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P. Bowen, EPFL. 20/09/2019 1
ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
Technologie des poudres
Des glissements de terrain au béton et des
avalanches au chocolat
Prof. P. Bowen, Dr. P. Derlet (PSI)
Week 2 – Lecture no. 3 - on website
PTG
•BOOKS
•The Colloidal Domain – D. F. Evans & H. Wennerström, Wiley, 1999,
• Principles of Ceramic Processing – J.S.Reed , Wiley, 1995. English
• T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic Press,1996
• Les Céramiques, J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Traité des Matériaux, Volume 16, PPUR, 2005
P. Bowen, EPFL. 20/09/2019 2
Course Contents - Plan
Réseau neurone – Neural network
- compaction
Laves Torrentielles–Debris Flow
Granular Dynamics –
DEM Modelling
Dr. Mark Sawley
1. Introduction – general introduction to course
– example transparent ceramics
2. Particle Packing and Powder Compaction
- Theoretical and empirical models (PB)
- Powder compaction (PD)
3 Particle-Particle Interactions (PB)
- Colloidal Dispersions
- DLVO –theory and limitations
- non-DLVO and steric forces
Exercises – particle interactions & rheology-HAMAKER & YODEL
4. Introduction to Atomistic Scale Simulations (PD)
- introduction to modeling of surfaces & interfaces at the atomic scale
- defects in metals – towards sintering
5. Sintering mechanisms (PD)
- metals, ceramics
- influence of microstructure
- simulation
Exercises – Atomistic modeling and DEM – LAMMPS
6. Advanced Powder Processing Technologies (PB)
- additive manufacturing – 3D printing
- laser sintering, Spark Plasma Sintering, Field assisted, cold sintering
P. Bowen, EPFL. 3
•Files of lectures to be found on PTG website : http://lmc.epfl.ch/PTG/Teaching
Week-day File # Powder Technology – Wednesday 10.15-13.00 – MXG 110
1- sept 18 1&2 PB PD General Course Introduction (1hr)– Example rheology – Yodel Intro (1hr)- Powder packing and
compaction – 1 (i) – (1hr)
2 – sept 25 2&3 PB/MS Powder packing and compaction – 1(ii), 2- Examples and DEM guest lecturer – (3hrs)
3 – oct 2 5&6 PB Particle – Particle Interactions 1 - 2hrs
Particle – Particle Interactions 2 (i) – 1hr
4 – oct 9 6&7 PB Particle – Particle Interactions 2 (ii)(1hr) &
Particle – Particle Interactions 3 (2hrs) - Download Hamaker & send YODEL-PB
5 – oct 16 PB Exercises – Intro to Hamaker & YODEL software & group projects (3hrs)
6 – oct 23 AM PB Exercises - Hamaker &Yodel Modelling – group projects (AM 2 hrs) presentation of interparticle
project results (1 hr)
7 – Oct 29 4 PD Powder packing and compaction -3 & 4(i) – (3hrs)
8 – nov 6 4&8 PD Powder packing and compaction - 4 (ii) – (1hr)
Introduction to atomistic scale simulations – (2hrs)
9 – nov -13 9& 11 PD Compaction, Sintering & Defects in metals at atomistic scale (2hrs)
Sintering Mechanisms – 1(i) (1 hr)
10 – nov 20 11 PD Sintering Mechanisms - 1 (ii) & 2 (3hrs)
11 -nov-27 10 PB New Technologies -1 Processing – Forming – Shaping (2hrs)
visit of Additive Manufacturing lab (1hr)
12 - dec 4 PD Excercises -Introduction to Molecular Dynamics Modelling using LAMMPS (3hrs) .
13 – dec 11 12 PB New Technologies-2 – Sintering Methods -
& Exam method
14 – dec 18 PD Excercises - MD- DEM modelling exercise using LAMMPS –particle packing - Effect of
parameters (3 hrs)
P. Bowen, EPFL. 20/09/2019 4
Particle Packing - Last week….started… today finish….
