [115], Ji [195] and Urbain [60]
5.2.4 Industrial Application
5.2.4.1 Blast Furnace Slag
The primary slag formed in the cohesive zone of the blast furnace contains high “FeO”
content. The “FeO” concentration in the slag will decrease when the burden moves
down and the reduction proceeds continuously. If initially formed primary slag is
viscous and stays locally, reduction of “FeO” will continuously increase its viscosity
making it more viscous. In the BF operation, if the primary slag forms at a lower
temperature, i.e., if the top of the cohesive zone moves upward, the viscosity of the
slag will be high and it may not be able to flow rapidly through the coke bed. The
localized viscous slag will fill the void, which reduces the surface area for indirect
reduction and also the gas permeability. It is desirable to have the primary slag
formed at a higher temperature so that its viscosity is low enough to allow the slag
drop quickly. As shown in Figure 5.13, the current model predictions are in very good
agreement with the experimental results that cover the “FeO” concentration from 0 to
25 wt%. The viscosities shown in Figure 5.13 are all for fully liquid slags. The
temperature impact on viscosity are more sensitive at low temperature than higher
temperature condition.
141
Figure 5.13 Comparisons of the viscosities between model predictions and
experimental data for different “FeO”-containing slags (in wt%) by Higgins [190];
Vyaktin [84] and Machin [80]
5.2.4.2 Coppermaking Slag
Figure 5.14 shows viscosity as a function of “FeO” at 1250 oC for a base slag 52 wt%
SiO2, 13.3 wt% Al2O3, 29.3 wt% CaO and 5.3 wt% MgO, which is a typical copper-
making slag. The viscosity of the fully liquid slag continuously increases with
decreasing “FeO” concentration in the slag. For example, it can be seen from Figure
5.14 that the viscosity of the slag with 30 wt% “FeO” is below 1 Pa.s. If “FeO” is
reduced to 15 wt% the viscosity of the slag will be 3.5 Pa.s at the same temperature
(1250 oC). The sensitivity of the viscosity to the “FeO” increases with decreasing the
“FeO” concentration in the slag. It can be seen from Figure 5.14 that FactSage
predicted viscosities are much lower than the predictions of the present model, in
particular at low “FeO” concentrations.
142
Figure 5.14 Viscosity as a function of “FeO” at 1250 oC, base slag 52% SiO2, 13.3%
Al2O3, 29.3% CaO, 5.3% MgO by Higgins [190]
5.2.5 Conclusion
In conclusion, an existing model by the present author has been optimized and
extended to describe the viscous behavior of fully liquid slag in the CaO-MgO-Al2O3-
SiO2-“FeO” system using a large number of reviewed experimental data. A new term
‘probability’ based on composition and electronegativity was introduced to describe
the distribution of cations within the acidic oxide. The new model can accurately
predict viscosities for both blast furnace primary slags, steelmaking slags and copper
making slags in the CaO-MgO-Al2O3-SiO2-“FeO” system.
143
Chapter 6 : Structure studies of silicate slag by Raman spectroscopy
In the present study, Raman spectroscopy was utilized on quenched glass samples of
SiO2-CaO, SiO2-CaO-Al2O3, and SiO2-CaO-MgO system to investigate the network
impact of CaO, MgO and Al2O3 referring to the network theory. The Raman
spectrum information, including peak location and intensity, were quantitatively
analyzed correspond to the network structure of silicate glass. Various
physiochemical properties such as viscosity, density, and liquidus temperature can be
derived from a proposed mathematical definition called “degree of polymerization”
(DP). The present methodology can be extended to predict the other physicochemical
properties of silicate melts for metallurgical processes.
144
6.1 Introduction
The structure and properties of amorphous slags are of widespread interest because of
their importance in the process optimization of pyro-metallurgy field. Many
spectroscopic methods have been developed to determine the structure of slags and
distinctively identify the microstructural units within the amorphous silicate glasses
[196-198]. Raman spectroscopy, as an analytical technique for the study of molten
slag, has been widely utilized and accepted by other researchers [41]. The
microstructural information was obtained through the analysis of peak shift and
intensity of Raman spectrum, which indicates the types of vibration units and its
relative concentration.
For CaO-MgO-Al2O3-SiO2 slag system, the Raman spectrum study was performed by
other researchers, as the summary in the Table 6.1. The alumina silicate system has
been well studied; however, the focus composition range is different from the blast
furnace slag composition. In addition, Different Raman spectrum will report varied
results of amorphous glass phase due to instrument factors, such as intensity of laser
light, which did not allow the cross-reference comparison of Raman results of
amorphous glass.
For silicate glass, most of the researchers focus on the high-frequency band ranging
from 800-1200 cm-1
[199]. However, limited information was provided for the low-
frequency band (300-700 cm-1
), which is the critical region in the study of fused silica
(amorphous phase). In the alumina silicate glass, it is accepted that the Al2O3 behavior
as a network former, connecting with SiO4, was not clearly revealed in the Raman
spectra of other researchers [4].
In the present study, Raman spectroscopy was utilized on quenched glass samples of
SiO2-CaO, SiO2-CaO-Al2O3, and SiO2-CaO-MgO system to identify the potential
vibration units in the low-frequency region to further investigate the impact of CaO,
MgO, and Al2O3 on fused silica. A quantitative analysis was performed on the Raman
spectroscopy to identify and estimate the abundance of silicate continuous ring and
discrete anions (Dn and Q
n) of silicate melts.
145
6.2 Methodology
6.2.1 Sample Preparation
The quenched slag samples were prepared for the SiO2-CaO, SiO2-CaO-MgO and
SiO2-CaO-Al2O3 system. The designed composition was shown in Table 6.1.
Approximately 0.25g mixture was prepared for each experiment runs. The CaCO3
(99%), SiO2 (98%), MgO (99%) and Al2O3 (99.9%) powders were weighed, mixed
and grinded for 30 minutes to obtain homogeneous mixtures. The mixture melted in a
graphite crucible at designed temperature for 2 hours to achieve complete fusion,
homogenization and equilibrium status under Ar atmosphere condition. The schematic
diagram is shown in Figure 6.1. The quenched glasses will be mounted and polished
for Raman spectroscopy analysis. In addition, the electro-probe microanalysis (EPMA)
were constructed for each sample to confirm the sample reliability, and the outcomes
were shown in Table 6.1.
Figure 6.1 Schematic diagram of equilibrium experiment settings
146
Table 6.1 The experiment designed condition and EPMA results
Design Composition Experiment
Temperature
EPMA Results
CaO/SiO2
Mol/Mol%
Additive
Mol%
oC SiO2
Mol%
CaO
Mol%
SiO2-CaO system
No.1-4
0.55 0 1773 63.2 36.8
0.7 0 1773 58.7 41.3
0.9 0 1553 52.6 47.4
1.1 0 1466 47.6 52.4
MgO Mol%
SiO2-CaO-MgO system
No.1-14
0.8 5 1500 52 43.1 4.9
1 5 1500 46.7 48.3 5
1.2 5 1500 43.4 51.5 5.1
147
0.8 10 1500 50.3 39.6 10.1
1 10 1500 44.1 45.9 10
1.2 10 1500 39.8 50.4 9.8
2 10 1500 58.3 32 9.7
2 10 1600 59.4 30.3 10.3
0.8 15 1500 47.1 37.8 15.1
1 15 1500 42.5 42.5 15
1.2 15 1500 37.1 48.1 14.8
0.8 20 1500 43.5 36.3 20.2
1 20 1500 41.1 39.5 19.4
1.2 20 1500 35.6 44.6 19.8
Al2O3
148
Mol%
SiO2-CaO-Al2O3 system
No.1-15
0.8 5 1500 52.7 42.8 4.5
1 5 1500 47.3 47.5 5.2
1.2 5 1500 43.1 51.8 5.1
0.8 10 1600 48.9 41.3 9.8
1 10 1500 45.5 44.6 9.9
1.2 10 1300 45.3 44.6 10.1
1.2 10 1500 45.2 44.5 10.3
1.2 10 1600 44.7 45.3 10
0.8 15 1500 47.2 38.1 14.7
1 15 1500 42 42.9 15.1
1.2 15 1500 37.6 46.9 15.5
149
0.8 20 1500 44.5 35.4 20.1
1 20 1500 38.9 40.7 20.4
1.2 20 1500 35.3 45.4 19.3
150
6.2.2 Raman Analysis
The quenched material was mounted in epoxy resin and polished for Raman
spectroscopy measurements (Company: Ranishaw; Model: inVia). The Raman
spectrum was recorded at room temperature in the frequency range of 100-1500
cm-1
using excitation wavelength of 514 nm semiconductor laser with a power of
1 mw. The instrument was calibrated in the air by utilization of electronic grade
silica. The measurements were performed under ambient pressure and room
temperature. There was no detectable temperature increase by laser touch to the
samples.
For one sample, measurements were taken on three different locations on
separate pieces of quenched glasses to evaluate the consistency and stability of
the instrument. The average deviations of three measurements at one sample
were within 1%. The peak deconvolution is necessary for the quantitative
analysis of the spectra by researchers. As Figure 6.2 shown, the baseline was
firstly removed for spectra of 52.6SiO2-47.4CaO system, and then the two bands
were fitted by Gaussian function using software “PeakFit” program.
Figure 6.2 Typical deconvolution of Raman spectrum of a 52.6 mol% SiO2-47.4 mol%
CaO sample
151
6.3 Raman Results
6.3.1 Structure of alumina silicate system
The random network theory was accepted for the description of amorphous silicate
structure. In silicate based slag of SiO2-CaO-Al2O3-MgO system, the SiO2 forms a
network structure by the connection of SiO4 tetrahedral unit. The addition of basic
oxide; the CaO and MgO tends to break the Si-O-Si bond. The AlO4 from Al2O3 binds
with a SiO4 unit with the existence of cations to compensate the charge, which
improves the polymerization degree of silicate slag. From Raman spectrum, the
interpreted microstructure units supported the development of network theory [200].
The fused glasses silica has been studied using Raman spectroscopy [201]. In the low-
frequency region, the two major peaks of glasses silica located at 495 cm-1
and 606
cm-1
in Raman spectrum. Galeener’s study pointed out that the two peaks can be
assigned to 4 and 3-folded rings respectively through the calculation of bond angle
using the energy minimization method [38]. The structure of fused silica can be
estimated as the combination of 4-3 folded rings due to the fact that the angel between
O-Si-O is approximately 133o. The required energy of 2-fold ring is >5eV comparing
to 3-fold=0.51 eV and 4-fold ring=0.16 eV; while 2-fold planar rings are not possibly
excepted since they require an unreasonably large amount strain energy for the bond
angle=60o [38].
In SiO2-CaO glasses, with the addition of basic oxide, a board band appears in the
spectra ranging 800-1200 cm-1
shift. The addition of Ca2+
and O- polarize the discrete
anions, which was expected as the breaking silicate planar ring and form 4 different
discrete anions with O2-
, according to the SiO4 structural unit. After the peak
deconvolution, 4 peaks were reported and assigned in the high-frequency region. The
description of microstructure units and assigned peak location were summarized in
Table 6.2. The peak Q4 indicated the initiation of network breakage, which
polymerize of non-bridging oxygen [O]-. As the continues addition O
2- from basic
oxide, the abundance of [O]- will increased upon to 4 and become individual unit,
which did not support the formation of network.
152
Table 6.2 The description of assigned peak information in Raman spectrum silicate structural units, black ball is Si and white ball is O. white
ball with – sign is O-
Peak Raman
Shift Structural Drawing
Ref
D2
4-fold ring 480-500 4[SiO4]
D3
3-fold ring 590-610 3[SiO4]
Q1
Individual SiO4 tetrahedral unit 850-880 [SiO4]
4-
153
Q2
Si2O7 dimer 900-930 (O)O
--Si-2O-Si-2O
-
Q3
Si2O6 chain 950-980
(O)O--Si-2O-Si-2O
-
Q4
Si2O6 sheet 1040-1060
SiO4-Si-O-(O)
154
6.3.2.1 Raman Peak Shift
In SiO2-CaO system, the increasing CaO content indicated the degradation of silicate network,
which means the polymerization degree of silicate network decreased. The Raman spectrum
of glasses with the composition different CaO/SiO2 is shown in Figure 6.3. In Figure 6.3, as
the green and red dot line indication, the low-frequency band shift from left to right, and the
high-frequency band shifts from right to left.
In the low-frequency region, as the discussion before, the low-frequency band (Dn)
represented the silicate planar ring. The addition of CaO tends to break the silicate network,
which degraded the 4 folded to 3 folded ring. The high-frequency band (Qn) represented the
broken silicate units with cations ions Ca2+
. The 2-fold rings possibly exist in SiO2-CaO
system and show a dominantly strong polarized Raman line at (ring-stretch) frequencies
around 1100 cm-1
under low CaO content condition. At high CaO/SiO2 ratio, the breakage of
silicate network potentially forms the individual SiO4 unit, which reported the Raman peak
shift from right to left.
From the view of vibration units, the insertion of CaO not only changed the silicate structure
but also vary the vibration modes from bending vibration to stretching vibration. The
attachment of CaO onto silicate will form [SiO4-x CaO] structural units, which initial the
stretching vibration and form the bands at 1000 cm-1
region. In high-frequency region, as
Figure 6.3 shown, the peak shifted to left due to the decreasing of electrons density from
Park’s study, which might be referred to degradation of silicate polymerization network.
From the study of McMillan, the doubly charged cations M2+
of the large ionic radius and
small ionization potential (small Z/r2) should preferentially occupy the Q3 (sheet) sites [4].
