kinetic studies in flotation columns: bubble size effect

Minerals Engineering, Vol. 7, No. 4, pp. 465--478, 1994 Copyright ~)1994 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0892-6875/94 $6.00+0.00

0892-6875(93)E0032.8

KINETIC STUDIES IN FLOTATION COLUMNS: BUBBLE SIZE EFFECT

P. DIAZ-PENAFIEL§ and G.S. DOBBY§t

§ Dept. of Metallurgy & Materials Science, University of Toronto, Toronto, Ontario, M5S 1A4, Ca~dA_

MinnovEX Technologies Inc., 955 Wilson 2 Av,, #4 Toronto, Ontario, M3K 1G1, Canada (Received 17August 1993; accepted 16 September 1993)

ABSTRACT

The collection first order rate constant of a flotation column was investigated as a function of bubble size within ranges commonly seen in industrial column flotation practice. The experimental work was done in a 2.5 cm diameter glass colmnn. High purity minerals (silica, pyrite and galena) were used for the test work. Bubble size was varied by varying theft'other dosage, and several flotation tests were performed with different bubble sizes at constant gas rate. Collection efficiencies were calculated using the relationship presented by Jameson. For silica flotation under typical column flotation conditions (of bubble size and gas rate) the collection rate constant was measured to be proportional to db-l.54. This is a much smaller effect of bubble size than other researchers had speculated. It was also observed that the magnitude of the bubble size effect on the rate constant was affected by the particle size. A size by size analysis of the results explains observations fout~l with some industrial columns.

Keywords Kinetics, column flotation, rate constant, gas bubbles

BACKGROUND

Many studies have been made to investigate the effect of bubble size on flotation kinetics. To date there is agreement that a decrease in the bubble size will improve the recovery because of increased surface area and, therefore, greater probability of contact between bubbles and particles. However, the effect has not been quantified over a wide range of operating conditions. Data about the effect of this variable on selectivity is sparse, mainly due to the difficulties in the determination of bubble size. As will be shown in the review, experimental data available on the bubble size effect upon performance of the flotation process has been obtained under extremely idealized situations, namely single bubble systems using diluted slurries with highly hydropbobic particles. Consequently, there is an incomplete understanding of the bubble size effect on flotation kinetics within the ranges and conditions usually seen in column flotation, which are gas rate between 0.5 and 2.5 cm/s and bubble size between 0.8 and 2.0 mm.

Mineral processing literature prior to 1970 records little information on the effect of bubble size. Reay and Ratcliff [1] studied the effect of bubble size using very small bubbles, which were typically less than 0.1 mm. The system under study was liquid effluent that contained particles which were too small to be removed economically in sedimentation tanks or by conventional filters. Because of the low solid concentration and the small particle size, the use of very small bubbles was justified. Despite the problem

465

466 P. DIAZ-PENAFIEL and G. S. BOBBY

associated with the small number of bubble and particle counts in Reay and Ratcliff's work, the trends they revealed were unmlstakeably important, and a major conclusion in this study was that E c o~ db'2.05, where E e is collision efficiency and d b is bubble diameter. Later work done by these authors [2] with bubbles of diameters 0.042 and 0.071 nun rising in a quiescent liquid determined that E ccx db -1.9. Anfruns and Kitchener [3], using a very simplified and controlled system with single bubble generation and very hydrophobic particles in a concentration of 0.1% solids by volume, studied the effect of bubble size on the collection efficiency. The bubble size range used in this study was from 0.6 to 1.0 ram. The experimental results of Anfruns and Kitehener clearly show that collection efficiency increases with decreasing bubble size for the whole range of particle size, which was from 12 to 40.5 I.tm. These studies still today stand up as one of the few sources of experimental data on bubble size effect. A later analysis done by Jameson et al. [4] on Anfruns' data shows that E ccx db-l.69.