Literature Models
– Empirical Models
– Semi-empirical models - physics of particles
– Numerical and analytical (computer aided simulations)
Models evaluate packing or porosity in a packed powder as a function of 4
characteristics:
– Particle Shape - sphericity
– Modal Size differences in multimodal distributions
– Mean particle size
– Size distribution
Effect of agglomeration also plays an important role on particle packing
P. Bowen, EPFL. 20/09/2019 5
Aims of todays course
Two examples of powders in application or research where particle packing and rheological
behaviour linked to particle shape and dispersion (leading us to the next section of the
course colloidal dispersions)
Neural Network – applied to the particle packing of alumina particles in spray dried
granules - Thesis de Violaine Guerin – EPFL No. 3021 (2004)
Landslides or Alpine Debris Flow…..Eric Bardou (Thesis EPFL- 2479(2002))
Numerical simulation of Granular Dynamics using DEM - Dr. Mark Sawley (EPFL)
Typical Questions - Section Particle Packing
English Books for ceramic processing and powder dispersion
1. T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic
Press,1996
2. J.S. Reed - Principles of ceramic processing – J. Wiley & sons, 2nd Edition (1995)
P. Bowen, EPFL. 20/09/2019 6
Comparaison de la prédiction théorique et des résultats
expérimentaux la densité verte de poudres Bayer et l’alumine
de haute pureté en utilisant un réseau neurone
Thèse de Violaine Guerin – EPFL No. 3021 (2004)
Comparison of theoretical prediction and experimental
green density of high purity and Bayer alumina powders
using a neural network
P. Bowen, EPFL. 20/09/2019 7
Introduction
Goals :
Predicting green and sintered density using a neural network
Better understanding of the densification behavior
Design and predict microstructure
Powder characteristicsDensification behaviour
?
P. Bowen, EPFL. 20/09/2019 8
Particle packing and Neural Network approach
Ceramic Manufacturing - Generalities
- Packing of particles
- Mathematical models
- Neural network
Characteristics of powders and densities of Green Bodies
Using the results of the neural network as a predictive tool
Conclusions and future development
P. Bowen, EPFL. 20/09/2019 9
Ceramic Fabrication - Generalities
Different manufacturing processes-from powders- Compaction of granulated powders – uni-axial – CIP*- Suspension - casting (slip, tape, pressure)
Compaction of spray-dried granules$
Effects of parameters of the powder on the green densities
Compaction 3 steps
–Re-arrangement
–Deformation of granules
–Fracture of granules (rarely achieved)
Consider two families of powders
1. Bayer aluminas - low agglomeration factor
2. Non-Bayer finer more agglomerated
Pores inside the granules between the primary particles
and between the granules
Pore distribution - bimodal (inter-granular, intra-granular)
Particule primaire (0.1 -1µm)
Granulée pour la compression
(50-300µm)
* CIP – Cold isostatic pressing $ - see BAR05 p. 204-219
P. Bowen, EPFL. 20/09/2019 10
Alpha alumina – effect of agglomerates – week 1 Intro
• Particle size distribution shows small tail of agglomerates – leads to defects in
microstructure and low sintered densities (94%) – poor (hard) granules (50 mm)
and aggregates (2 mm)
0.1
1
.01 .1 1 5 10 2030 50 7080 9095 99 99.999.99
AKP50-non-broyéeAKP50-broyée
ES
Dia
mèt
re (
µm
)
% volume cumulés
P. Bowen, EPFL. 20/09/2019 11
Alpha alumina – effect of agglomerates
• Attrition milling 1 hr agglomerates removed
• Improved sintered density & microstructure
• Can we predict this from an analytical modelling approach?
Attrition milled 1hr – slip cast – 99%As received – slip cast – 94 %
F-S. Shiau, T-T. Fang, T-H Leu, Materials Chemistry and Physics, 57, 33-40 (1998).
P. Bowen, EPFL. 20/09/2019 12
Neural Network Approach
Neural network- compaction
P. Bowen, EPFL. 20/09/2019 13
Réseau neurone – Neural Network
• IW – weighted
hidden layer
- non-linear
function
• LW – weighted
output layer
- linear function
• b- bias
• Adjust until target
value achieved
P. Bowen, EPFL. 20/09/2019 15
Powder Characteristics & Treatment
31 a-alumina commercial powders from different producers (Prof. Hofmann,
Alusuisse)
2 families Bayer* (18) and Non-Bayer*(precipitated) (13)
Characterised by:
– Chemical Composition (Na, Si, Ti, Fe, Mg)
– Particle size distributions (laser diffraction)
– Powder X-ray diffraction (XRD)
– Specific Surface Area (SSA, BET model)
– Particle shape (SEM)
Spray dried (atomisation-spray drying)$ after wet milling
Addition of PVA as binder and PEG as plasticizer
Cold Isostatic Pressing (CIP)
– 200 MPa
– Cylinders, 2cm de diameter and 10 cm long
Spray dried granules
* Voir BAR05 – pages 111-113 $- BAR05 pages 196-203
P. Bowen, EPFL. 20/09/2019 16
Log-normal - Bayer Aluminas