The Z/r2 of Ca2+
(=2) is much smaller than Mg2+
(=3.9). Therefore, due to the cations size
difference, the Ca2+
ion would charge compensate two open O- ions because of the large size
of the [CaO6], whereas the Mg2+
is balanced with two adjacent corner-shared O- ions because
of the small size the [MgO6]. The substitution of Ca2+
by Mg2+
will slightly increase the
polymerization degree of silicate network, which is also shown in the viscosity study of SiO2-
CaO-MgO system [56, 57, 202].
155
Figure 6.3 the Raman spectrum of SiO2-CaO system, which covers the CaO/SiO2 ratio from
0.55 to 1.1
From the network theory and experiment viscosity data, it is known that MgO has a similar
impact as CaO, which modify and reduce the polymerization degree of silicate network. The
Raman spectrum of SiO2-CaO based with different MgO content is shown in Figure 6.4. As
the green and red dot line indication, the low-frequency band shift from left to right, and the
high-frequency band shifts from right to left. The peak shifting become steady comparing to
Figure 6.3, which indicate that the internal micro-structure of molten slag approaches
equilibrium status. Also, it can be noted that the intensity of peak at approximate 800 cm-1
significantly increased from 5mol % MgO to 20 mol% MgO, which will be discussed in the
later section.
Figure 6.4 the Raman spectrum of SiO2—MgO—CaO system under CaO/SiO2=1 and 1500 oC condition, which covers the different MgO concentrations.
From the network theory, it is known that Al2O3 would be converted to [AlO4]-, which binds
with SiO4 units and form the silicate network. As amphoteric oxide Al2O3, its role was
156
dependent on the amount of basic oxide. Large amounts of basic oxide are capable of
compensating [AlO4]- charges and push the Al towards the network former and vice versa.
The Raman spectrum of SiO2-CaO- Al2O3 of different Al2O3 content was shown in Figure 6.5.
As Figure 6.5 (a) shown, it is obvious that the addition of Al2O3 increase the width of the
band in the low-frequency region comparing to the Raman spectrum of SiO2-CaO and SiO2-
CaO-MgO system, which evidently indicated the formation of combinations between [AlO4]-
and SiO4 units. The polymerization length could not be directly identified using Raman
techniques. After peak deconvolution, a novel peak was identified and recorded as D1 at
approximately 500 cm-1
regions. The bands were further deconvluted to compare the trend.
As Figure 6.5 (b) shown, The addition of Al2O3 shift the peaks Q1-Q4 to the right, which
indicates the enhancement of polymerization degree of silicate network.
Figure 6.5 (a) left, the Raman spectrum of SiO2—Al2O3—CaO system under CaO/SiO2=1
and 1500 oC condition, which covers the different Al2O3 concentrations. (b) Right, the peak
deconvolution outcomes of left spectra
6.3.2.2 Peak Intensity
It is known that the peaks area is proportional to the abundance of the structural unit. The
relative occupancy of deconvolution peak can be utilized as a supporting information to
determine the viscosity impact of CaO, MgO, and Al2O3 on the silicate network.
Theoretically, the addition of CaO and MgO would decrease the polymerization degree of
silicate network; and Al2O3 is considered to be the contrary. The role of peaks can be
determined within silicate through the comparison of peak area at different basicity and slag
system.
157
The relative area occupancy of different peaks of (a) SiO2-CaO-MgO and (b) SiO2-CaO-
Al2O3 system were shown in Figure 6.6 under CaO/SiO2 =1 condition. As Figure 6.6 (a), for
SiO2-CaO-MgO system, the addition of MgO decreased the relative abundance of peak Q4,
D2, and D3; however, the concentration of Q1, Q2 and Q3 increased. It is known that the role
of basic oxide is to break the silicate network; therefore, the structure units of peak Q4, D2
and D3 contributed to the formation of silicate network.
For the SiO2-CaO-Al2O3 system, when Al2O3 content increased, Figure 6.6 (b) showed the
increasing of the relative abundance of peak D1, D2, and Q4; however, the concentration of Q1,
Q2, Q3 and D3 decreased. From the analysis of peak shift and concentration of SiO2-CaO-
Al2O3 system, it should be noted that peak D1 and D2 is relevant to SiO4-AlO4 network units;
and D3 should belong to pure SiO4 network unit. However, both the increasing slope and
decreasing slope is gently comparing to the Raman spectrum of SiO2-CaO and SiO2-CaO-
MgO system; because the cations Ca2+
or Mg2+
was utilized for charge compensation of
[AlO4]- unit.
Figure 6.6 The relative area occupancy of different peaks of (a) SiO2-CaO-MgO system
ranging of CaO/SiO2 =1, (b) right, relative area occupancy of different peaks of SiO2-CaO-
Al2O3 system ranging of CaO/SiO2 =1
6.3.2.3 Temperature Impact
It is accepted that the temperature will influence the silicate melts structure, which could be
identified by Raman spectrum. A 45 SiO2- 10 Al2O3- 45 CaO mol% sample was molten at
100 oC interval from 1300-1600
oC, which knew that the liquidus temperature is approximate
1268 oC from FactSage prediction. The target composition belongs to the wollastonite
primary phase field. When the quenching temperature decreased, as Figure 6.7 shown, the
high frequency region of spectra of become closer comparing to the Raman spectra of
158
wollastonite mineral [202]. This phenomenon can only be observed in the high frequency
region of spectra; because the low frequency region is relevant to the network former unit
AlO4 and SiO4.
Figure 6.7 Raman spectrum of 45 SiO2- 10 Al2O3- 45 CaO mol% sample at 1300, 1500 and
1600 oC and wollastonite [202]
6.3.3 Bond energy and the lattice energy
The shift of a vibration frequency is originated from the shift of energy [203]. Assuming CaO,
MgO, and Al2O3 as ionic compounds in the molten slag, the bond force (energy) should be
considered to explain the peak shift. Coulomb interaction [203, 204], the interacting force
between static electrically charged particles, is given by the formula:
Equation 6-1 Coulomb interaction calculation
E = k𝑄1𝑄2
𝑟1−2
Where k is the Coulomb’s constant 8.99 *109 Nm
2/C
2, Q1=Z1Qe is the quantity of charge on
the charge 1, Q2=Z2Qe is the quantity of charge on the charge 2, Z1 and Z2 is the number of
electrons in the outermost energy level, Qe=1.602*10-19
C is the charge of the electron and r1-
2 is the distance between the two charges.
In the case of CaO, MgO and Al2O3, the nature of electrostatic forces of cations and O- are
attractive. The ionic radius of Al3+
, Ca2+
, Mg2+
and O2-
ions were 0.535Å, 0.329Å, 1.068Å,
159
and 1.4 Å respectively [207, 208]. The electrostatic energy was calculated for one Al-O, Ca-
O and Mg-O bond according to the Coulomb interaction. The bond energy of one mole bond
is given by multiplication of Avogadro’s number, NA=6.022 * 1023
.
For one mol Al-O bond
Equation 6-2 Examples of Coulomb interaction calculation
EAl−O = 8.99 ∗ 1093 ∗ 2 ∗ (1.602 ∗ 10−19)2
(0.535 + 1.4) ∗ 10−10= 7.1541 ∗ 10−18 ∗ 6.022 ∗ 1023
= 4308 KJ/mol
For one mole Ca-O bond
ECa−O = 8.99 ∗ 1092 ∗ 2 ∗ (1.602 ∗ 10−19)2
(1.068 + 1.4) ∗ 10−10= 3.739 ∗ 10−18J ∗ 6.022 ∗ 1023
= 2251 KJ/mol
For one mole Mg-O bond
EMg−O = 8.99 ∗ 1092 ∗ 2 ∗ (1.602 ∗ 10−19)2
(0.329 + 1.4) ∗ 10−10= 5.337 ∗ 10−18J ∗ 6.022 ∗ 1023
= 3214 KJ/mol
For one mole SiO4 tetrahedral unit by Bongiorno [209]
ESi−O = 1.441 ∗ 10−17 ∗ 6.022 ∗ 1023 = 8677 𝐾𝐽/𝑚𝑜𝑙
As a result, in the SiO2-CaO-Al2O3 system, when SiO4 units are substituted by AlO4, the
lattice energy is weaker by an amount of 4369 (KJ/mol). The lattice energy decreases; hence
the respective Raman bands shift to smaller wavenumber (shift to left). In the SiO2-CaO-
MgO system, when Ca2+
ions were substituted by Mg2+
ions, the lattice energy is enlarged by
an amount of 963 (KJ/mol), which cause the Raman bands shift to larger wavenumbers (shift
to right)
6.3.4. Summary
From the quantitative analysis of Raman spectra of quenched slag sample of SiO2-CaO, SiO2-
CaO-MgO and SiO2-CaO-Al2O3 system, it can be concluded that:
When system basicity increased, the low-frequency band (400-700 cm-1
) shift to right
and high-frequency band (800-1200 cm-1
) shift to left
160
A new peak appears at the 350 cm-1
position in the Raman spectra of SiO2-Al2O3-
CaO comparing to SiO2-CaO system, which can be assumed as AlO4-SiO4 ring
structure unit.
Peak D1, D2, D3 and Q4 can be classified as network former group contributing to the
polymerization of silicate network. In contrast, the peak Q1, Q2, and Q3 can be
classified as network modify the group, which degraded the silicate network.
It can be noted that when sample quenched temperature close to its liquidus
temperature, the Raman spectrum is closer to its primary phase field.
6.4 Thermodynamic Analysis
6.4.1 Degree of Polymerization
The degree of polymerization (DP) is defined as the abundance of monomeric units in a
polymer. In the silicate based system, DP referred to the silica tetrahedral, which can be
determined from the frequency shifts and intensity changes of Raman spectra [198]. From the
Raman study of SiO2-CaO, SiO2-CaO-MgO and SiO2-CaO-Al2O3 system, the peaks can be
classified into two groups. The peak D1, D2, D3, and Q4 should be classified as network
formed group; because the increasing basicity will also increase these peaks intensity. And
the peak Q1, Q2, and Q3 should be classified as network modify group. In the present study,
the ratio (high polymerized unit)/ (low polymerized unit) was used to represent the DP index
for one quenched slag sample, as shown below.
In silicate network, CaO, MgO, and Al2O3 as ionic compounds in the molten slag, the bond
force (energy) should be involved to determine the DP. The correspond bond energy was
calculated using Coulomb interaction equation as Equation 6-2. The details is shown in Table
6.3. It should be noted that the distribution of Ca2+
and Mg2+
charge compensation is not
determined, which has to assume 50% equal share.
Equation 6-3 the degree of polymerization calculation
DP =D1 + D2 + D3 + 𝑄4
Q1 + Q2 + Q3=
∑ 𝑄𝑛 ∗ 𝐸𝑛 ∗ 𝐶𝑛𝐻𝑖𝑔ℎ 𝑝𝑜𝑙𝑦𝑚𝑒𝑟𝑖𝑧𝑒𝑑 𝑢𝑛𝑖𝑡
∑ 𝑄𝑛 ∗ 𝐸𝑛 ∗ 𝐶𝑛𝐿𝑜𝑤 𝑝𝑜𝑙𝑦𝑚𝑒𝑟𝑖𝑧𝑒𝑑 𝑢𝑛𝑖𝑡
161
Where Q is the number of the structural unit within the peak n, for example, in peak D2 (4
folded ring), there are 4 connected SiO4 units. En is the bond energy of structural units within
the peak from D1 to Q4, which is calculated using Coulomb equation, Cn is the relative
concentration of the peak n in Raman spectrum
Table 6.3 Summary of the bond energy of each deconvoluted peaks
Peak Structural Unit Bond Energy (KJ/mol)
D1 AlO4-SiO4 7553
D2 4 [SiO4] 23368
D3 3 [SiO4] 17526
Q1 [SiO4]4-
individual unit 8677
Q2 Si2O7 dimer 10721
Q3 Si2O6 chain 13421
Q4 Si2O5 sheet 15772
As Figure 6.8 shown, the proposed DP was a plot against the slag sample in the present study.
It can be seen that the DP index decreased as basicity increased within SiO2-CaO, SiO2-CaO-
MgO, and SiO2-CaO-Al2O3 system. In the basicity = 0.8-1.1 ranges, the DP index slightly
increases as Mg2+
ion substitutes for Ca2+
.
162
Figure 6.8 DP index again basicity of SiO2-CaO, SiO2-CaO-MgO, and SiO2-CaO-Al2O3
system
6.4.2 Density
Density is a physical variable of molten oxides in operation optimization, which is relevant to
the slag/metal separation. It is also an important thermodynamic variable for calculating
critical dimensionless numbers, such as Reynolds, Prand, and Nusselts, which are used in
fluid transmission and can be extended to the estimation of blast furnace operation [210]. The
densities of molten slags can be simulated using the partial molar volume. The effect of the
SiO2 and Al2O3 on density can be represented by empirical equation from Mill’s study [211].
It should be noted that the reference temperature for calculation is 1773 K and require
adjustment to other temperatures by applying a temperature coefficient of -0.01%/K [211].
The relationship between density and DP is shown in Figure 6.9. A linear equation can be
proposed to estimate the slag density with Raman spectrum information.
Figure 6.9 DP index against the estimated densities of slag samples
163
6.4.3 Viscosity & Activation Energy
Viscosity is a measure of the impediment of flow. The size of the constituents present in the
melt constitutes the barrier or impediment to movement. Since silicates contain different
structural units with varying sizes; it is necessary to relate the viscosity to the structure of
silicates. The abundance of several structural units is consistent with the activation energy of
slags. Consequently, it is possible that activation energy of a composition is a mathematical
function of the DP index.