The flotation rate constant was modeled by Jameson et al. [4] who used a simplified system, what they called a 'bubble column', in which bubbles were generated at the bottom of a vessel containing an essentially stagnant liquid. According to Jameson's model, the flotation rate constant depends directly on the frequency of particle-bubble collision and their subsequent attachment, the bubble size d b and the gas rate Jg. Jameson's model is the following:

k f l"SJ g EJdb (1)

where E k is the collection efficiency, defined as the fraction of the total particles swept out by a bubble that collide with, attach to and remain attached to the bubble.

Weber [5] derived an expression for particle bubble collision efficiency using most of the assumptions of Reay and Ratcliff. With the sparse data available, mainly from Anfruns and Kitchener, Weber made a comparison between theory and experimental data, finding good agreement for bubbles smaller than 0.6 mm but not for larger bubbles. He attributed the disagreement in the region of large bubbles to several causes: deformation of larger bubbles from spbedcal shape and the effect of the container walls on the larger bubbles, among others. Ahmed and Jameson [6] tried to quantify the effect of bubble size using different materials that were chosen to give a wide range of specific gravity. In this work the researchers also tried to get away from highly idealized conditions and to work in stirred turbulent conditions, which are closer to practical flotation cells. The apparatus used was a typical laboratory flotation cell. The mean bubble size ranged from 0.075 to 0.65 mm. Their results showed an increasing collection efficiency with decreasing bubble size, but because of the effect of other variables, especially the level of agitation, they could not make a general analysis on the effect of bubble diameter in isolation.Yoon and Luttrell [7] derived expressions for the collision and attachment efficiencies of t'me particles by calculating their trajectory as they flow past a bubble in streamline flow. Using very hydrophobic coal particles (the experimental technique was the same as the one used by Anfruns and Kitchener), they determined experimentally the collision efficiency with results that were in close agreement to those predicted theoretically. A general expression for the collection efficiency given by Yoon is:

ek=A(aJd~) n (2)

where A and n are parameters which vary with the bubble Reynolds number. The range of bubble size investigated by Yoon was between 0.05 and 0.55 nun, very small bubbles not commonly found in column flotation. Yoon's work did not deal with selectivity.

Dobby and Finch [8] suggested that water recovery (or entrainment) increases when bubble size is reduced. They acknowledged that smaller bubbles would increase particle-bubble collision and, therefore, recovery, especially of free particles. However, they advised that the advantage of using small air bubbles in column flotation was not as straightforward as first impression would indicate. Considering the interaction between bubble size, gas rate and slurry flowrate, they studied the combined effect of these variables upon the rate of particle collection in columns. Two major conclusions from this study were:

Kinetic studies in flotation columns 467

there is a maximum gas rate, Jgm, that can be applied, above which flooding will occur. Smaller gas bubbles and higher downward liquid velocity both act to decrease this maximum limit on gas rate. for a specific bubble diameter, the maximum collection rate constant is obtained while operating at (or close to) Jgm" There exists a bubble diameter that optimize8 the rate of particle collection if column operation is at Jgm"

From this study two arguments to establish a minimum bubble size can be derived:

selectivity: smaller bubbles will increase the feed water recovery and the bubble collection efficiency. The increase in recovery might be at the expense of selectivity. Experimental evidence on the effect of bubble size upon selectivity is sparse. maximum air flow-rate: a decrease in bubble size will decrease the maximum limit for the gas rate at which the column can operate; over this limit gas slugging will appear. There is satisfactory evidence about this effect.

Objective

To determine the effect of bubble size on the collection zone flotation rate constant on a size by size basis within ranges commonly found in industrial flotation columns.

EXPERIMENTAL APPROACH

Apparatus

The experimental work was performed in a glass laboratory column, 2.5 cm in diameter and 250 cm in height. The experimental setup is shown in Figure 1.