Neuron network compared with
Kavanagh and Nolan log-normal model &
Experimental values for coarse powders
Median diameter (Dv50) and standard deviation (sv)
– verified experimentally
22 of the 32 followed reasonably well a log-normal
distribution (see BAR05 pages 64-65)1 µm
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
% F
req
uen
cy
Equivalent spherical diameter (µm}
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5 6
Fre
quen
cy
Diameter (µm)
Normal distribution Log Normal distribution
P. Bowen, EPFL. 20/09/2019 17
Neural Network (NN) - method
Program used NETS –
– Developed by NASA
Input Parameters – 5 neurons
– d10,d50 d90 volume based particle size
distribution
– Specific surface area
– Type of powder
- Bayer or Non-Bayer
NN – 10 intermediate neurons, 1 output
optimised with 28 powders then tested on 3
– Results predicted better than 5%
– Within the powder characteristics
« box » or set used to train the NN
Min (µm) Max (µm)
d90 0.60 20.0
d50 0.25 12.5
d10 0.15 4.0
• Can now use NN to predict behaviour
of powders within this range –
• Even if we do not have exact data for
particular Dv50 and s etc
• For clearer trends split Bayer and Non-
bayer into different Dv50 size ranges
P. Bowen, EPFL. 20/09/2019 18
Log-normal - Bayer Aluminas– fine particles (< 2mm)
For green (compact ) densities after CIP but before sintering
Predictions
RCP – Random Close
Packed
RLP - Random Loose
Packed
Particle packing model –
density of packing
increases with increasing
standard deviation(s)
Bayer Aluminas
corresponds to Random
Loose Packed when
s > 2.5
P. Bowen, EPFL. 20/09/2019 19
Log-normal - Bayer Aluminas
•Bayer aluminas (< 2mm) correspond
well to experimental data for the RLP
•after spray drying of granules
•Slight increase in the packing
fraction with the s of the original
PSD
•Compaction - 3 stages - re-
arrangement, deformation, fracture
•3rd stage rarely is reached with
typical technical conditions
•The packing fraction of the powder
within the granules dominates the
behavior
•Assuming that the binders* and
plasticizers* behave the same way for
all powders * See BAR05 – p.218-219
P. Bowen, EPFL. 20/09/2019 20
Log-normal - Bayer Aluminas
200 µm granule
Surface of
granule
1 µm
The density or packing in the granule depends on the following parameters
– Particle shape – non-spherical negative →lower packing fraction
– Broad size distribution – positive improves packing fraction
– Need good dispersion and colloidal stability with low degree or no aggregates or agglomerates
– The dispersion also influences the rheology – important for spraying
– We need a minimum viscosity but with a maximum of solids loading to create dense granules via spray drying – optimum with respect to above parameters
P. Bowen, EPFL. 20/09/2019 21
Influence of PSD width and particle size dv50
Precipitated powders
Non-Bayer
Bayer Powder
sg rv
1 2 3 4 50.3
0.4
0.5
0.6
0.7
0.8
De
nsi
té r
ela
tive
Déviation standard géométrique sg
RCP S&M
RLP N&K
RCP N&K
RLP D&T
d50
=0,75mm
d50
=1,6mm
d50
=3,75mm
sg et/ou dv50 rv
1 2 3 4 50.3
0.4
0.5
0.6
0.7
0.8
De
nsité
re
lative
Déviation standard géométrique sg
d50
=0.75mm
d50
=1.6mm
d50
=3mm
RCP N&K
RLP N&K
Application of Neural Network
P. Bowen, EPFL. 20/09/2019 22
Spray Dried Alumina Powders
* ' 1*0.6 0.6granules particules facteur d empilementr r= = =
30mm
Primary Particles Bayer
Theoretical Density
(relative density =1)
Granules
Density RLP
(relative density =0.6)
BAYER
* ' 0.6*0.6 0.36granules agglomérats facteur d empilementr r= = =
PrimaryAgglomerates
Density RLP
(relative density =0.6
)
Granules
DensityRLP
(relative density =0.6)
PRECIPITATED
Non-BAYER
Packing factor
Packing factor
= 𝜌𝑎𝑔𝑔𝑙𝑜𝑚é𝑟𝑎𝑡𝑠
P. Bowen, EPFL. 20/09/2019 23
Conclusions
Neural Networks
Useful tool for prediction of ceramic green body densities (and sintered see thesis (Violaine Guerin – EPFL No. 3021 (2004))
Allows insight into behaviour of powder during compaction and sintering from standard powder characteristics
Useful for optimisation in industry – evaluation of new powder lots
Should also be applicable to metallic powders
Can in fact use the programme in reverse – machine learning approach – i.ewe have optimised an algorithm for a given range of powder characteristics –now we can create virtual powder needed to create certain green or sintered density or microstructure – or find which powder needed for desired sintered density
Modelling
Modelling of materials processing and microstructures – numerical modelling methods
e.g. Finite Element Methods (FEM)– Discrete Element Methods (DEM) –
P. Bowen, EPFL. 20/09/2019 24
Les laves torrentielles en milieu alpin
Eric Bardou
EPFL Thesis No. 2479 (2002)
Effect of the Clay Type on the Rheology of an Heterogeneous Dense
Granular Material.