As Equation 6-4 shown, the Arrhenius type equation was used to determine the activation
energy. The activation energy of slag samples in the current study can be determined from
existing viscosity data. As Figure 6.10 shown, the calculated activation energy from
experimental results has a positive relationship with DP for SiO2-CaO, SiO2-CaO-MgO, and
SiO2-CaO-Al2O3 system. A polynomial equation, as Equation 6-4 shown, can use to describe
the trend. The DP index, which can be experimentally measured, can potentially be used to
quantify and predict the viscosity of the melts [210].
Equation 6-4 Arrhenius-type equation
η = A ∗ exp (𝐸𝐴
T)
E𝐴 = 0.214 ∗ 𝐷𝑃2 + 4.453 ∗ 𝐷𝑃 + 11.73
Figure 6.10 DP index of each Raman spectrum against the activation energy
164
6.5 Conclusion
The structure and properties of amorphous slags are of widespread interest because of their
importance in the process optimization of pyro-metallurgy field. Raman spectroscopy is an
analytical technique for the study of the microstructure of molten slag of the silicate-based
system. The impact of Al2O3 and MgO on SiO2-CaO based system was investigated by
utilization of Raman spectrum on quenched glasses samples. A significant correlation was
determined between the quantitative information of Raman spectrum and a polymerization
degree of slag sample in the present study, which supported the silicate network theory. In the
present study, a quantitative analysis was performed on the Raman spectrum to estimate the
degree of polymerization of silicate slag, which can extend to the relevant physiochemistry
properties, such as density and chain dimensions (DP). The present methodology can be
extended to predict the other physicochemical properties of silicate melts for metallurgical
processes.
165
Chapter 7 : Experimental and modeling study of suspension system
7.1 Introduction
The dynamic viscosity of suspensions is of interest in many disciplines of engineering, such
as mechanical, chemical and civil engineering. The suspension viscosity ηsus primarily
depends on (1) the solid fraction, (2) shape and size of particles, (3) the suspending
Newtonian liquid, (4) Temperature, and (5) shear rate (for non-Newtonian suspension). There
is a research gap that the suspension viscosity was rarely studied in high-temperature region
and its correlation with room temperature data. It is known that the precipitation of solid
particles in molten slag was commonly observed in iron, steel, copper and other
pyrometallurgy process. Most of viscosity measurement assumed the full liquid slag system.
As literature review in the Section 2.5, limited viscosity study of molten slag was constructed.
With the assumption of suspension at 25 oC, the suspension viscosity model did not include
the temperature information, why may not suitable for the prediction at smelting temperature
(>1000 oC). It is necessary to explore and compare the suspension viscosity by the systematic
variation of the parameters at both room and smelting temperature conditions.
For the viscosity measurements at high temperature, the potential fault was caused from
obtaining the steady viscosity values and determination of the solid proportion. In Kondratiev
and Wu’s study, the solid proportion of molten slag was determined using software FactSage
prediction and Slag Atlas respectively [9, 213]. From the researches on phase equilibrium, the
experimental results demonstrated that both tools can’t provide an accurate prediction of
phase mixture at a high temperature, which may cause large deviation on the determination of
solid fraction. A reliable technique is required to obtain reliable viscosity values and the solid
proportion of solid/liquid mixtures.
The mathematical models of viscosity simulation were significant for both the fundamental
development and industrial application. Early on 1909, as Equation 7-1 shown, Einstein
proposed a mathematical expression to predict the suspension viscosity using liquid viscosity
and solid fraction f [173]. Thomas, Roscoe and other researchers continue on the
development of viscosity model through varying the mathematical expression of solid
fraction f, which extend the prediction range of different suspension system [173]165-175].
166
Equation 7-1 relative viscosity calculation
η𝑠𝑢𝑠
η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = f(𝑓)
Where η𝑠𝑢𝑠 is suspension viscosity in Pa.s, η𝑙𝑖𝑞 is the liquid viscosity in Pa.s, f is the solid
volume fraction in vol%
The present study aims to: 1) Experimentally measure the suspension viscosity at room and
smelting temperature using reliable techniques and 2) examine the applicability of the
existing models and optimize them if necessary.
7.2 Methodology
The viscosities of two-phase mixtures at both room and smelting temperatures were measured
by rotation spindle techniques. Two model series, LV III and HB III from Brookfield, were
utilized to cover the viscosity range 0-1 Pa.s and 0.6-20 Pa.s respectively. The Rheocalc
software on PC was utilized to control the rotation speed and record the torque readings.
The suspension viscosity was calculated using Equation 7-2 below. The equipment constant
K, a function of the spindle/crucible geometries and the rheometer, was determined using the
standard silicon oil (Brookfield product) with known viscosity.
Equation 7-2 Viscosity calculation
𝜂 = 𝐾τ
𝛺
Where η [Pa.s] is the viscosity of the suspension, τ [N.m-1
] is the torque at a certain rotation
speed Ω [m.s-1
], and K is the equipment constant. The K value was calculated through
calibration of standard silicon oil.
7.2.1 Calibration
The equipment constant K, a constant parameter of the spindle/crucible, was determined
through calibration of standard silicon oil from Brookfield Engineering. The standard silicon
oil is a liquid polymerized siloxane with a certain length of polydimethylsiloxane chain,
which determine the standard viscosity at 25 oC. From Brookfield Engineering, the physical
167
properties of silicon oil are shown in Table 7.1. In the present study, five standard silicon oil
were utilized for calibration, which covering the viscosity ranges from 0.05 to 1 Pa.s.
Table 7.1 Physical properties of silicon oil in present study
Silicon Oil Viscosity
(Pa.s)
Density
(kg/m3)
A 0.0498 965±4
B 0.098 965±4
C 0.21 968±4
D 0.498 968±4
E 1 968±4
In a general run, the crucible, spindle bob, and silicon oil were kept inside the water bath (25
oC) for 30 minutes to achieve homogeneous temperature condition. The rheometer will report
70 torque at the 3-second interval at 3 different rotational speed. The overall equipment
constant K was calculated using Equation 7-2 and accepted if the relative difference is within
1% from 5 standard silicon oil. The calibrated crucible, spindle, and rheometer were later
used in the room-temperature, and the devices for high-temperature viscosity study were re-
calibrated through the same procedure.
7.2.2 Viscosity Study of Suspension at Room Temperature
In the viscosity study at room temperature, the silicon oil and paraffin were employed to
simulate the molten slag liquid and precipitated minerals respectively. The standard silicon
oil with known viscosity at 25 oC was purchased from Brookfield Engineering. The piece of
paraffin was grinded to fine particles and sieved to three group sizes: <100, 100-200 μm and
200-300 μm. The impact of various parameters have been systematically investigated, which
include, 1) liquid viscosity, 2) solid fraction, 3) particle size and 4) temperature. The
experimental conditions were shown in Table 7.2 below.
Table 7.2: Experimental condition of viscosity measurement at room temperature
Run Silicon
Oil
Temperature
(oC)
Paraffin Solid Proportion
(vol %)
Paraffin
Size
168
(Pa.s) (μm)
1-3 0.05 10, 25, 40 0-32 (at 25 oC)
0-21 (at 10 and 40 oC)
100-200
4-8 0.1 10, 25, 40 0-32 (at 25 oC)
0-21 (at 10 and 40 oC)
<100
100-200
200-300
9-11 0.2 10, 25, 40 0-32 (at 25 oC)
0-21 (at 10 and 40 oC)
100-200
12-14 0.5 10, 25, 40 0-32 (at 25 oC)
0-21 (at 10 and 40 oC)
100-200
15-19 1 10, 25, 40 0-32 (at 25 oC)
0-21 (at 10 and 40 oC)
<100
100-200
200-300
The experimental setup is schematically shown in Figure 7.1. A crucible having an inner
diameter of 28 mm was used to hold the solution mixture. In a general run, the container with
silicon oil, paraffin particle, and spindle bob was kept inside the water bath for 30 minutes,
which allow the mixture achieve the designed temperature. The oil-paraffin mixtures were
stirred extensively by the spindle to ensure homogenization environment. During the
measurement, the Rheocale software from computer controlled and recorded the measured
torque readings at three different pre-set rotation speed. 70 values were taken at 3-second
interval at each rotation speed. The first part fluctuation values were ignored because the
solid dispersion did not achieve equilibrium. With the known equipment constant from the
calibration process, the viscosity value was calculated using Equation 7-2. The results were
averaged and calculated over the measurements of 3 different rotation speeds.
169
Figure 7.1 Schematic diagram of room temperature measurements
7.2.3 Viscosity Study of Suspension at Smelting Temperature
The experimental of high-temperature viscosity measurement include two parts: the first part
is to measure the suspension viscosity at designed temperature. Synchronously, the
equilibrium experiments were constructed to determine the phase information at the
temperature of solid appearing within the viscosity measurement. Electron probe X-ray
microanalysis (EPMA) was used for microstructural and elemental analyses of the quenched
samples, which can determine the accurate solid proportion and phase.
The equipment for high-temperature viscosity measurements and equilibrium experiments
were schematically shown in Figure 7.2 below. The features and description of the devices
have been introduced, by the present author in a previous publication. Two industrial slag
samples from blast furnace of Baosteel (BS slag) and JingTang (JT slag) were tested in the
present study.
170
Figure 7.2 Schematic diagram of (a) left, high-temperature viscosity measurement (b) right,
equilibrium experiments
7.3 Results
In the viscosity study of suspension, the effect of various parameters on the suspension
viscosity has been investigated. These parameters are:
Liquid viscosity & solid fraction
Particle diameter
Temperature
Shear rate
7.3.1 Room Temperature
All results were obtained by varying the shear rate (rotational speed) and measuring the
corresponding shear stress. These measurements have been constructed at the five species
standard silicon oil and three sizes of paraffin, which is displayed in Table 7.3. It has been
found that at low solid proportion, the suspension behavior as a Newtonian fluid, which
report the constant ratio of shear stress to rate. However, when the solid proportion increased
above 25%, the suspension deviated to shear thinning fluid, which was separately shown in
Table 7.4 at a different shear rate (rotational speed). The shear thinning fluid behavior would
be discussed in the later section.
171
Table 7.3. Viscosity measurements of suspension of solid proportion from 0-22 vol%
Viscosity (Pa.s) at different Solid Proportion (vol %)
ηLiq
(Pa.s)
D
(um)
T (oC) 0 2 5 7 10 12 15 17 20 22
0.05 100-200 10 0.0678 0.082 0.102 0.142 0.17
0.05 25 0.04975 0.053 0.06 0.067 0.076 0.089 0.101 0.121 0.141 0.16
0.05 40 0.03948 0.046 0.054 0.076 0.096
0.1 100-200 10 0.183 0.21 0.235 0.269 0.318
0.1 <100 25 0.0961 0.115 0.145 0.18 0.245
0.1 100-200 25 0.0961 0.102 0.117 0.13 0.145 0.167 0.199 0.223 0.266 0.298
0.1 200-300 25 0.0961 0.121 0.147 0.193 0.288
0.1 100-200 40 0.0727 0.085 0.107 0.146 0.215
0.2 100-200 10 0.259 0.312 0.357 0.537 0.63
0.2 25 0.192 0.207 0.235 0.255 0.276 0.325 0.381 0.451 0.53 0.59
172
0.2 40 0.148 0.177 0.23 0.302 0.432
0.5 100-200 10 0.653 0.776 1.043 1.38 1.91
0.5 25 0.484 0.525 0.601 0.683 0.796 0.877 0.994 1.15 1.39 1.57
0.5 40 0.386 0.461 0.598 0.812 1.226
1 100-200 10 1.72 2.03 2.77 4.8
1 <100 25 1.26 1.66 2.05 2.9
1 100-200 25 1.185 1.25 1.41 1.65 1.75 2.03 2.35 2.89 3.33
1 200-300 25 1.3 1.7 2.06 2.91
1 40 1.31 1.655 2.33 4.04
Table 7.4. Viscosity measurements of suspension of solid proportion from 25-32 vol %
Shear Stress (torque) at different rotational speed (rpm)
ηLiq
(Pa.s)
T
(oC)
26.5 vol% paraffin
Torque / rpm
29 vol% paraffin
Torque / rpm
32 % paraffin
Torque / rpm
173
0.05 25 44.6 / 75
59.4 / 100
71.1 / 125
85.2 / 150
98.1 / 175
Average viscosity = 0.179 Pa.s
34.4 / 50
51.7 / 75
65.8 / 100
83.9 / 125
97.6 / 150
Average viscosity = 0.207 Pa.s
41.5 / 50
62.2 / 75
80.9 / 100
98.8 / 125
Average viscosity = 0.25 Pa.s
0.1 25 48.8 / 30
53.32 / 35
62.2 / 40
70.1 / 45
78.9 / 50
Average viscosity = 0.345 Pa.s
62.3 / 150
72.7 / 175
82.1 / 200
89.4 / 225
95.8 / 250
Average viscosity = 0.415 Pa.s
58.4 / 125
70.1 / 150
77.6 / 175
86.4 / 200
95.1 / 225
Average viscosity = 0.49 Pa.s
0.2 25 53.32 / 150
62.2 / 175
70.1 / 200
78.9 / 225
53.32 / 150
62.2 / 175
70.1 / 200
78.9 / 225
53.32 / 150
62.2 / 175
70.1 / 200
78.9 / 225
174
86.9 / 250
Average viscosity = 0.71 Pa.s
86.9 / 250
Average viscosity = 0.81 Pa.s
86.9 / 250
Average viscosity = 1.03 Pa.s
0.5 25 38.7 / 20
48.4 / 25
57.1 / 30
65.7 / 35
74.5 / 40
83.1 / 45
90.32 / 50
Average viscosity = 1.86 Pa.s
50.9 / 20
63.67 / 25
73.4 / 30
85.1 / 35
95.4 / 40
Average viscosity = 2.14 Pa.s
16.1 / 5
32 / 10
48 / 15
64.1 / 20
79 / 25
89 / 30
Average viscosity = 2.56 Pa.s
1 25 53.32 / 150
62.2 / 175
70.1 / 200
78.9 / 225
86.9 / 250
Average viscosity = 3.89 Pa.s
53.32 / 150
62.2 / 175
70.1 / 200
78.9 / 225
86.9 / 250
Average viscosity = 4.53 Pa.s
53.32 / 150
62.2 / 175
70.1 / 200
78.9 / 225
86.9 / 250
Average viscosity = 5.32 Pa.s
175
7.3.2 Smelting Temperature
Figure 7.3 presents the viscosity of Baosteel slag and JingTang slag with a variation
of temperature ranging from 1575 to 1375 oC. The viscosity information and
elemental analysis from EPMA were summarized in Table 7.5. The solid fraction was
calculated using matrices method with a known composition. Both of the elemental
analysis results and viscosity increasing confirmed the solid precipitation when the
temperature reduced to 1400 oC. The solid proportions were calculated from the
composition of liquid (glass phase) and solid (melilite phase) by EPMA analysis. In
addition, the FactSage (version 6.2) and phase equilibrium chart (from Slag Atlas)
were utilized to compare the liquid and solid proportion and composition for these
two samples, which is quite different from the EPMA results.