Variable speed peristaltic pumps were employed for feed, tailing and wash water pumping and control. Calibrated Cole Palmer rotameters, which required manual setting, were used to monitor the air and wash water entering the column. Bubbles were generated by porous stainless steel spargers mounted in the bottom of the column. The column used laboratory quality compressed air, which was set to 25 psi using a Matheson regulator then passed through a rotameter. The feed port was located approximately 1.0 m below the concentrate lip. Manometers were used to determine gas holdup. A plexiglass box filled with water was placed midway between the two manometers around the column to reduce the distortion caused by the curved wall. A Minolta 3xi camera, provided with close up lenses, was used to obtain photographs of the bubble swarm.

The test colunm was operated with sufficiently high bias to ensure that an interface did not exist. Therefore, the results of flotation tests provide information on the collection process only, i.e. no froth zone effects.

Bubble Size Determination

Drift flux analysis, first used for estimation of bubble size by Dobby et al. [9], was chosen to determine bubble size because of its simplicity. The validity of the method has been established by comparing the calculated bubble diameter with photographic measurements [10]. Confirmation of the drift flux approach was also obtained as part of this project.

Air-Water System

Tests were run in counter-current mode to determine bubble size as a function of air flow rate and frother concentration. Gas rates were between 0.4 and 2.7 cm/s (expressed as the value midway between pressure points) and liquid rate was around 0.8 cm/s. The average bubble size determined by the drift flux

468 P. DIAZ-PENAFIEL and G. S. DoaeY

approach was compared to photographic measurements. In the latter technique the average bubble size was determined by projection of the negatives; with this an enlargement of approximately 8 times was obtained. Bubbles were counted and measured with the Tektronix digitizer which was connected to a computer that registered each bubble size and the number of counts. This data was processed by the computer to calculate average bubble size (expressed here as volumetric mean) and the standard deviation.

Vu~t m0

bed,

eaJleetJo| /ame

J3

10

lht~

t e,tmtat,

Ig,

T~Ubp

6

1 Golumn 2 8ptrger 3 OlsJJ box 4 Rottmetor 5 Gtmert 6 Mtnometor8 7 Vtritble spoed pump 8 Pump.Oontro l 9 Mixer 10 Gonts lner

Fig. 1 Experimental setup

Figure 2 shows bubble size (ram) obtained with the two above mentioned techniques, from both the current research and from Yianatos' work; as can be seen, there is excellent agreement for both sets of data. The bubble size estimation is within the experimental error range reported to be around 15 % [10]. An important fact to mention is that the determination of gas holdup and therefore bubble size is difficult (larger experimental error) at low values of gas holdup. This is clearly shown in Figure 2 (lowest bubble size value) where the agreement between the two techniques was poorer (in this data the lowest gas rate was used to obtain the smallest gas bubbles and therefore a low value in gas holdup was reached).

Entrainment Test

The research is focused on the collection zone, working without an interface to eliminate dropback from the froth zone. To achieve this condition a high positive bias rate is needed. Falutsu [11], working with


a similar setup, found that with a positive bias higher than 0.13 cm/s and a washing zone height over 87 cm, the entrainment in a 2.5 cm diameter column is negligible. Thus, with these conditions the particles will reach the top of the column only by flotation. The washing zone, shown in Figure 1, is created as a result of adding water to the collection zone. (Wash water is not added at this point in a conventional column operation.)

2.0

1.5

1.0

O.S ~ J

E x

m

Q ~

m

'U

E 2 ,L~ 'U

pS ppS

+ls~," / I

#sS SSSp / ssSSSSI

I ss SSS ssss 1 5%

/ I

S t

0.0 , , , . I , , , , I

0.0 0.5 1.0

o Yianatoe L • Thb work

i l l . . . |

1.5 2.0

db from photograph (mm)

Fig.2 Comparison of measured (photographically) and predicted (drift flux) bubble diameters.

Silica, with a ds0 of approximately 35 pm, was used to confirm the bias level necessary to minimize the recovery due to entrainment. Flotation experiments were run at gas rates between 0.8 and 2.5 era/s, using slurry with 10 w % solids, 20 ppm Dowfroth and no collector. The bubble size range was between 1.0 and 1.3 ram.