Implication for the Study of Alpine Debris Flow
Eric Bardou, Paul Bowen, Pascal Boivin (EPFL), Phil Banfill (HWU, UK)
Powder Page – Landslide simulation - http://www.granular.com/
Earth Surface Processes and Landforms
Earth Surf. Process. Landforms 32, 698–710 (2007)
P. Bowen, EPFL. 20/09/2019 25
Scope of working length scale!!!
Du bassin versant – Alpine Watershed…..
Aux feuillets argileux
- Clay platelets
-Diameter Microns
--thickness 20-100nm
P. Bowen, EPFL. 20/09/2019 26
Exemple
P. Bowen, EPFL. 20/09/2019 27
Description du phénomène – Description of the phenomenon
Transport of bed load (charge de fond)
Debris (mud) flow
The transfer of sediment a problem
between geology and hydraulics
Bed load – saltation (hopping), rolling, sliding
P. Bowen, EPFL. 20/09/2019 28
Definition
front
tailbody
Lateral section
• Grains >400
microns
• Fluid – matrix
• < 400microns
• Model system for
sizes < 20mm
The debris or mudflows are granular flows - lubricated kinematically –
they are of a transient nature - simple model - two-phases
- grains and fluid
P. Bowen, EPFL. 20/09/2019 29
Particle sizes – (grains & matrix < 20mm)
ar g
il es silts
sabl e
sfi n
s
sabl e
sm
oye
ns
sabl e
sgr o
ssi e
r s
graviers
0.001 0.01 0.1 1 100
20
40
60
80
100
[mm]20
fracti
on
cu
mu
lée [
%]
viscoplastic
collisional-frictional
frictional-viscous
Bed load
Argiles
• Fluid – matrix < 400microns • Grains >400 microns
Clays Fine Medium CoarseSands
Gravels
P. Bowen, EPFL. 20/09/2019 30
Rheological Models➢ Different types of fluid behaviour – Newtonian and non-Newtonian
➢Various models used to extract information e.g. yield stress – all give very similar results
M. Palacios. -Química del Cemento – Enero 2010
(Ferraris, C. F. , 1999)
• Yield Stress – t0 Minimum stress to make liquid or suspension flow
• Typical of systems with attractive network
• Yoghurt – Cement - Ceramic slurries – (see BAR05)
30
P. Bowen, EPFL. 20/09/2019 31
Influence of clays
Size
range
(mm)
Particle class Solids
weight
(%)
Solids
volume
(%)
0.0 - 0.02 clay size 4.1 11.4
0.02 - 0.05 silt size 13.0 12.0
0.05 - 0.1 fine sand 5.7 5.4
0.1 - 0.5 medium sand 26.4 24.4
0.5 - 1.0 coarse sand 13.1 12.1
1.0 - 2.0 very coarse sand 3.5 3.2
2.0-20.0 gravel 34.2 31.6
• Grains >400 microns
• Fluid – matrix
• < 400 microns
With clays
Without clays
P. Bowen, EPFL. 20/09/2019 32
Model system PSD – (grains & matrix < 20mm)
Argiles
Model PSD
P. Bowen, EPFL. 20/09/2019 33
2,8 mm
Why – plate –plate?
• easy to use
• No jamming of particles
• Roughened surfaces to
avoid wall-slip
• Low cost….
150 tests
Rheometer plate-plate
Rheology – Matrix (<400mm)
P. Bowen, EPFL. 20/09/2019 34
Rheology with model PSD up to 20 mm
Herriot Watt University (UK) – ciment expert – Prof. Phil Banfill
Sample wieghts for each test
30 kg !!! dry!!!
Measure torque – off-centre to
avoid moving through same area
of sample – effective viscosity
P. Bowen, EPFL. 20/09/2019 35
Clays – main industrial use – porcelain ceramics!