The quantity of SiO2 content performs a critical role in the slag fluidity. At high
temperature, SiO2 from gangue mineral integrated with CaO, formed molten slag,
resulted in a good fluency of slag within blast furnace operation. As Figure 7.3 shown,
the viscosity of BS slag is slightly higher than JT slag (approximate 0.05 Pa.s) in the
full liquid region. The viscosity difference was enlarged as temperature decreasing,
because of SiO2. According to the elemental analysis from EPMA, in fully liquid slag,
BS slag has 2 wt% SiO2 higher than JT slag, which contributed to the higher viscosity.
When temperature decreased, the melilite precipitation of BS slag occurred at a higher
temperature than JT slag, which reports high solid fraction at the same temperature;
hence enlarge the viscosity difference. At the same temperature, according to the
results at Table 7.5, the solid proportion of BS slag is higher than JT slag, 20% > 10%
at 1400 and 40 %> 27 % at 1375 oC respectively. In the present study, it has found
that only small quantity of SiO2 will impact on the viscosity of both fully liquid slag
(1500oC) and solid containing slag (1400
oC), which can become a critical issue in the
low-temperature region of the smelting process.
Table 7.5. The elemental analysis of Baosteel and JingTang slag from EPMA analysis,
where the minor element include Na2O, K2O, FeO and etc
Slag Temperature
(oC)
Phase SiO2 CaO Al2O3 MgO Viscosity
(Pa.s)
176
JT 1400 Liquid 33.1 39.4 14.5 7.7 Bulk
Viscosity=
0.553
JT Solid
10 vol%
21.9 43 31.7 3.5
JT 1375 Liquid 33.1 38.8 13.3 8.4 Bulk
Viscosity=
0.746
JT Solid
27 vol%
28.9 42.5 24.4 4.3
BS 1400 Liquid 35.3 39.9 14.6 8 Bulk
Viscosity=
0.888
BS Solid
20 vol%
29.9 42.1 20.7 7.3
BS 1375 Liquid 37.3 39 9.7 10 Bulk
Viscosity=
1.226
BS Solid
40 vol%
28.9 41.8 24.7 4.5
Figure 7.3 The viscosity measurements of Baosteel and Jintang blast furnace slag
sample
177
7.3.3 Effect of liquid viscosity and solid fraction
It is accepted that the liquid viscosity and solid fraction are the two significant
parameters for the viscosity of suspensions. From the view of model simulation
(Einstein Model [9] Equation 7-3), it is expected that the relative viscosity has a
proportional positive correlation with solid fraction only and not dependent on the
liquid viscosity.
Figure 7.4 shows that the effect of liquid viscosity and solid fraction [f] on the relative
viscosity for particle diameters d=100-200 µm at 25 oC. From low (2 vol%) to high
(32 vol%) solid fraction, the relative viscosity of the suspension rapidly increased
upon to 5 times of the liquid viscosity. And, it can be noted that the deviations of
relative viscosity among different liquid viscosity is negligible at low solid fraction
range (0-15 vol%) and slightly increased to 5% at high solid fraction (15-32 vol%). It
indicated that the effect of liquid viscosity is not constant and raised as a solid
addition. At a high solid fraction, the liquid with large viscosity will momentarily
retain and accelerate the particles. This dissipation of energy will appear as “extra
viscosity”, which was observed in the torque measurements.
Equation 7-3 Einstein equation of relative viscosity
η𝑠𝑢𝑠
η𝑙𝑖𝑞= η𝑟𝑒𝑙𝑎 = (1 +
5
2𝑓)
178
Figure 7.4 The relative viscosity of oil-paraffin system at different solid fraction and
liquid viscosity at 25 oC
7.3.4 Effect of particle diameter
In the present study, the impact of particle diameter on solution viscosity was
investigated using three different sizes’ paraffin, which was <100 µm, 100-200 µm
and 200-300 µm. Figure 7.5 (a) and (b) demonstrate the viscosities of different
particle size group at low (0.1 Pa.s) and high (1 Pa.s) liquid viscosity condition
respectively. For suspensions based on a liquid with high viscosity (1 Pa.s), the effect
of particle size on the suspension viscosity is negligible, which reported only 0.5%
deviations. But for suspensions based on a liquid with low viscosity (0.1 Pa.s), a trend
can be observed that larger particle will generate a higher suspension viscosity. At 32
vol% solid fraction, the 200-300 and <100 µm reported 0.523 Pa.s and 0.48 Pa.s
respectively, which is approximately 8% deviations. In the low liquid viscosity
condition (0.1 Pa.s), the particles of greater size possess more inertia such that on
interaction with rotational bob, which will momently stop and accelerate during
rotation. This energy dissipation appears as “extra viscosity”. However, in the high
liquid viscosity condition (1 Pa.s), this inertia phenomenon occurred on all three sizes
paraffin because of the increment of liquid viscosity.
179
Figure 7.5 The suspension viscosity at different solid fraction and particle size at (a)
top, 0.1 Pa.s liquid viscosity and (b) bottom, 1 Pa.s liquid viscosity
7.3.5 Effect of Temperature
Temperature is another significant factor impacting on the viscosity, which was
encounter within the calculation of liquid viscosity. It is known that temperature has a
negatively proportional correlation with solution viscosity. When the temperature
increase, the liquid viscosity will decrease but did not impact on the expression of a
solid fraction under the assumption of thermal expansion of solid particle is negligible.
Therefore, the suspension viscosity will reduce as [ηsus]= [ηLiq]*[f], which is
confirmed by the viscosity measurements at room and steelmaking temperatures.
180
The Arrhenius type equation can express the temperature dependence of the slag
viscosity as Equation 7-4 shown, which was widely utilized in the model development
of liquid slag. In the present study, it has found that the applicable range of Arrhenius
type equation can be extended to the dilute suspension with a solid fraction from 0-15
vol% at different liquid viscosity. The suspension viscosity follows the correlation in
the form lnη = A +B
𝑇, where constants B are close for present paraffin/oil study. As
Figure 7.6 (b) shown, the temperature dependence of 15 vol% suspension was
confirmed at different liquid viscosity and Namburu’s viscosity study {Namburu,
2007 #1976}.
Equation 7-4 Arrhenius-type Equation
η = A ∗ e𝐵𝑇
Where η is the apparent viscosity Pa.s and T is the temperature K.
181
Figure 7.6 The temperature dependence on the oil-paraffin system suspension
viscosity (a) 0.05 liquid viscosity suspension at 5, 10, 15 and 20 vol% and (b) 15 vol%
suspension at liquid viscosity 0.05, 0.2 and 0.5 Pa.s by Wright [163]
7.3.6 Effect of Shear Rate
It is known that the viscosity of a fluid is correlated with the shear stress and shear
rate. Figure 7.7 (a) and (b) shows the shear rate has been investigated for a various
solid fraction and liquid viscosity. Figure 7.7 (a) compared that the shear rate
(rotational speed) of 5% solid fraction at different liquid viscosity suspension. As the
liquid viscosity increased, the suspension kept as Newtonian behavior. The R2 value
of 5% solid fraction at low viscosity suspension (0.05 Pa.s) and high viscosity liquid
suspension (1 Pa.s) is 0.998 and 0.999 respectively, which was the Newtonian fluid
behavior. The impact of liquid viscosity on fluid behavior is negligible.
When the solid fraction increased, it is found that fluid slightly shifts to shear thinning
behavior. Figure 7.7(b) compared that the shear rate of 0.1 Pas liquid viscosity
suspension at a different solid fraction (10%, 20%, and 30%). The results indicated
that at high solid proportion, the suspension slightly shifted to shear thinning solution,
which can be observed from R2=0.997 at 10% solid fraction to R
2=0.989 at 30% solid
fraction. This behavior was also observed in Wu’s viscosity study at above 15% solid
suspension system. The critical point transforming the Newtonian to non-Newtonian
fluid could not be accurately determined, because the boundary condition between
them is not quantitatively defined.
In Coussot’s study, he proposed that at high shear rates an increase of the suspension
viscosity could occur due to secondary flow, grain-inertia effects (i.e. momentum
transfer due to collisions between particles with fluctuating velocities or transition to
turbulence) [215]. This phenomenon was observed in section 3.3 and 3.4 as discussed
before. At high shear rates, the shear rate brought in additional rotational force and
may cancel the impact of “extra viscosity”, which cause decreasing of shear stress and
shift the fluid from Newtonian to shear-thinning type.
182
Figure 7.7 The measured torque at different rotational speed for (a) 5% solid fraction
at 0.05 and 1 Pa.s silicon oil. (b) 10, 20 and 30 % solid fraction at 0.5 Pa.s silicon oil
7.4 Model Simulation
7.4.1 Model Review and Evaluation
11 existing models were reviewed and evaluated in the present study using the
viscosity database at room temperature condition. Equation 7-5 is used to calculate
the difference between the measured and the calculated viscosity values.
183
Equation 7-5 error deviation calculation
1*
exp Calc
expn
Where Δ is the average deviation, exp is the experimental viscosity, Calc is the
calculated viscosity and n is the number of data.
Figure 7.8 (a) and (b) present the comparison of viscosity deviations of existing
models. Ranging from 0.05 to 5.5 Pa.s, the Kunitz model reported an outstanding
agreement with experimental data with 2.95% deviations [174]. Figure 7.8 (b) also
demonstrated that the Kunitz model fitted well with the experiment measurements
comparing to other models. The model prediction of 0-20% solid fraction fitted with
Happel model, which matches the conclusion of Wu. However, with the continues
addition of solid, the suspension viscosity will shift towards to the Kunitz prediction.
184
Figure 7.8 The model prediction vs experimental results at (a) top, different models
and (b) bottom, 1 Pa.s liquid viscosity
Figure 7.9 (a) and (b) present the predicted viscosities as functions of particle fraction
for JT and BS slag samples respectively. The prediction of high-temperature viscosity
involving two steps, which is the prediction of liquid viscosity and then suspension
viscosity. The liquid viscosity can be accurately determined using the existing Han
model, which report an outstanding agreement with slag viscosity ranging from 1450-
1600 oC as Figure 7.9 shown. The liquid viscosity of slag was re-calculated at
different liquid compositions of JT and BS slag as temperature decreasing. Then, the
information of solid fraction and liquid viscosity were utilized to calculate final
suspension viscosity by different models as Figure 7.9 shown. A comparison of the
experimental data with the model predictions evidently shows that Einstein model
reported an outstanding prediction performance in the present study.
As the model reviewed, Einstein model is applicable only to dilute sphere particles,
which is contracted to the known solid %. From EPMA analysis, the solid fraction at
1375 oC is 40 and 27 wt% for BS and JT slag respectively. The contradiction
indicated that there is a factor impacting on suspension viscosity, which wasn’t
considered. It is necessary to address the limitations of direct methods by further
model modifications.
185
Figure 7.9 The model prediction vs experimental results of (a) top JingTang slag and
(b) bottom, Baosteel slag
7.4.2 Model Optimization
The Kunitz model was investigated as a basement; due to its outstanding performance
for the viscosity measurements at room temperature. As Table 7.6 shown, Kunitz
model includes two parts: 1) the numerator (1+0.5f) and 2) the denominator (1-f)4,
where f is the solid fraction.
The numerator (1+0.5f) is derived from the velocity gradient equation by considering
the perturbation in the flow field due to the presence of a continuously decreasing
number of particles per unit volume. Thomas pointed out that the (1+0.5f) expression,
186
which is derived from Einstein study, only applicable to the dilute suspension system.
With concentrated suspensions, it is necessary to account for the hydrodynamic
interaction of particles, particle rotation, collision and higher order agglomerate
formation. The parameter 0.5 can only utilize when the solid spheres with diameter
large compared to liquid molecule dimensions, which is suitable for the present study.
Many of the existing theoretical and experimental equations can be expressed as a
power series as Equation 7-6 shown. Present study continues to use 0.5 for the
coefficient k1, because of outstanding prediction performance from Kunitz model.