The level of entrainment recovery at different gas rates was measured to be negligible when the column is operated with a positive bias. The test was run without collector and it was assumed that particles reaching the top of the column were entrained and not attached to the bubbles. From the experimental results and previous work [11] it was concluded that operating the column with a bias rate around 0.1 em/s and a washing zone height over 87 em ensured that the recovery due to the entrainment mechanism was negligible, and could therefore be ignored.

Material

Silica (s.g. 2.7), pyrite (s.g. 4.9) and galena (s.g. 7.6) were used to run flotation experiments (providing a wide range in specific gravity). High purity minerals were chosen to eliminate liberation concerns and the need for assaying. Silica from the U.S. Silica Company was selected to start the experimental campaign because there was practically no need for material preparation.

Galena and pyrite were purchased from Ward Minerals. The original size of the samples was between 1.5 and 2.0 inches. The minerals were crushed in a lab jaw crusher and then by a gyratory crusher before

470 P. DIAZ-PENAFIEL and G. S. DOBBY

being ground in a dry ball mill. The grinding time for pyrite was approximately 1 hour. Wet sieving using a 53 I~m sieve (270 mesh) was performed on the pyrite. The undersize was saved and frozen while the oversize was dried and sent back to the ball mill. For the galena a shorter grinding time of 35 min was found to be appropriate, and a 106 ~m sieve (150 mesh) was used to classify the material following a procedure similar to the one mentioned above.

Silica Flotation Tests

Flotation tests in countemurrent mode were run using silica slurry at 15 95 solids, 30 ppm of dodecylamlne collector and Dowfroth 250C as frother with concentration ranging between 0 and 50 ppm. The air flow rate range was from 0.47 to 2.5 cm/s. Tailing flow rate was set between 230 and 250 cc/min and the feed flowrate was set around 210 cc/min to ensure a positive bias (of about 0.1 cm/s). Typical liquid residence time was around 5 minutes. In all the tests the interface between the collection and froth zones was eliminated. As a result of the different frother concentrations used, different bubble sizes were obtained.

Sulphide Flotation Tests

The sulphide tests were run using pyrite and galena (separately) with the slurry at 10 weight 95 solids. The flowrates and bias level were similar to the ones used in the silica flotation tests. Preliminary batch flotation tests were performed to determine an appropriate dosage of collector, which was found to be around 300 ppm of sodium isopropyl xanthate for pyrite and 50 ppm of Aerofloat 241 promoter for galena.

Particle size analysis

Particle size analysis was conducted with the Brinkmarm PSA model 2010 which uses a rotating laser beam to scan the particles contained in a diluted suspension. Further information on this technology can be found elsewhere [12]. The samples were tested using a glycerol solution as a dispersant (glycerol increases the density and viscosity of the liquid mixture, helping to maintain the solids in suspension). Prior to the measurement, ultrasound was applied to the sample for 15 minutes t o break down agglomerates.

RESULTS and DISCUSSION

Silica system

A plot of silica recovery versus bubble size at a constant gas rate of 1.53 crrds is shown in Figure 3; bubble size has been varied by changing the frother dosage from 1 to 50 ppm. The plot shows the strong effect of bubble size on the recovery of silica, with smaller bubbles producing the highest recovery.

Residence time varied by :t: 0.6 minute. To compensate for this variability, collection rate constant needs to be considered. Assuming a plug flow regime the kinetic rate constant can be determined, since the recovery and retention time are either known or can be calculated.

Figure 4 shows the effect of bubble size on the collection rate constant for air rates between 1.0 and 2.5 cm/s. There is a strong and non linear effect of bubble size on the rate constant. The relationship between k and d b has been reported as k ot db'n. From a linear regression on the data in Figure 4, the exponent n for gas rates between 1 and 2.5 cm/s is 1.54 with a regression coefficient of 0.88. Therefore, for the silica sample:

J~(g - - 1


(3)

over the bubble size range of 0.8 to 2.0 mm

Substituting eq. (3) in the expression for the first order kinetic rate constant, eq. (1), yields the result:

l (4)

d ~

when the gas rate is held constant.