Kaolin
(50-55%)
Feldspath
(25%)
Quartz
(20-25%)
Porcelaine
(dure)
P. Bowen, EPFL. 20/09/2019 36
Structure of clays 1:1 & 2:1
Konan eta l J.Coll.Interf.Sci
307(1) 2007, 101–108
(a) Structure of 1:1 clay mineral e.g. kaolin
(b) Structure of 2:1 clay mineral, e.g montmorillonite
P. Bowen, EPFL. 20/09/2019 37
Argile (2:1) – swelling – Na Montmorillonite
Atomistic model of the one-layer
hydrate of sodium montmorillonite
O: red,
H: white,
Si: yellow,
Na: blue,
Al: purple,and
Mg: green
This simulation super cell consists of
two interlayer regions made up by 8
unit cells
Exchange of Na+ with Li+ - extra
water of hydration interlayer spacing
increased – pillared clays – catalysis
Mg2+ substitutes Al3+ ….Na+ in
interlayer charge compensation
Si
Si
Si
Si
Al(Mg)
Na
P. Bowen, EPFL. 20/09/2019 38
Variation of clay - Evolution of effective-viscosity
Sample SCR [g/g] Swelling clay proportion in
the bulk [g/g]
Md 1 0 0 ( only kaolinite)
Md 2 0.27 0.005
Md 3 0.54 0.01
Md 4 0.8 0.02
Relation between water content (%wt) (W) and
effective viscosity(K) for 4 mixtures
1:1 clay - Kaolinite China Clay™ (commercial)
2:1 clay - Smectite - extracted from watershed
soils (SCR swelling clay ratio = 2:1 / 1:1)
K
w
P. Bowen, EPFL. 20/09/2019 39
Comparaison with Natural Debris Flows
swelling
Non
-swelling
MD1
Model
Mixture
MD4
Model
Mixture
P. Bowen, EPFL. 20/09/2019 40
Future …….
• Theory : harmonise the classification (fluid-grains) and flow regimes….
• Lab : better understand the effects of the different clays and particles (size
and disitribution)
• Observations in-situ : modes of release – the trigger….
• Modelling : try and relate to regional parameters – clay content, soluble
ions, degree of aggregation, interparticle forces….
Submitted project failed maybe another project… some day….
P. Bowen, EPFL. 20/09/2019 41
Can you answer these questions? (1)
Give a field of application or an everyday example of Powder Technology
How is particle packing important for rheology?
How do aggregates influence the microstructure of a ceramic?
How can this effect the optical properties of polycrystalline alumina ceramics?
What are the different types of models used to describe the packing of particles?
Describe an example of a model in detail.
What is the difference between Random loose packed (RLP) and Random close packed (RCP) ?
For monodispersed spherical particles what is the maximum packing fraction for random close packing RCP? For an ordered array of monodispersed spheres ?
How is the packing of particle modified
- when the particle size has a log-normal distribution?
- if the particles are not spherical ?
- for dry powder as a function of size e.g when the size is reduced?
P. Bowen, EPFL. 20/09/2019 42
Can you answer these questions? (2)
What are the different forces that can act on particles and influence their packing .
-which forces dominate for particles < 1 micron
- which force dominates for particles > 100 microns
What is the effect of agglomeration on the particle packing – how can one describe quantitatively the degree of agglomeration ?
For a bimodal distribution of two monodispersed powders what is the maximum packing fraction that can be attained?
For a multimodal distribution of powders what is the maximum packing fraction that can be attained – give an example of where this is used in practice.
What are the limitations of using a multimodal packing method for ceramic fabrication?
What type of packing is found for ultrafine alumina powders produced by precipitation and how could this be improved ? What is its significance for the dry pressing of ceramic pieces?
Describe DEM modeling and give an example of its application to Particle Technology
P. Bowen, EPFL. 20/09/2019 43
BIBLIOGRAPHIE
BAR05 J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Céramiques, Les Traité des Matériaux, Volume 16, PPUR, 2005
BRO50 G. BROWN, Flow of fluids through porous media 1 - Single Fluid phase,1950, pp. 210-216
DEX72 A.R. DEXTER, D.W. TANNER, Packing densities of mixtures of spheres withlog-normal size distributions, Nature physical science, 1972, vol. 238, pp. 31-32
DIN00 D.R. DINGER, One-dimensional packing of spheres, Part I, American ceramic society bulletin, 2000, pp. 71-76
*FLA04aR.J. Flatt, ‘Towards a prediction of superplasticized concrete rheology’, Materials and structures 27 (269) (2004) 289-300
FLA04b R.J. Flatt, N. Martys, L.Bergström The Rheology of Cementitious Materials, MRS Bulletin, may 2004, pp. 314-318
GER89A R.M. GERMAN, Packing of monosized nonspherical particles, Book “Powder packing characteristics”, 1989, pp. 122-133
GER89B R.M. GERMAN, Introduction to particle packing, Book “Powder packing characteristics”, 1989, pp. 1-20
MIL78 J.V. MILEVSKI, Handbook of fillers and reinforcement plastics, Eds Van Nostrand, 1978
NAR85 M. NARDIN, E. PAPIRER, J. SCHULTZ, Powder Technology, 1985, 44, pp.131-140
NAV99 P. Navi, C. Pignat, Three - dimensional characterization of the pore structure of a simulated cement paste, Cement and Concrete Research 29 (1999) 507-514
*NOL93 G.T. NOLAN, P.E. KAVANAGH, Computer simulation of random packings of spheres with log-normal distributions, Powder technology, 1993, vol. 76, pp.