After accounting for the hydrodynamic interaction of spheres, the coefficient ranges
from -2.3 to 50 to the value of k2 from different authors. The coefficients of various
combinations of terms in Equation 7-5 were determined using a nonlinear least
squares procedure by minimizing the deviations, which report k2=1.
Equation 7-6 relative viscosity calculation
η𝑟𝑒𝑙𝑎 = (1 + 𝑘1𝑓 + 𝑘2𝑓2 + 𝑘3𝑓3 + ⋯ 𝑘𝑛𝑓n)
The denominator is (1-f)4 is an argued mathematical expression, which was derived
from the integral under the condition of consistently irregular distribution of
dispersing particles. Einstein, Toda, and Kunitz proposed the index parameter as 2, 3
and 4 respectively. The index 2, 3 and 4 was derived from the dispersion energy
calculation. With the solid fraction increased, the index parameters step wisely
increased from 2 to 4, which reflects suspension changing from smooth to rigid
structure because of the high solid fraction. This phenomenon was also approved in
the present study in previous sections. The suspension with large liquid viscosity
reported a higher relative viscosity than a suspension with low liquid viscosity as the
mixing behaviors changed when solid fraction and liquid viscosity increased. At room
temperature condition, the index parameter is 4, which demonstrate an outstanding
prediction performance.
At high-temperature condition, it is widely accepted that the liquid molecular is more
violent, which can be observed from the viscosity decreasing. Wilson reported that the
relation between temperature and excess energy of mixing was smoothed to the
187
temperatures for the mixtures by plotting against the temperature in the liquid/gas
interface. Although, the mixing behavior could not be directly observed at the high-
temperature condition. It can be estimated that the mixing behaviors are smooth
structure due to the excess energy of mixing. Therefore, the index parameter should
decrease stepwise decreased as temperature increasing. In the present study, for
different temperature range, from 10-50 oC and 1300-1500
oC, the index parameter
was and 1.8 respectively. Overall, the mathematical expression of Kunitz model was
optimized for different temperature range and a solid fraction as Table 7.6 shown.
Table 7.6. Summary of optimized model
Old Kunitz Equation Room Temperature Steelmaking Temperature
η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓
(1 − f)4
η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓 + 𝑓2
(1 − f)4
η𝑟𝑒𝑙𝑎 =1 + 0.5𝑓 + 𝑓2
(1 − f)𝑥
Where x is 1.8 for 1400 oC
suspension viscosity, will
decrease if temperature
increase and vice versa
As Figure 7.10 shown, the optimized model demonstrated an outstanding agreement
with experimental data of the present study, Wu, and Wright at both temperature
ranges [9, 163]. It indicated that the viscosity estimation should be divided into two
temperature ranges because of different mixing behaviors.
188
Figure 7.10 The comparison between experimental data and model predictions by
Wright [163] and Wu [9]
7.4.3 Model Application
The modified model has shown superior prediction performance on the silicon
oil/paraffin and two industrial slags systems for a range of viscosity between 0.05 Pa.s
to 5 Pa.s. A further application would be considered on the suspension viscosity on a
wider viscosity temperature range of other disciplines of engineering. At room
temperature condition, as Figure 7.11 shown, the present model is capable of
predicting the suspension viscosity ranging from 0.005 Pa.s to 200 Pa.s. At high
temperature, it can be noted that, under the condition of minimizing deviations, the
index parameter is 3.8 and 1.7 for Louise and Wright respectively [162, 163]. It again
approved the conclusion that the index parameter is decreased from 4 when
189
temperature increased upon 25 oC. Further study is required for the correlation
between temperature and energy of dispersion terms.
Figure 7.11 The comparison of model prediction and other researchers results at (a)
room temperature by Chong [153] and Namburu [160], (b) high temperature by
Louise [159] and Wright [163]
190
7.5 Conclusion
In summary, the experiments at both room temperature and steelmaking temperature
were carried out to study the effect of the presence of solid particles in liquid on
viscosity. Five silicon oil with different viscosities and paraffin particles were
employed to simulate the molten slag condition and confirm the impact of (a) liquid
viscosity, (b) solid fraction, (c) particle diameter, (d) temperature and (e) shear rate on
the suspension viscosity. The viscosities of two industrial slags were determined to
range from 1375 to 1575 oC. It has been found, at either high liquid viscosity
condition or large particle size condition, the particles are momentarily retarded and
then accelerated. Their inertia affects the amount of energy required. This dissipation
of energy appears as “extra viscosity”. The two-phase mixtures slightly deviated from
Newtonian fluid to shear thinning fluid when the particle fraction above 25 wt%.
In the present study, 11 existing viscosity models were reviewed, which use the
different mathematical equation to determine the nrela. While the experimentally
determined viscosities were agreed well by Kunitz model in the room temperature
results, which was optimized to covering concentrated suspension at the high-
temperature condition. The coefficient of the numerator (1+0.5f) was re-optimized to
(1+0.5f+f2) by accounting the hydrodynamic interaction of particles. The index of the
denominator (1-f)4 is 4 at room temperature, and stepwise decreased as temperature
increasing due to the excess energy of mixing. The optimized model demonstrated an
outstanding prediction performance covering the viscosity range from 0.005 Pa.s to
200 Pa.s at different temperatures (room-1500 oC). Further study is required for the
correlation between temperature and energy of dispersion terms.
191
Chapter 8 : Conclusions
There is an increasing focus on process optimization and energy usage efficiency of
blast furnace ironmaking. During the operation, slag viscosity plays a significant role
in controlling the process, which has a direct impact on the metal/slag efficiency. In
the present study, the viscosity of blast furnace slag relevant to ironmaking process
was systematically investigated. A comprehensive literature review has been
constructed covering the fundamentals of the viscosity theory, experimental data and
mathematical models on the CaO-MgO-Al2O3-SiO2, its binary and ternary system.
Due to uncertainty, the viscosity measurements of the CaO-MgO-Al2O3-SiO2 system
were critically evaluated following the three steps: 1 Experimental techniques, 2 Data
consistency, and 3 Cross-reference comparison. In addition, the viscosity
measurements of minor elements’ impact on molten slag were reviewed. The structure
of silicate melts (glass phase) were reviewed using different characterization
techniques. The viscosity behavior of solid impact on molten slag was investigated to
fully understand and control the slag fluidity in blast furnace operation.
The following list represents the work that has been completed by the present Ph.D.
candidate:
1. Review and evaluated the experimental methodologies, viscosity data, and models
relevant to the blast furnace slag in CaO-MgO-Al2O3-SiO2 system (Chapter 2)
2. Based on the collected data and models, an accurate viscosity model has been
developed to predict the viscosity of blast furnace slag in CaO-MgO-Al2O3-SiO2
system (Chapter 4-5)
3. Research on the viscosity impact of minor elements on the blast furnace final slag
in CaO-MgO-Al2O3-SiO2 based system. (Chapter 4-5)
4. Quantitative investigation of the microstructural units of silicate slag utilizing
Raman spectroscopy. (Chapter 6)
5. Investigation of the solid phase impact on the viscosity of liquid slag. (Chapter 7)
192
Chapter 9 : Reference
[1] AK.Biswas, "Principles of Blast Furnace Ironmaking", Coothea Publishing House,
Brisbane, Australia, 1981
[2] R. Benesch, R. Kopec, A. Ledzki, JB. Guillot and W. Zymla: "The physico-
chemical properties of the blast furnace slags with TiO2 addition", Archives of
metallurgy, 1996, vol. 41, pp. 15-24.
[3] V.D. Eisenhüttenleute: "Slag Atlas", Verlag Stahleisen, 1995
[4] T.S. Kim and J.H. Park: "Structure-viscosity relationship of low-silica calcium
aluminosilicate melts", ISIJ International, 2014, vol. 54, pp. 2031-2038.
[5] B.Y. Guo, P. Zulli, D. Maldonado and A.B. Yu: "A model to simulate titanium
behavior in the iron blast furnace hearth", Metallurgical and Materials Transactions
B, 2010, vol. 41B, pp. 876-885.
[6] G. Astarita and G. Marrucci: "Principles of non-Newtonian fluid mechanics",
McGraw-Hill, London, 1974,
[7] N.Platzer: "Non-Newtonian flow and heat transfer", New York, 1966
[8] R.P. Chhabra: "Bubbles, drops, and particles in non-Newtonian fluids", Indian
Institue of Technology Kanpur, India, 2nd
edition, 2006
[9] L. Wu, M. Ek, M. Song and D. Sichen: "The effect of solid particles on liquid
viscosity", Steel Research International, 2011, vol. 82, pp. 388-397.
[10] A. Tanaka, H. Ohkubo and M. Takahashi: "Study on fluidity of liquid-solid
mixtures - measurements of effective viscosity", Nippon Netsubussei Gakkai, 2007
[11] E.F. Riebling: "Improved counterbalanced sphere viscometer for use to 1750 oC",
Review of Scientific Instruments, 1963, vol. 34, pp. 568-572.
[12] T. Saito and Y. Kawai: "The viscosities of molten slags I: Viscosities of lime,
silica, alumina slags", Science Reports Research Ubstutytes, Tohoku University, Ser.
A, 1951, vol. 3, pp. 491-501.
[13] M. Chen, S. Raghunath and B.J. Zhao: "Viscosity measurements of "FeO"-SiO2
slag in equilibrium with metallic Fe", Metallurgical and Materials Transactions B,
2013, vol. 44, pp. 506-515.
[14] K.C. Mills: "Viscosities of molten slags", National Physical Laboratory, pp. 116-
118
[15] R. Brooks, A. Dinsdale and P. Quested: "The measurement of viscosity of alloys-
areview of methods, data and models", Measurement science and technology, 2005,
vol. 16, pp. 354.
[16] M.J. Assael, K. Kakosimos, R.M. Banish, J. Brillo, I. Egry, R. Brooks, P.N.
Quested, K.C. Mills, A. Nagashima and Y. Sato: "Reference data for the density and
viscosity of liquid aluminum and liquid iron", Journal of physical and chemical
reference data, 2006, vol. 35, pp. 285-300.
[17] S.H. Maron, I.M. Krieger and A.W. Sisko: "A capillary viscometer with
continuously varying pressure head", Journal of Applied Physics, 1954, vol. 25, pp.
971-976.
193
[18] S.H. Sheen, W.P. Lawrence, H.T. Chien and A.C. Raptis: "Method for measuring
liquid viscosity and ultrasonic viscometer", Google Patents, 1994
[19] A.S. Reddy, R. Pradhan and S. Chandra: "Utilization of basic oxygen furnace
(BOF) slag in the production of a hydraulic cement binder", International journal of
mineral processing, 2006, vol. 79, pp. 98-105.
[20] A. Brough and A. Atkinson: "Sodium silicate-based, alkali-activated slag mortars:
Part I. Strength, hydration and microstructure", Cement and Concrete Research, 2002,
vol. 32, pp. 865-879.
[21] L. Forsbacka, L. Holappa, T. Iida, Y. Kita and Y. Toda: "Experimental study of
viscosities of selected CaO-MgO-Al2O3-SiO2 slags and application of the Iida model",
Scandinavian journal of metallurgy, 2003, vol. 32, pp. 273-280.
[22] E.E. Hofmann: "Dependence of the viscosity of synthetic slags on composition
and temperature", Stahl und Eisen, 1959, vol. 79, pp. 846-853.
[23] G. Hofmaier: Berg und Huttenm. Monatsh. Montan. Hochschule in Loeben, 1968,
vol. 113, pp. 270-281.
[24] F. Johannsen and H. Brunion: "Untersuchungen zur viskositat von rennschlaken",
Zeitschrift fur Erzbergbau und Metallhutten-Wesen, 1959, vol. 12, pp. 272-279.
[25] T. Koshida, T. Ogasawara and H. Kishidaka: "Viscosity, surface tension, and
density of blast furnace slag and synthetic slags at manufacturing condition of hard
granulated slag", Tetsu to Hagane, 1981, vol. 67, pp. 1491-1497.
[26] M. Nakamoto, T. Tanaka, J. Lee and T. Usui: "Evaluation of viscosity of molten
SiO2-CaO-MgO-Al2O3 slags in blast furnace operation", ISIJ International, 2004, vol.
44, pp. 2115-2119.
[27] Y. Kita, A. Handa and T. Iida: "Measurements and calculations of viscosities of
blast furnace type slags", Journal of High Temperature Society of Japan(Japan), 2001,
vol. 27, pp. 144-150.
[28] C. Merlet and X. Llovet: "Uncertainty and capability of quantitative EPMA at
low voltage–A review", 2012, IOP Conference Series: Materials Science and
Engineering, vol. 32, pp. 12-16.
[29] GH. Zhang, K. Chou and X. Lv: "Influences of different components on
viscosities of CaO-MgO-Al2O3-SiO2 melts", Journal of Mining and Metallurgy,
Section B: Metallurgy, 2014, vol. 50, pp. 157-164.
[30] YM. Gao, SB. Wang, C. Hong, XJ. Ma and F. Yang: "Effects of basicity and
MmgO content on the viscosity of the SiO2-CaO-MgO-9wt%Al2O3 slag system",
International Journal of Minerals, Metallurgy, and Materials, 2014, vol. 21, pp. 353-
362.
[31] N.M. Piatak, M.B. Parsons and R.R. Seal: "Characteristics and environmental
aspects of slag: A review", Applied Geochemistry, 2015, vol. 57, pp. 236-266.