100

80

g =z

40

20 e I t I e I m I , e

0 . 6 0 . 8 1 . 0 1 .2 1 . 4 1 . 6 1 . 8 2 . 0

Bubble diameter (mm)

Fig.3 Bubble size effect on recovery of silica. I |=0 .8 cm/s ~1=4.5 :t: 0.6 rain, collector--30 mg, frother dosage from 1 to 50 ppm

Gee rate (enVe)

o.4~ ~ A ,,= I

L " ' i

0.1

0 . 0 . . . . ' . . . . ' , , ! , O.S 1.0 1.8 1.0 2.6

BubMe size (ram)

Fig.4 Silica collection rate constant as a function of bubble diameter, for five levels of gas rate. Jl-- 0.8 cm/s, z1=4.5 :t: 0.6 rain, collector-- 50 mg

472 P, DIAZ-PENAFIEL and G. S. DOBBY

The exponent of 0.54 for the relationship in eq. (4) is considerably lower than the value reported by Anfruns and Kitchener (1.69) and even lower than the values found by Reay and Ratcliff (1.9 to 2.05) and Yoon and Luttrell (1 to 2, depending on d b range). Figure 5, where the collection efficiency versus the bubble size has been plotted on a log-log scale for a particle size range between 11.4 and 13 Ism, clearly shows the difference among the authors. This difference can be explained by considering the following three factors:

(i) Bubble size was less than 0.1 mm for Reay and Rateliff's work and less than 0.55 nun for Yoon's work. Bubble size used not only in the present study but also in industrial flotation plants is considerably larger (0.8 to 2.0 ram). According to previous research, the bubble size effect is stronger for the region of small bubbles than for larger bubbles. Therefore, a decrease in the exponent is expected when moving to larger bubble size.

(ii) Anfruns and Kitchenor, as well as Yoon and LuttreU, used very hydrophobic particles. This high level in hydrophobicity allowed them to assume the attachment efficiency equal to one. Therefore, these two studies dealt with bubble size effect upon collision efficiency, rather than on collection efficiency as the current study does.

(iii) The work by the other authors was conducted with single bubble, diluted slurry systems. While this facilitates the assessment of the effect of bubble size on the collision efficiency for a sp~ifie type and size of particle, the real system has high bubble voidages. Therefore, the question is raised as to how close the collision effieiencies measured in single bubble systems represent the actual situation.

o I : o

m

o

4D

I: o

m

o _e m

o O

.01

.001

%

A dp 11.4 um (Yoon) c0ei

• dp 12.0 tan (Anfrum) silica

12 dp 13.0 urn (This work) silica

~o d ] n r l n

. 0 0 0 1 . . . . . . . . . . . . . . 100 I000 10000

Bubble diameter (urn)

Fig.5 Collection efficiency of silica versus bubble diameter for fine particles and three sets of research results.

Using eq. (1) the collection efficiency was determined for the results given in Figure 4. Figures 6 and 7 show, respectively, the rate constant and the calculated collection efficiency versus particle size for three bubble sizes (0.8, 1.2 and 2.0 ram). As already discussed, d b clearly has a strong effect on the collection efficiency; smaller bubbles are more efficient in the collection of particles. An important observation to


make is that the collection efficiency versus particle size curve passes through a maximum. The existence of this maximum was reported and modelled by Dobby and Finch [13]. They explained the maximum by taking into consideration the opposing effect of particle size upon collision and attachment; as dp increases E c increases but E a decreases. There has been recovery-size data reported for many systems [14] that are also in accord with the existence of this peak. Another observation from the theoretical work of Dobby and Finch is that the peak shifts to larger dp as the bubble size decreases, which implies that smaller bubbles will be more effective in the collection of larger particles.