309-316
*NOL94 G.T. NOLAN, P.E. KAVANAGH, The size distribution of interstices in random packings of spheres, Powder technology, 1994, vol. 78, pp. 231-238
NOL95 G.T. NOLAN, P.E. KAVANAGH, Random packing of nonspherical particles, Powder technology, 1995, vol. 84, pp. 199-205
PHI96 A.P. PHILIPSE, The random contact equation and its implications for(colloidal) rods in packings, suspensions, and anisotropic powders, American chemical society, 1996, 12, n°5, pp. 1127-33
PHI97 A.P. PHILIPSE, A. VERBERKMOES, Statistical geometry of caging effects in random thin-rod structures, Physica A, 1997, 235, pp. 186-193
SOH68 H.Y. SOHN, C. MORELAND, The effect of particle size distribution on packing density, Canadian journal of chemical engineering, 1968, vol. 46, pp.162-167
P. Bowen, EPFL. 20/09/2019 44
BIBLIOGRAPHIE
SUZ01 M. SUZUKI, H. SATO, M. HASEGAWA, M. HIROTA, Effect of size distribution on taping properties of fine powders, Powder technology, 2001,118, pp. 53-57
SUZ83 M. SUZUKI, T. OSHIMA, Estimation of the coordination number in a multicomponent mixture of spheres, Powder technology, 1983, 35, pp. 159-166
SUZ85 M. SUZUKI, T. OSHIMA, Coordination number of a multicomponent randomly packed bed of spheres with size distribution, Powder technlogy,1985, 44, pp. 213-8
WAK75 R.J. WAKEMAN, Packing densities of particles with log-normal sizedistributions, Powder technology, 1975, 11, pp. 297-299
*YU93 A.B. YU, N. STANDISH, Characterisation of non-spherical particles from theirpacking behaviour, Powder technology, 1993, vol. 74, pp. 205-213
YU97 A.B. YU, J. BRIDGWATER, A. BURBIDGE, On the modelling of the packingof fine particles, Powder technology, 1997, 92, pp. 185-194
ZOK91 F. ZOK , F.F. LANGE , Packing density of composite powder mixtures,journal of American ceramic society , 1991, 74
n°8, pp. 1880-85
Mark L. Sawley
Maître d’enseignement et de recherche (MER)
SGM – STI – EPFL
Numerical simulation of granular dynamics
using the Discrete Element Method
SMX course - Powder Technology
Autumn semester 2018
2
General aspects
§ Motivation
§ Industrial applications
§ Numerical simulation
Implementation
§ DEM technology
§ DEM implementation
§ Basic examples
Applications
§ Particulate flows
§ Materials processing
§ Multiphase flows
General aspects Presentation overview
3
Why study granular dynamics?
• granular materials are omnipresent
• granular materials exhibit a wide range of interesting fundamental behaviour
• granular dynamics are important for numerous industrial processes
General aspects Motivation
Why use the Discrete Element Method?
• conceptually simple technique
• can be applied to a wide range of different cases
• provides very detailed information regarding granular processes
• can provide results in agreement with experimental observation
4
Physical characteristics
& behaviour
• shape
• microstructure
• dilatancy
• cohesion
• segregation
• clustering
• self-organization
• …
General aspects Motivation
5
Industrial applications
• food & agriculture
• mineral processing
• steel making
• chemical
• pharmaceutical
• plastic
• metal
• ceramic
• geophysical
• …
General aspects Motivation
Dry granulation of pharmaceutical tablets
milling active ingredientsblending with excipients
granulation
screening
blending with lubricant
tabletting
final product
General aspects Industrial applications
6
multiphase processes
Manufacturing of breakfast cereals
grain storage conveying
drying
flaking
extrudingfinal products
mixing
General aspects Industrial applications
7
8
Numerical simulation of granular dynamics
-0.1
0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
number
verti
cal p
ositi
on, z
[m
]
10 - 80 mm
10 - 20 mm
20 - 40 mm
40 - 80 mm
vsi_4000
table ejecteurs
cylindre
Provides valuable information :
• both qualitative and quantitative
• increase basic understanding of process
• virtual prototyping tool
• reduce significantly production costs
• improve product performance
• minimize time-to-market for new products
• complementary to experimentation
General aspects Numerical simulation
9
Types of particulate materials to be simulated
• Free-flowing granular materials
- dry (inter-particle collisional forces, e.g. dry sand)
- moist (inter-particle attractive forces, e.g. wet sand, powder)
• Powders
- large cohesive assemblies
• Rheologically-complex flowing materials
- polymers, paste, sludge …
• Wet particulate materials
- suspensions, blood …
• Agglomerate solid materials