[32] A. Shankar, M. Görnerup, A.K. Lahiri and S. Seetharaman: "Experimental
investigation of the viscosities in CaO-SiO2-MgO-Al2O3 and CaO-SiO2-MgO-Al2O3-
TiO2 slags", Metallurgical and Materials Transactions B, 2007, vol. 38, pp. 911-915.
194
[33] G.H. Kim, C.S. Kim and I. Sohn: "Viscous behavior of alumina rich calcium-
silicate based mold fluxes and its correlation to the melt structure", ISIJ International,
2013, vol. 53, pp. 170-176.
[34] J. Liao, Y. Zhang, S. Sridhar, X. Wang, Z. Zhang, Y. Gao, H.G. Kim, H.Y. Sohn
and C.W. Kim: "Effect of Al2O3/SiO2 ratio on the viscosity and structure of slags",
ISIJ international, 2012, vol. 52, pp. 753-758.
[35] H. Kim, H. Matsuura, F. Tsukihashi, W. Wang, D.J. Min and I. Sohn: "Effect of
Al2O3 and CaO/SiO2 on the viscosity of calcium-silicate-based slags containing 10
mass% MgO", Metallurgical and Materials Transactions B, 2012, vol. 44, pp. 5-12.
[36] A.M. Lejeune and P. Richet: "Rheology of crystal-bearing silicate melts: an
experimental study at high viscosities", Journal of Geophysical Research: Solid Earth,
1995, vol. 100, pp. 4215-4229.
[37] R.A. Vaia, K.D. Jandt, E.J. Kramer and E.P. Giannelis: "Microstructural
evolution of melt intercalated polymer-organically modified layered silicates
nanocomposites", Chemistry of Materials, 1996, vol. 8, pp. 2628-2635.
[38] F. Galeener: "Planar rings in glasses", Solid State Communications, 1982, vol. 44,
pp. 1037-1040.
[39]. P. McMillan, "Structural studies of silicate glasses and melts-applications and
limitations of Raman spectroscopy", American Mineralogist, 1984, 69 (7-8), pp. 622-
644
[40]. I. Lecomte., C. Henrist, M. Liegeois, F. Maseri, A. Rulmont and R. Cloots,
"(Micro)-structural comparison between geopolymers, alkali-activated slag cement
and Portland cement", Journal of the European Ceramic Society, 2006, 26 (16), pp.
3789-3797
[41]. J.H.Park, "Structure-Property Relationship of CaO-MgO-SiO2 Slag:
Quantitative Analysis of Raman Spectra", Metallurgy and Material Transaction B,
2013, 44 (4), pp. 938-947
[42] Y. Iguchi, S. Kashio, T. Goto, Y. Nishina and T. Fuwa: "Raman spectroscopic
study on the structure of silicate slags", Canadian metallurgical quarterly, 1981, vol.
20, pp. 51-56.
[43] W. Mueller, M. Haehnert, P. Reich and K.W. Brzezinka: "Raman spectroscopic
investigation of glasses of the system calcia/alumina/silica", Crystal research
technology, 1983, vol. 18, pp. K49-K52.
[44]. D. Papanastassiou and A. Send, "Operational and environmental benefits by
using bauxite in blast furnace (BF)", Ironmaking Conf. Proc., 1998, 57, pp. 1671-
1676
[45] W.L. Konijnendijk and J.M. Buster: "Raman-scattering measurements of arsenic-
containing oxide glasses", Journal of Non-Crystal Solids, 1975, vol. 17, pp. 293-297.
[46] J.D. Frantz and B.O. Mysen: "Raman spectra and structure of BaO-SiO2, SrO-
SiO2 and CaO-SiO2 melts to 1600 oC", Chemical Geology, 1995, vol. 121, pp. 155-
176.
[47] R. J. Hemley, P. M. Bell and B. O. Mysen: "Raman spectroscopy of SiO2 glass at
high pressure", Physical review letters, 1986, vol. 57, pp. 747-750.
195
[48] Š. Peškova, V. Machovič and P. Prochazka: "Raman spectroscopy structural
study of fired concrete", Ceramics–Silikáty, 2011, vol. 55, pp. 410-417.
[49] R. Mozzi and A. Paladino: "Cation distributions in nonstoichiometric magnesium
ferrite", The Journal of Chemical Physics, 1963, vol. 39, pp. 435-439.
[50] Y. Waseda and J.M. Toguri: "Structure of silicate melts determined by X-ray
diffraction", Dynamic Processes of Material Transport and Transformation in the
Earth’s Interior, Terra Scientific, Tokyo, 1990, vol. 37-51.
[51] H. Maekawa, T. Maekawa, K. Kawamura and T. Yokokawa: "The structural
groups of alkali silicate glasses determined from 29Si MAS-NMR", Journal of Non-
Crystalline Solids, 1991, vol. 127, pp. 53-64.
[52] H. Kim, W.H. Kim, J.H. Park and D.J. Min: "A study on the effect of Na2O on
the viscosity for ironmaking slags", Steel research international, 2010, vol. 81, pp.
17-24.
[53] C. Masson, I. Smith and S. Whiteway: "Molecular size distributions in
multichain polymers: application of polymer theory to silicate melts", Canadian
Journal of Chemistry, 1970, vol. 48, pp. 201-202.
[54] J.O.M. Bockris, J. Mackenzie and J. Kitchener: "Viscous flow in silica and
binary liquid silicates", Transactions of the Faraday Society, 1955, vol. 51, pp. 1734-
1748.
[55] P. Kozakevitch: "Tension superficielle et viscosité des scories synthétiques",
Review Metallurgy, 1949, vol. 46, pp. 505-516.
[56] T. Licko and V. Danek: "Viscosity and structure of melts in the system CaO-
MgO-SiO2", Physics and chemistry of glasses, 1986, vol. 27, pp. 22-26.
[57] G. Urbain, Y. Bottinga and P. Richet: "Viscosity of liquid silica, silicate and
alumino-silicates", Geochimica et Cosmochimica Acta, 1982, vol. 46, pp. 1061-1072.
[58] V.P. Elyutin, V.I. Kostikovm, B.C. Mitin and Y.A. Nagibin: "Viscosity of
alumina", Russian Journal of Physical Chemistry A, 1969, vol. 43, pp. 579-583.
[59] P. Kozakevitch: "Viscosite et elements structuraux des aluminosilicates fondus:
laitiers CaO-Al2O3-SiO2 entre 1600 et 2100 oC", Review Metallurgy, 1960, vol. 57, pp.
149-160.
[60] G. Urbain: "Viscosity of silicate mlets: measure and estimate", Journal of
materials education, 1985, vol. 7, pp. 1007-1078.
[61] G. Hofmaier and G. Urbain: "The viscosity of pure silica", Journal of ceramic
science, 1968, vol. 4, pp. 25-32.
[62] N. Saito, N. Hori, K. Nakashima and K. Mori: "Effect of additive oxides on the
viscosities of CaO-SiO2-Al2O3 and CaO-Fe2O3 melts", High Temperature Materials
and Processes, London, United Kingdom, 2003, vol. 22, pp. 129-139.
[63] S.P. Leiba and E.P. Komar: "Viscosity of synthetic slags of ternary systems CaO-
FeO-SiO2 and MnO-FeO-SiO2 to which are added chromium oxide, magnesium oxide
and liquifiers", Soveshchanie po Vyazkosti Zhidkostei., 1941, vol. 3, pp. 32-56.
[64] P.M. Bills: "Viscosities in silicate slag systems", Journal of Iron Steel Instituent,
1963, vol. 201, pp. 133-140.
196
[65] I.I.Z. Gul'tyai, N.L. Sokolov and G. A. Tsylev: "Effect of magnesium on physical
properties of blast furnace slgas", Izvestiya Akademii Nauk SSSR, Metallurgiya I
Toplivo, 1959, vol. 20-24.
[66] F. Johannsen and H. Brunion: "Studies for the viscosity of Rennschlaken",
Zeitschrift fur Erzbergbau und Metallhutten-Wesen, 1959, vol. 12, pp. 211-210.
[67] M. Kato and S. Minowa: "Viscosity measurements of molten slag. Properties of
slag at elevated temperature (Part I).", Transactions of the Iron and Steel Institute of
Japan, 1969, vol. 9, pp. 31-38.
[68] J.S. Machin and D.L. Hanna: "Viscosity Studies of System CaO–MgO–Al2O3–
SiO2: I, 40% SiO2", Journal of the American Ceramic Society, 1945, vol. 28, pp. 310-
316.
[69] R. Rossin, J. Bersan and G. Urbain: "Etude de la viscosite de laitiers liquides
appartenant au systeme ternaire: SiO2-Al2O3-CaO", Rev. Hautes Temper. Refract,
1964, vol. 1, pp. 159-170.
[70] C. Scarfe, D. Cronin, J. Wenzel and D. Kauffman: "Viscosity-temperature
relationships at 1 atm in the system diopside-anorthite", American Mineralogist, 1983,
vol. 68, pp. 1083-1088.
[71] M. Solvang, Y. Yue, S.L. Jensen and D.B. Dingwell: "Rheological and
thermodynamic behaviors of different calcium aluminosilicate melts with the same
non-bridging oxygen content", Journal of Non-Crystalline Solids, 2004, vol. 336, pp.
179-188.
[72] H. Taniguchi:"Entropy dependence of viscosity and the glass-transition
temperature of melts in the system diopside-anorthite", Contributions to Mineralogy
and Petrology, 1992, vol. 109, pp. 295-303.
[73] R. Lyutikov, L and Tsylev: "Viscosity and Electrical Conductivity of Magnesia-
Silica-Alumina Melts", Izv. AN SSSR, Metallurgiya i gornoye delo, 1963, vol. 41-52.
[74] J.S. Machin, T.B. Yee and D.L. Hanna: "Viscosity Studies of System CaO–
MgO–Al2O3–SiO2: III, 35, 45, and 50% SiO2", Journal of the American Ceramic
Society, 1952, vol. 35, pp. 322-325.
[75]K. Mizoguchi, K. Okamoto and Y. Suginohara: "Oxygen Coordination of Al3+
ion in Several Silicate Melts Studied by Viscosity Measurements", Journal of the
Japan Institute of Metals, 1982, vol. 46, pp. 1055-1060.
[76]E. Riebling: "Structure of Molten Oxides. I. Viscosity of GeO2, and Binary
Germanates Containing Li2O, Na2O, K2O, and Rb2O", The Journal of Chemical
Physics, 1963, vol. 39, pp. 1889-1895.
[77]M.J. Toplis and D.B. Dingwell: "Shear viscosities of CaO-Al2O3-SiO2 and MgO-
Al2O3-SiO2 liquids: Implications for the structural role of aluminium and the degree
of polymerisation of synthetic and natural aluminosilicate melts", Geochimica et
Cosmochimica Acta, 2004, vol. 68, pp. 5169-5188.
[78]N.L. Zhilo and L.M. Tsylev: "The viscosity of primary and final slags in the
ferroalloys smelting in blast furnaces", Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, 1955,
vol. 1, pp. 90-106.
197
[79] Y. Kawai: "On the viscosities of molten slags. II. Viscosities of CaO-SiO2-
Al2O3-MgO slags", The science reports of the Research Institutes, Tohoku University.
Series A, Physics,, 1952, vol. A, pp. 615-621.
[80] J.S. Machin, "Viscosity Studies of System CaO–MgO–Al2O3–SiO2: IV, 60 and
65% SiO2", Journal of the American Ceramic Society, 1954, vol. 37, pp. 177-186.
[81] F. Johannsen and W. Weize: "The settling of copper stone and copper slag in
liquid", Z. Erz. u. Metal., 1958, vol. 11, pp. 1-15.
[82] E.E. Hofmann: "Die Bedeutung eines Betriebsviskosimeters mit
Temperaturanzeige für die überwachung von Schmelzvorgängen", Berg-und
hüttenmännische monatshefte, 1959, vol. 106, pp. 397-407.
[83] I. Gul’tyai: "Effect of Al2O3 on the viscosity of slags of the system CaO–MgO–
SiO2", Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, Metall. Toplivo, 1962, vol. 5, pp. 52-
65.
[84] G.P. Vyatkin, N.L. Ostroukhov and M.Ya: "Viscosity of high magnesium blast
furnace slags with 10 and 20 % FeO", Izvestiya Vysshikh Uchebnykh Zavedenii.
Chernaya Metallurgia., 1962, vol. 5, pp. 2939-2943.
[85] K. Kodama, A. Shigemi, T. Horio and R. Takahashi: "Viscosity and fluidity of
high-alumina slag", Tetsu to Hagane, 1963, vol. 49, pp. 1869-1873.
[86] L.N. Sheludyakov, E.T. Sarancha and A.A. Vakhitov: "Viscosity of
aluminosilicate melts of the MxOy-alumina-silica system", Tr. Inst. Khim. Nauk,
Akad. Nauk Kaz. SSR, 1967, vol. 15, pp. 158-163.
[87] V.K. Gupta and V. Seshadri: "Viscosity of high alumina blast furnace slags",
Transactions of the Indian Institute of Metals, 1973, vol. 26, pp. 55-64.
[88] A.I. Tsybulnikov, G.A. Toporishchev, G.A. Vachugov, E.D. Mokhir and V.V.
Vetysheva: "Vyazkost' i rafiniruyushchaya sposobnost' izvestkovo-glinozemistykh
slakov.", Izvestiya Vysshikh Uchebnykh Zavedenii. Chernaya Metallurgia, 1973, vol.
2, pp. 5-9.
[89] A.M. Yakushev, V.M. Romashin and V.A. Amfiteatrov: " Vyazkost' shlakov na
osnove CaO s peremennym soderzhaniem Al2O3, SiO2, MgO", Izvestiya Vysshikh
Uchebnykh Zavedenii. Chernaya Metallurgia, 1977, vol. 55-58.