ME 7:4-D

1.5

1.0

i oo

J 0.5,

0.0

• db 0.8 mm

rt db 1.~ mm

0

D •

10 20 3'0 40 50

Particle size (um)

Fig.6 Rate constant versus particle size, for three d b. Jl=0.8 era/s, Jg= 1.53 cm/s

le-3

O ,me U

I s C O i

g O 0

8e-4

6e.4

4e-4

2e-4

Bubble size

• 0.8 mm

[] 1.2 mm

• 2.0 mm

D

o . . o , , , , , , - • , . 0 5 10 15 20 2 5 0 3 35 40 45

Particle size (urn)

Fig.7 Collection efficiency on a size by size, for three d b. J l = 0 . 8 c m / s , Jg= 1.53 cm/s

474 P. DXAZ-PEN^F]EL and G. S. DoBsY

Finally, Figure 7 shows that collection efficiency is quite insensitive to bubble size for very small particles, dp < 3-5 I.tm. This observation is important because it is in disagreement with the general belief that smaller bubbles are more efficient in the collection of fine particles.

The rate constant as a function of average bubble size is presented in Figure 8 for four mean particle sizes and a Jg ffi 1.53 cm/s. The trend reported for the overall rate constant (Figure 4) is reproduced in the size by size analysis; k ,,, db'n. The exponent n was calculated for nine mean particle sizes (the regression coefficient R 2 was 0.73 and 0.84 for particle sizes of 4 and 7 I.tm respectively and over 0.95 for the other sizes). The results are shown in Figure 9. Clearly, the bubble size effect on the rate constant is a strong function of the mean particle size; as particle size increases the bubble size effect becomes stronger. A summary of these observations is that the bubble size effect on the collection efficiency is weak for freer particles, dp < 5 I~m, and the magnitude of the bubble size effect increases with increasing particle size.

£ I I

0 0

e W n"

1.5

1.0

0.5

\

0

Particle size

• 4 um

O 7 um

• 13 um

/1 34um

A

0.0 m I , I n I n I , I n I ,

0 . 6 0 . 8 1 .0 1 .2 1 .4 1 . 6 1 . 8 2 . 0

Bubble size (ram)

Fig. 8 Silica collection rate constant as a function of bubble size, for four mean particle sizes. Jl=0.8 cm/s, Jg= 1.53 cm/s

Sulphide system

Figures 10 and 11 show rate constant as a function of mean particle size, for pyrite and galena, respectively. These curves can be compared with the data for silica Figure 6. Note that the range of d b is not as large for the pyrite and galena tests as it was for the silica tests.

Simulated effect of bubble size on recovery

Using the kinetic data from the experiments with silica, a simulation of full scale column performance has been conducted, with the objective of examining bubble size effect on a size by size performance. Three bubble sizes were used. The underlying assumption is that longer residence time, i.e. lower feed rate, is required for operation with larger gas bubbles (which compensates tbr the lower rate constant observed with larger bubbles) in order to achieve the same recovery for a given particle size class.


2.2

2.O

1.6

1.4

1.2

• I . I • I . |

1 0 2 0 SO 4 0 6 0

Particle size (um)

Fig.9 Exponent n (in the expression k a db "n) versus particle size

s

W

G o u

E )

4 1 n.

1.0

0.8

0.6

0.4

02

Bubb le size

• 1.13 mm

D 1.64 mm

• I J ~ m m

1.0 0

D

0 , 0 ! • I , | • I • ! • | • |

0 5 10 15 20 25 30 35 40

Particle size (um)

Fig. 10 Pyrite collection rate constant versus particle size, for thr¢o bubble sizes. 31.:0.8 cm/s, Jg= 1.53 cm/s, collector--320 mg

The University of Toronto simulator [15] was used for the calculations. The simulation was made for an industrial colunm of 2.5 m diameter and 6 m collection zone height in which the froth zone recovery was assumed to be 40 %. The residence time was varied until the recovery for an average particle size of 13 ~m was the same (preset value of 72.5 %) for the threo bubble sizes used in the simulation.