- natural materials (e.g. rocks)
- man-made materials (e.g. concrete)
General aspects Numerical simulation
10
Coupled multi-method applications for multiphase flows
solidsprocessing
fluidprocessing
dry
granular
moist
granular
wet
granular
particle-laden
fluid fluid
coupled DEM/CFDDEM CFD
• Complementary simulation technologies can be coupled
- Computational Fluid Dynamics (CFD)
- Discrete Element Method (DEM)
[ coupled DEM / Finite Element Method (FEM) is also employed ]
General aspects Numerical simulation
11
Discrete Element Method (DEM)
• Basic aspects
- particle-based (Lagrangian) method
- based on solving Newton equations for an ensemble of
particles and their neighbouring boundary objects
- track the position, velocity and spin of all the individual
particles
- detect all contacts between particles and with the
boundary objects
- model the contact forces & torques acting on the particles
(and boundary objects)
Implementation DEM technology
12
General approach
• “Soft particle” approach
- continuous interaction between “deformable” particles (particles can slightly overlap)
- calculate time-dependent collisional process
- “time driven” methodology
- most commonly employed approach
Implementation DEM technology
• Improved computational performance using a two-step contact detection process :
- spatial sorting (find near neighbours)
- individual contact testing
Goal is to reduce operation count from O(N2) to O(N) or O(N logN)
13
Implementation DEM technology
define geometry (boundary objects)
set initial positions and velocities
find near neighbours
calculate forces & torques on particles
calculate physical quantities of interest
move particles and objects due to forces
t2 >> t
1
t1
test for particle contacts
Basic DEM algorithm
• Soft particle approach
14
Modelling of inter-particle forces & torques
• “Physics” is incorporated in the inter-particle interaction model
• Different physical phenomena can be modelled :
- contact forces
- body forces (e.g. gravity)
- rolling resistance
- cohesion (due to moisture, electrostatics, van der Waals …)
- interstitial fluid
- breakage / agglomeration
- …
Implementation DEM technology
15
Implementation DEM technology
Modelling of inter-particle forces & torques
• Contact (collision)
• repulsive force between particles
• Cohesion
• attractive force between particles
• Cluster
• particles in cluster “glued” together
16
Implementation DEM technology
Modelling of inter-particle forces & torques (cont.)
• Bond
• force inhibits relative motion of particles
• Torsional beam
• repulsive force between particles
• Sintering
• overlapping particles “glued” together
17
Modelling of inter-particle contact : relationship between force and overlap
• Example : Cundall model
- based on a combination of linear springs & dashpots
Implementation DEM technology
18
Implementation DEM technology
• The normal contact force Fn (aligned with particle centres) is :
Fn = kn dn + Cnnn ,
where dn is the overlap between particles in the normal direction
nn is the relative velocity of the particles in the normal direction
kn is the normal spring constant (spring stiffness)
Cn is the normal damping coefficient
The damping constant Cn is related to the coefficient of restitution e :
Cn = 2 g [ mred kn ]½
; g = - ln(e) / [ p2+ ln
2(e) ] ½
where mred is the reduced mass = m1
m2
/ ( m1
+ m2
)
Modelling of inter-particle contact : Cundall model
19
Modelling of inter-particle contact : Cundall model
Implementation DEM technology
• The tangential contact force Ft (aligned normal to the particle centres) is :
Ft = kt dt + Ctnt ,
where dt is the overlap between particles in the tangential direction
nt is the relative velocity of the particles in the tangential direction
kt is the tangential spring constant (spring stiffness)
Ct is the tangential damping coefficient
The tangential contact force is limited by the Coulomb frictional limit
Þ particles slide over each other (surface contact shears)
Ft = min ( µ Ft , ò kt nt dt + Ct nt )
where µ is the coefficient of friction
20
Implementation DEM technology
Moving particles due to forces & torques
• Solve Newton equations of motion for particles (and boundary objects)
where
Fij is the total force on particle i due to contact with particle j
Mi j is the total torque on particle i due to contact with particle j
position xi = ui
velocity ui = S Fij / mi
orientation qi = wi
spin wi = S Mij / Iij
j
.
.
.
.