[90] U. Mishra, B. Thakur and M. Thakur: "Investigation on Viscosity of very high
Alumina Slags for Blast Furnace", SEAISI Quarterly, 1994, vol. 23, pp. 72-82.
[91] Y.J. Lee and S.H. Yi: "Viscosities of CaO-MgO-SiO2-Al2O3 slag systems in a
melter-gasifier", Taehan Kumsok Hakhoechi, 1997, vol. 35, pp. 1047-1051.
[92] S.H. Kim and J.D. Seo: "Slag viscosity and its wettability with respect to
graphite", Iron & Steelmaker, 1999, vol. 26, pp. 51-57.
[93] J.W. Han, E.H. Kwon, S.S. Han, J.H. Chi, B.S. Kim and J.C. Lee: "Effect of
viscosity on the separation of copper from Al2O3-CaO-SiO2-10 wt.% MgO slag
system", Materials Science Forum, 2003, vol. 439, pp. 149-155.
[94] J.R. Kim, Y.S. Lee and D.J. Min: "Effect of MgO and Al2O3 on the viscosity of
CaO-SiO2-Al2O3-MgO-FeO slag", ISSTech. Conference, Indianapolis, USA, 2003, pp.
515-526.
198
[95] N. Saito, N. Hori, K. Nakashima and K. Mori: "Viscosity of blast furnace type
slags", Metallurgy and Materials Transactions B, 2003, vol. 34B, pp. 509-516.
[96] J.R. Kim, Y.S. Lee, D.J. Min, S.M. Jung and S.H. Yi: "Influence of MgO and
Al2O3 contents on viscosity of blast furnace type slags containing FeO", ISIJ
International, 2004, vol. 44, pp. 1291-1297.
[97] J.H. Park and D.J. Min: "Effect of fluorspar and alumina on the viscous flow of
calcium silicate melts containing MgO", Journal of Non-Crystalline Solids, 2004, vol.
337, pp. 150-156.
[98] A.M. Yakushev and L.A. Golubev: "Viscosities of CaO-based CaO-Al2O3-SiO2-
MgO system slags", Izvestiya Vysshikh Uchebnykh Zavedenii, Chernaya Metallurgiya,
2006, pp. 9-11.
[99] X.L. Tang, Z.T. Zhang, M. Guo, M. Zhang and X.D. Wang: "Viscosities
Behavior of CaO-SiO2-MgO-Al2O3 Slag With Low Mass Ratio of CaO to SiO2 and
Wide Range of Al2O3 Content" Journal of Iron and Steel Research, International,
2011, vol. 18, pp. 1-17.
[100] A.M. Muratov and I.S. Kulikov: "Viscosity of the melts of the system SiO2-
Al2O3-CaO-MgO-CaS", Izvestiya Akademii Nauk SSSR. Metally., 1965, pp. 57-62.
[101] J.H. Park, D.J. Min and H.S. Song: "Amphoteric behavior of alumina in viscous
flow and structure of CaO-SiO2(-MgO)-Al2O3 slags", Metallurgical and Materials
Transactions B, 2004, vol. 35B, pp. 269-275.
[102] S.H. Kim and J.D. Seo: "Slag viscosity and its wettability with respect to
graphite", Iron & steelmaker, 1999, vol. 26, pp. 51-57.
[103] J.R. Kim, Y.S. Lee and D.J. Min: "Effect of MgO and Al2O3 on the viscosity of
CaO-SiO2-Al2O3-MgO-FeO slag", 2003, ISSTech. Conference, Indianapolis, USA, pp.
515-526.
[104] G.R. Li: "Effect of strong basic oxide (Li2O, Na2O, K2O and BaO) on property
of CaO-based flux", Journal of Iron Steel Research International, 2003, vol. 10, pp.
6-9.
[105] Y.S. Lee, D.J. Min, S.M. Jung and S.H. Yi: "Influence of basicity and FeO
content on viscosity of blast furnace type slags containing FeO", ISIJ International,
2004, vol. 44, pp. 1283-1290.
[106] H. Park, J.Y. Park, G.H. Kim and I. Sohn: "Effect of TiO2 on the Viscosity and
Slag Structure in Blast Furnace Type Slags", Steel research international, 2012, vol.
83, pp. 150-156.
[107] M. Song, Q. Shu and D. Sichen: "Viscosities of the Quaternary Al2O3-CaO-
MgO-SiO2 Slags", Steel Research International, 2011, vol. 82, pp. 260-268.
[108] L.N. Sheludyakov, S.S. Nurkeev, E.T. Izotova, M.M. Kospanov and A.R.
Sabitov: "Viscosity of homogeneous melts of calcium oxide-aluminium oxide-silicon
dioxide-ferrous oxide and calcium oxide-aluminium oxide-silicon dioxide-ferrous
oxide-magnesium oxide systems", Comprehensive utilization of mineral resources,
1983, vol. 62-65.
[109] W.H. Zachariasen: "The atomic arrangement in glass", Journal of the American
Chemical Society, 1932, vol. 54, pp. 3841-3851.
199
[110] I. Sohn and D.J. Min: "A Review of the Relationship between Viscosity and the
Structure of Calcium ‐ Silicate ‐ Based Slags in Ironmaking", Steel Research
International, 2012, vol. 83, pp. 611-630.
[111] J.M. Bockris, J. Tomlinson and J. White: "The structure of the liquid silicates:
partial molar volumes and expansivities", Transactions of the Faraday Society, 1956,
vol. 52, pp. 299-310.
[112] K. Tang and M. Tangstad: "Modeling Viscosities of Ferromanganese Slags",
Communicated to INFACON XI, 2007, pp. 345-357
[113] M. Naito: "Development of Ironmaking Technology", Nippon Steel Technical
Report, 2006, vol. 94, pp. 1-15.
[114] F.Z. Ji, D. Sichen and S. Seetharaman: "Experimental studies of the viscosities
in the CaO-FenO-SiO2 slags", Metallurgical and Materials Transactions B, 1997, vol.
28, pp. 827-834.
[115] M. Chen, S. Raghunath and B. Zhao: "Viscosity Measurements of SiO2-“FeO”-
MgO System in Equilibrium with Metallic Fe", Metallurgical and Materials
Transactions B, 2014, vol. 45, pp. 58-65.
[116] G. Handfield and G. Charette: "Viscosity and structure of industrial high TiO2
slags", Canadian Metallurgical Quarterly, 1971, vol. 10, pp. 235-243.
[117] J. Van: "Viscosities, electrical resistivities, and liquidus temperatures of slags in
the system", Journal of the South African institute of mining and metallurgy, 1979,
vol. 327.
[118] D. Xie, Y. Mao, Z. Guo and Y. Zhu: "Viscosity of titanium dioxide-containing
blast furnace slags under neutral condition", Gangtie, 1986, vol. 21, pp. 6-11.
[119] J. Liao, J. Li, X. Wang and Z. Zhang: "Influence of TiO2 and basicity on
viscosity of Ti bearing slag", Ironmaking & Steelmaking, 2012, vol. 39, pp. 133-139.
[120] H. Park, J.Y. Park, G.H. Kim and I. Sohn: "Effect of TiO2 on the Viscosity and
Slag Structure in Blast Furnace Type Slags", Steel Research International, 2012, vol.
83, pp. 150-156.
[121] H. Park, J.Y. Park, G.H. Kim and I. Sohn: "Effect of TiO2 on the Viscosity and
Slag Structure in Blast Furnace Type Slags", Steel Research International, 2012, vol.
83, pp. 150-156.
[122] G.H. Kim and I. Sohn: "Effect of Al2O3 on the viscosity and structure of
calcium silicate-based melts containing Na2O and CaF2", Journal of Non-Crystalline
Solids, 2012, vol. 358, pp. 1530-1537.
[123] H. Kim, W. Kim, J. Park and D. Min: "A Study on the Effect of Na2O on the
Viscosity for Ironmaking Slags", Steel Research International, 2010, vol. 81, pp. 17-
24.
[124] N. Takahira, M. Hanao and Y. Tsukaguchi: "Viscosity and Solidification
Temperature of SiO2―CaO―Na2O Melts for Fluorine Free Mould Flux", ISIJ
international, 2013, vol. 53, pp. 818-822.
[125] G. Wu, E. Yazhenskikh, K. Hack, E. Wosch and M. Mueller: " Viscosity model
for oxide melts relevant to fuel slags. Part 1: Pure oxides and binary systems in the
200
system SiO2–Al2O3–CaO–MgO–Na2O–K 2O", Fuel Process of Technology, 2015, vol.
137, pp. 93-103.
[126] Y. Bottinga, D.F. Weill: "Viscosity of magmatic silicate liquids. Model for
calculation", American Journal of Science, 1972, vol. 272, pp. 438-475.
[127] M. Hanao, M. Kawamoto, T. Tanaka and M. Nakamoto: "Evaluation of
viscosity of mold flux by using neural network computation", ISIJ International, 2006,
vol. 46, pp. 346-351.
[128] D. Giordano, A. Mangiacapra, M. Potuzak, J.K. Russell, C. Romano, D.B.
Dingwell and A. DiMuro: "An expanded non-Arrhenian model for silicate melt
viscosity: A treatment for metaluminous, peraluminous, and peralkaline liquids",
Chemical Geology, 2006, vol. 229, pp. 42-56.
[129] L. Zhang and S. Jahanshahi: "Modelling viscosity of alumina‐containing
silicate melts", Scandinavian journal of metallurgy, 2001, vol. 30, pp. 364-369.
[130] S. Seetharaman, D. Sichen and J.Y. Zhang: "The computer-based study of
multicomponent slag viscosities", Journal of the Minerals, metals, and Materials
Society, 1999, vol. 51, pp. 38-40.
[131] G. Urbain: "Viscosity estimation of slags", Steel Research International, 1987,
vol. 58, pp. 111-116.
[132]. G. Urbain, F. Cambier, M. Deletter and M. R. Anseau, "Viscosity of silicate
melts", Trans. J. Br. Ceram. Soc., 1981, 80 (4), pp. 139-141
[133] P. Riboud, Y. Roux, L. Lucas and H. Gaye: "Improvement of continuous
casting powders", Fachberichte Huttenpraxis Metallweiterverarbeitung, 1981, vol. 19,
pp. 859-869.
[134]. A. Kondratiev and E. Jak, "Predicting coal ash slag flow characteristics
(Viscosity model in the Al2O3-CaO-FeO-SiO2 system)", Fuel, 2001, 80 (1), pp.
1990-2000
[135]. L. Forsbacka, L. Holappa, A. Kondratiev and E. Jak, "Experimental Study and
Modelling of Viscosity of Chromium Containing Slags", Steel research international,
2007, 78 (9), pp. 678-684
[136] T. Iida, H. Sakai and Y. Kita: "Extension of a Viscosity Equation Based on the
Network Parameter to Blast Furnace Type Slags", Koon Gakkaishi, 1999, vol. 25, pp.
93-102.
[137] T. Iida, H. Sakai, Y. Kita and K. Shigeno: "An equation for accurate prediction
of the viscosities of blast furnace type slags from chemical composition", ISIJ
International, 2000, vol. 40, pp. S110-S114.
[138] K.C. Mills and S. Sridhar: "Viscosities of ironmaking and steelmaking slags",
Ironmaking Steelmaking, 1999, vol. 26, pp. 262-268.
[139] J.A. Duffy and M.D. Ingram: "Optical basicity. IV. Influence of
electronegativity on the Lewis basicity and solvent properties of molten oxyanion
salts and glasses", Journal of Inorganic and Nuclear Chemistry, 1975, vol. 37, pp.
1203-1206.
[140]. A.J. Duffy, "A review of optical basicity and its applications to oxidic systems",
Geochimica et Cosmochimica Acta, 1993, 57, pp. 3691-3970
201
[141] A. Shankar: "Studies on high alumina blast furnace slags", 2007, School of
Industrial Engineering and Management. Royal Institute of Technology, Stockholm
[142] X.J. Hu, Z.S. Ren, G.H. Zhang, L.J. Wang and K.C. Chou: "A model for
estimating the viscosity of blast furnace slags with optical basicity", International
Journal of Minerals, Metallurgy, and Materials, 2012, vol. 19, pp. 1088-1092.
[143] Q. Shu: "A viscosity estimation model for molten slags in Al2O3-CaO-MgO-
SiO2 system", Steel Research International, 2009, vol. 80, pp. 107-113.
[144] Q. Shu, X. Zhang and K. Chou: "Structural viscosity model for aluminosilicate
slags", Ironmaking and Steelmaking, 2015, vol.
[145] G.H. Zhang, K.C. Chou and K. Mills: "Modelling viscosities of CaO-MgO-
Al2O3-SiO2 molten slags", ISIJ International, 2012, vol. 52, pp. 355-362.
[146] G.H. Zhang and K.C. Chou: "Influence of Al2O3/SiO2 Ratio on Viscosities of
CaO-Al2O3-SiO2 Melt", ISIJ international, 2013, vol. 53, pp. 177-180.
[147] L. Gan and C. Lai: "A General Viscosity Model for Molten Blast Furnace Slag",
Metallurgy and Materials Transaction B, 2013, vol. 45, pp. 875-888.
[148] X.L. Tang, M. Guo, X.D. Wang, Z.T. Zhang and M. Zhang: "Estimation model
of viscosity based on modified (NBO/T) ratio", Beijing Keji Daxue Xuebao, 2010, vol.
32, pp. 1542-1546.