476 P. DIAZ-PENAFIEL and G. S. DoBB¥

o.e

0.5

0.4

=. 0.3

-" o=

0.1

0.0 0

Bubble ,size •

•

(2 1.66 mm ~ - -

.A 1 . . r am . ~

i 5 10 15 20 25 30 35

Part ic le s ize (urn)

Fig. 11 Galena collection rate constant versus particle size, for three bubble sizes. Jl=0.8 cm/s, Jg= 1.53 cm/s, collector=52 mg

The size by size recoveries are given in Figure 12. From this figure it can be observed that larger bubbles have a higher rejection of coarse particles (lower recovery).

lOO

8O

o ~

g , o ¢c

20

• b •

I

0 1.86 mm

0 i I i I i I i I ,

0 10 20 30 40 50

Particle size (um)

Fig. 12 Simulated recovery for an industrial column on a size by size basis. (see text for conditions)


This phenomenon has been reported in industrial colurnn A by Espinosa-Gomez and Johnson [16]. The authors made several size by size comparisons for two columns at Mount Isa's Hilton Mine in Australia. The columns of 2 m diame-te+ r and 50 mm diameter were operated under similar conditions, except with the important difference of gas holdup used in each (gas holdup was higher in the 50 mm column, which indicates the presence of smaller bubbles). The most important difference in performance between the units reported by Espinosa-Gomez was the higher rejection in the plant columns of coarse particles (+ 30 microns) containing galena and non sulphide gangue. A similar behaviour was observed for sphalerite in zinc cleaner columns.

The mechanisms which most likely cause the preferential rejection of coarse particles in the plant columns according to these authors are:

a) more coalescence tak/ng place in the froth due to both the larger bubble size and higher residence time (60 minutes vs 10 minutes) in the plant column, and

b) proportionately higher solids drop-back of coarse particles due to the longer distance that particles need to travel to be discharged (0 to 1000 nun vs 0 to 25 ram).

Neither of these two mechanisms can be discarded without more information on the froth zone behaviour. However, a third one can now be added, this one based on the different bubble sizes present in the two units. In practice, as shown by Espinosa-Gomez, this behaviour has important implications in the metallurgical performance of an industrial column. Larger particles are likely to be composites (valuable- gangue particles) and the desired destination for these composites is the tailing stream. According to our results, this would more likely be achieved if larger bubble sizes were used. A comparison made in the bulk lead-zinc concentrate circuit at Mount Isa, where it is known that the proportion of composite is higher than in the other column circuits, shows that plant columns (larger bubbles) always give a better performance than the 50 mm column (smaller bubbles). Certainly these practical results support the suggestion that sometimes better metallurgical performance can be achieved by using larger bubbles.

(1)

(2)

(3)

(4)

(5)

CONCLUSIONS

The collection rate constant is affected by the average bubble size. Smaller bubbles deliver a higher rate constant, as theoretically derived and experimentally proven previously by other authors. For the bubble range 0.8 to 2.0 nun and gas rate range 1.0 to 2.5 cm/s the rate constant is an exponential function of the bubble size; for the silica tests k = db'l'54- and E k a db'0.54. These are the first known measurements on the effect of bubble size on collection rate constant for these gas rate and bubble size conditions, which represent industrial practice.

The exponent n in the relationship k a db'n varies with particle size. For the silica system n ranged from 1.15 to 2.08 for dp = 4 to 41 I.tm.

For the bubble size range studied (0.8 to 2.0 ram) smaller bubbles are more efficient in the collection of coarse particles. For very small particles (dp < 5 I.tm) the bubble size effect on the collection efficiency is quite weak. Above 5 I.tm the bubble size effect becomes stronger with increasing particle size.

Using smaller bubbles will not always bring an improvement in metallurgical performance, especially when a high proportion of composites is present in the flotation circuit.

A rational explanation for the difference in size by size behaviour observed between pilot and full scale columns at Mount Isa Mines has been given.

478 P. DIAZ-PENAFIEL and G. S. DOBeY

ACKNOWLEDGEMENTS

Funding by the Natural Sciences and Engineering Research Council is gratefully acknowledged.

R E F E R E N C E S

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15.

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