Time-dependent differential equations are solved using a explicit integration method
21
Schematic diagram of DEM implementation
Implementation DEM implementation
geometry design &
surface meshing
Newton
solver
visualization
quantitative
analysis
Pre-processing Computation Post-processing
particle
initializationmodelling
improvement
22
Influence of model choice
• Rectangular hourglass containing 400 identical particles
standard cohesive particles agglomerate material
Implementation Basic examples
23
Influence of particle shape
• Different basic approaches :
• composite particles
(e.g. form cluster by joining spheres)
• non-spherical primitives
- ellipsoids
- spherocylinders
- superquadrics
…
• polygonal assemblies
Implementation Basic examples
non-spherical particles
(5-particle cluster)
24
Influence of interstitial fluid
• Three basic approaches :
• solve Navier-Stokes equations for
interstitial region (coupled DEM/CFD)
• solve Navier-Stokes equations for
porous medium (coupled DEM/CFD)
• add empirical drag force to each particle
(DEM only)
Implementation Basic examples
spherical particles
(empirical drag force)
25
Different types of simulations involving particulate flows and
materials processing of industrial interest have been computed
• industrial flow processing (e.g. mixing, transport)
• geological flows (e.g. avalanches, landslides)
• industrial materials processing (e.g. drilling)
Applications Overview
26
Pétanque
Applications Particulate flows
DEM simulationexperimentation
A candidate for the 2024 Olympic Games
. . . and a physical model for granular damping
27
Blast furnace filling – granular damping in a rotating chute
Results Particulate flows
without support plates with support plates
in collaboration with ArcelorMittal
28
Ball millfor crushing and grinding
of mineral ore
courtesy Magotteaux SA
Comparison of computed and
experimental power draw
800 mm x 400 mm cylindrical mill
rotational speed : 70% critical
19,116 spherical balls
particle diameter : 15 mm
Applications Particulate flows
29
Landslides, rockfalls & debris flow
courtesy of CSIRO, Australia
2.5 x 4 km2
rectangular section
165,000 spherical particles
particle diameter : 2 - 10 m
total mass : 10 million tonnes (2.5 million m3)
S. Wiederseiner – EPFL semester project
Applications Particulate flows
30
Ribbon blender
Applications Particulate flows
high cohesionlow cohesion
500 mm x 300 mm container
dual ribbons rotating at 30 rpm
100,000 spherical particles
particle diameter : 6 mm
particles coloured according
to initial position
influence of inter-particle cohesion on mixing
31
Ribbon blender
Applications Particulate flows
computed mixing in lateral direction :
GMMI(x,y,z) =
0.0
0.5
1.0
1.5
2.0
2.5
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0time [s]
Mix
ing
(GM
MI x
)
no cohesion
low inter-particle cohesion
high inter-particle cohesion
fully mixed
v = 30 rpmd = 6 mm
e = 0.3µ = 0.75
Δ t = 5 ms
Mixing rates
g no = -0.300
g low = -0.143
g high = -0.044
centre of mass of one colour particle
centre of mass of all particles
32
Applications Particulate flows
in collaboration with Sika
33
Applications Particulate flows
34
Applications Particulate flows
35
Agglomerate solid materials
• Three basic steps :
• creation of agglomerate material sample
• creation of inter-particle bonds
• testing of material structural properties
Applications Materials processing
36
Agglomerate solid materials
• Growing particle technique for constructing material :
Applications Materials processing
3D rectangular slab (160 mm x 40 mm x 20 mm)
11,009 spherical particles
particle diameter - initial : 0.8 - 2.0 mm
final : 1.1 - 3.4 mm
37
Agglomerate solid materials
• Flexion testing :
Applications Materials processing
2D rectangular slab (160 mm x 40 mm)
21,243 circular particles
particle diameter : 0.3 - 1.0 mm
inter-particle cohesion
38
Applications Materials processing
Particle comminution
• complex mechanisms involving breakage (normal forces) and attrition (tangential forces)
• particles coloured by normal force
• breakage depends on cumulative
energy loss and/or maximum force
• appropriate material breakage
properties required
39
Applications Materials processing
40
Applications Materials processing
40
41
Sprouted bed
S. Wiederseiner – SGM Master project
Applications Multiphase flows
forced air flow
vertical silo containing
glass beads
Coupled DEM-CFD simulation
for advanced drying of
granular material
42
Coupled fluid-particle simulation
• Pouring beer - “the ultimate multiphase flow”
- liquid (simulated by CFD - Smoothed Particle Hydrodynamics)
- bubbles (simulated by DEM)
Applications Multiphase flows
courtesy of CSIRO, Australia
43
General aspects Further information
Basic DEM textbooks are not common
• A. Munjiza “The combined finite discrete element method” (Wiley 2004)
• Book chapters / review articles (e.g. by P.A. Cundall, J.R. Williams or P.W. Cleary)
• CSE Master course “Particle-based methods” at EPFL-SMA (Spring semester)
Conference proceedings
• e.g. International conference on discrete element methods,
Powder & Grains, ECCOMAS Particles conference
• General engineering conferences
Rapidly growing number of scientific papers
• e.g. Granular Materials, Powder Technology
• Many other engineering journals
2018