[149] S.K. Pal, P. Choudhury, S. Sircar and H.S. Ray: "Application of Urbain's model
for slag systems in the estimation of viscosity of some commercial glasses",
Transactions of the Indian Ceramic Society, 2003, vol. 62, pp. 213-216.
[150] P.C. Li and N. Xiaojun: "Effects of MgO/Al2O3 Ratio and Basicity on the
Viscosities of CaO-MgO-SiO2-Al2O3 Slags: Experiments and Modeling",
Metallurgical and Materials Transactions B, 2016, vol. 47, pp. 446-457.
[151] A. Kondratiev, P.C. Hayes and E. Jak: "Development of a quasi-chemical
viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system.
Part 1. Description of the model and its application to the MgO, MgO-SiO2, Al2O3-
MgO and CaO-MgO sub systems", ISIJ International, 2006, vol. 46, pp. 359-384.
[152] M.A. Bibbo, S.M. Dinh and R.C. Armstrong: "Shear flow properties of
semiconcentrated fibre suspensions", Journal of Rheology, 1985, vol. 29, pp. 905-929.
[153] J. Chong, E. Christiansen, A. Baer: Journal of applied polymer science, 1971,
vol. 15, pp. 2007-2021.
[154] R. Darton and D. Harrison: "The rise of single gas bubbles in liquid fluidized
beds", Transactions of the Institution of Chemical Engineers, 1974, vol. 52, pp. 301-
304.
[155] X. Fan, N. Phan-Thien and R. Zheng: "A direct simulation of fibre suspensions",
Journal of Non-Newtonian Fluid Mechanics, 1998, vol. 74, pp. 113-135.
[156] C. Joung, N. Phan-Thien and X. Fan: "Viscosity of curved fibers in suspension",
Journal of Non-Newtonian Fluid Mechanics, 2002, vol. 102, pp. 1-17.
[157] T. Kwon, M. Jhon and H. Choi: "Viscosity of magnetic particle suspension",
Journal of Molecular Liquids, 1998, vol. 75, pp. 115-126.
202
[158] B. Konijn, O. Sanderink and N. Kruyt: "Experimental study of the viscosity of
suspensions: Effect of solid fraction, particle size and suspending liquid", Powder
technology, 2014, vol. 266, pp. 61-69.
[159] L. Marshall, C.F. Zukoski and J.W. Goodwin: "Effects of electric fields on the
rheology of non-aqueous concentrated suspensions", Journal of the Chemical Society,
Faraday Transactions 1: Physical Chemistry in Condensed Phases, 1989, vol. 85, pp.
2785-2795.
[160] P.K. Namburu, D.P. Kulkarni, D. Misra and D.K. Das: "Viscosity of copper
oxide nanoparticles dispersed in ethylene glycol and water mixture", Experimental
Thermal and Fluid Science, 2007, vol. 32, pp. 397-402.
[161] K. Tsuchiya, A. Furumoto, L.S. Fan and J. Zhang: "Suspension viscosity and
bubble rise velocity in liquid-solid fluidized beds", Chemical Engineering Science,
1997, vol. 52, pp. 3053-3066.
[162] A. Lejeune, Y. Bottinga, T. Trull and P. Richet: "Rheology of bubble-bearing
magmas", Earth and Planetary Science Letters, 1999, vol. 166, pp. 71-84.
[163] S. Wright, L. Zhang, S. Sun and S. Jahanshahi: "Viscosity of a CaO-MgO-
Al2O3-SiO2 melt containing spinel particles at 1646K", Metallurgical and Materials
Transactions B, 2000, vol. 31, pp. 97-104.
[164] A. Einstein: "Berichtigung zu meiner Arbeit:„Eine neue Bestimmung der
Moleküldimensionen", Annalen der Physik, 1911, vol. 339, pp. 591-592.
[165] I. Van Der Molen and M. Paterson: "Experimental deformation of partially-
melted granite", Contributions to Mineralogy and Petrology, 1979, vol. 70, pp. 299-
318.
[166] D.G. Thomas: "Non-Newtonian Suspensions—Part I", Industrial &
Engineering Chemistry, 1963, vol. 55, pp. 18-29.
[167] B.J. Konijn, O.B.J. Sanderink and N.P. Kruyt: "Experimental study of the
viscosity of suspensions: Effect of solid fraction, particle size and suspending liquid",
Powder Technology, 2014, vol. 266, pp. 61-69.
[168] G. Gust: "Observations on turbulent-drag reduction in a dilute suspension of
clay in sea-water", Journal of Fluid Mechanics, 1976, vol. 75, pp. 29-47.
[169] H. De Bruijn: "The viscosity of suspensions of spherical particles.(The
fundamental η‐c and φ relations)", Recueil des travaux chimiques des Pays-Bas,
1942, vol. 61, pp. 863-874.
[170] M. Nawab and S. Mason: "Viscosity of dilute suspensions of thread-like
particles", The Journal of Physical Chemistry, 1958, vol. 62, pp. 1248-1253.
[171] J.F. Brady and G. Bossis: "The rheology of concentrated suspensions of spheres
in simple shear flow by numerical simulation", Journal of Fluid Mechanics, 1985, vol.
155, pp. 105-129.
[172] J. Happel and H. Brenner: "Low Reynolds number hydrodynamics: with special
applications to particulate media", Springer Science & Business Media, 2012,
[173] A. Einstein: "Viscosity of a dilute suspension", Ann Physik, 17, 1905, vol. 549,
pp.
203
[174] M. Kunitz: "An empirical formula for the relation between viscosity of solution
and volume of solute", The Journal of general physiology, 1926, vol. 9, pp. 715-725.
[175] I.M. Krieger and T.J. Dougherty: "A mechanism for non‐Newtonian flow in
suspensions of rigid spheres", Transactions of the Society of Rheology, 1959, vol. 3,
pp. 137-152.
[176] R.F. Probstein, M. Sengun and T.C. Tseng: "Bimodal model of concentrated
suspension viscosity for distributed particle sizes", Journal of rheology, 1994, vol. 38,
pp. 811-829.
[177] K. Toda and H. Furuse: "Extension of Einstein's viscosity equation to that for
concentrated dispersions of solutes and particles", Journal of bioscience and
bioengineering, 2006, vol. 102, pp. 524-528.
[178] J. Happel: "Viscosity of suspensions of uniform spheres", Journal of Applied
Physics, 1957, vol. 28, pp. 1288-1292.
[179] D.G. Thomas:"Transport characteristics of suspension: VIII. A note on the
viscosity of Newtonian suspensions of uniform spherical particles", Journal of
Colloid Science, 1965, vol. 20, pp. 267-277.
[180] R. Roscoe: "The viscosity of suspensions of rigid spheres", British Journal of
Applied Physics, 1952, vol. 3, pp. 267.
[181] M. Mooney: "The viscosity of a concentrated suspension of spherical particles",
Journal of colloid science, 1951, vol. 6, pp. 162-170.
[182] G. Batchelor: "The effect of Brownian motion on the bulk stress in a suspension
of spherical particles", Journal of fluid mechanics, 1977, vol. 83, pp. 97-117.
[183] J. Bergenholtz, J. Brady and M. Vicic: "The non-Newtonian rheology of dilute
colloidal suspensions", Journal of Fluid Mechanics, 2002, vol. 456, pp. 239-275.
[184] M. Chen: "Viscosity and phase equilibrium studies relevant to copper smelting
and converting slags " University of Queensland PhD Thesis, Queensland, Australia,
2014
[185] G. Urbain and M. Boiret: "Slag viscosity: measurement and estimate",
Memoires et Etudes Scientifiques de la Revue de Metallurgie, 1989, vol. 86, pp. 209-
214.
[186] H. Weymann: "On the hole theory of viscosity, compressibility, and expansivity
of liquids", Kolloid-Zeitschrift und Zeitschrift für Polymere, 1962, vol. 181, pp. 131-
137.
[187] Q.F. Shu, X.J. Hu, B.J. Yan, J.Y. Zhang and K.C. Chou: "New method for
viscosity estimation of slags in the CaO-FeO-MgO-MnO-SiO2 system using optical
basicity", Ironmaking Steelmaking, 2010, vol. 37, pp. 387-391.
[188] G.H. Zhang and K.C. Chou: "Modeling the Viscosity of Alumino-Silicate Melt",
Steel Research International, 2013, vol. 84, pp. 631-637.
[189] V.P. Gorbachev, M.S. Bykov, N.L. Valov, P.V. Pershikov, S.V. Korshikov,
"Viscosity of anomaly magnesium0alumina slag", News of higher educational
institutions. ferrous metaalurgy, 1977, vol. 23, pp. 31-34.
[190] R. Higgins, T.J.B. Jones, "Viscosity characteristics of Rhodesian copper
smelting slags", Bull. Inst. Min. Metall., 1963, vol. 682, pp. 825-684.
204
[191] H. Ramberg: "Chemical bonds and distribution of cations in silicates", The
Journal of Geology, 1952, vol. 331-355.
[192] S. Wright, L. Zhang, S. Sun and S. Jahanshahi: "Viscosities of calcium ferrite
slags and calcium alumino-silicate slags containing spinel particles", Journal of non-
crystalline solids, 2001, vol. 282, pp. 15-23.
[193] M. Chen, S. Raghunath and B. Zhao: "Viscosity of SiO2-“FeO”-Al2O3 System
in Equilibrium with Metallic Fe", Metallurgical and Materials Transactions B, 2013,
vol. 44, pp. 820-827.
[194] J.O.M. Bockris and D.C. Lowe: "Viscosity and the structure of molten silicates",
Proc. Royal Soc. London, 1954, vol. A226, pp. 423-435.
[195] F.Z. Ji and S. Seetharaman: "Experimental studies of viscosities in FenO-MgO-
SiO2 and FenO-MnO-SiO2 slags", Ironmaking & steelmaking, 1998, vol. 25, pp. 309-
316.
[196] B.O. Mysen, D. Virgo and I. Kushiro: "The structural role of aluminium in
silicate melts; a Raman spectroscopic study at 1 atmosphere", American Mineralogist,
1981, vol. 66, pp. 678-701.
[197]. T. Furukawa, K. E. Fox and W. B. White, "Raman spectroscopic investigation
of the structure of silicate glasses. III. Raman intensities and structural units in sodium
silicate glasses", The Journal of chemical physics, 1981, 75 (7),pp. 3226-3237
[198]. A. Osipov, L. Osipova and R. Zainullina, "Raman spectroscopy and statistical
analysis of the silicate species and group connectivity in cesium silicate glass forming
system", Int. J. Spectrosc., 2015, 15, pp. 1-16
[199]. S.A. Brawer and W. B. White, "Raman spectroscopic investigation of the
structure of silicate glasses (II). Soda-alkaline earth-alumina ternary and quaternary
glasses", J. Non-Cryst. Solids, 1977, 23 (2), pp. 261-278
[200]. B.O. Mysen, D. Virgo and I. Kushiro, "The structural role of aluminum in
silicate melts; a Raman spectroscopic study at 1 atmosphere", American Mineralogist,
1981, 66 (7-8),pp. 678-701
[201] G. Walrafen and J. Stone: "Raman spectral characterization of pure and doped
fused silica optical fibers", Applied Spectroscopy, 1975, vol. 29, pp. 337-344.
[202] L. Wang, Y. Wang, Q. Wang and K. Chou: "Raman Structure Investigations of
CaO-MgO-Al2O3-SiO2-CrOx and Its Correlation with Sulfide Capacity", Metallurgy
and Materials Transactions B, 2016, vol. 47, pp. 10-15.
[203] P. Colomban and F. Treppoz: "Identification and differentiation of ancient and
modern European porcelains by Raman macro‐and micro‐spectroscopy", Journal
of Raman Spectroscopy, 2001, vol. 32, pp. 93-102.
[204] D. Phan, T. Häger and W. Hofmeister: "The influence of the Fe2O3 content on
the Raman spectra of sapphires", Journal of Raman Spectroscopy, 2016, vol. 3, pp.
124-132
[205] R.P. Feynman: "Feynman lectures on physics. Volume 2: Mainly
electromagnetism and matter", Addison-Wesley, 1964, vol. 1, pp.
[206] J. Newman, "Electric Current and Cell Membranes", 2008, Physics of the Life
Sciences. Springer, pp. 1-30.
205
[207] W.H. Baur: "Variation of mean Si–O bond lengths in silicon–oxygen
tetrahedra", Acta Crystallographica Section B: Structural Crystallography and
Crystal Chemistry, 1978, vol. 34, pp. 1751-1756.
[208] I.t. Brown and R. Shannon: "Empirical bond-strength–bond-length curves for
oxides", Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical
and General Crystallography, 1973, vol. 29, pp. 266-282.
[209]. Bongiorno, A. and A. Pasquarello, "Validity of the bond-energy picture for the
energetics at Si− SiO 2 interfaces", Physical Review B, 2000, 62 (24), R16326
[210]. Fetters, L., D. Lohse, D. Richter, T. Witten and A. Zirkel, "Connection
between polymer molecular-weight, density, chain dimensions, and melt viscoelastic
properties", Macromolecules, 1994, 27 (17), 4639-4647
[211]. Mills, K., L. Yuan and R. Jones, "Estimating the physical properties of slags",
Journal of the Southern African Institute of Mining and Metallurgy, 2011, 111 (10),
649-658
[212] A. Kondratiev, A., P. C. Hayes and E. Jak, "Prediction of viscosities in fully and
partially molten slag system", 2001
[213]. Coussot, P. and C. Ancey, "Rheophysical classification of concentrated
suspensions and granular pastes", Physical Review E, 1999, 59 (4), 4445