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Effect of flotation frothers on bubble size and foam stability
Int. J. Miner. Process. 64 Ž2002. 69–80 www.elsevier.comrlocaterijminpro
Effect of flotation frothers on bubble size and foam stability Y.S. Cho, J.S. Laskowski ) Department of Mining and Mineral Process Engineering, UniÕersity of British Columbia, 6350 Stores Road, VancouÕer, B.C., Canada V6T 1Z4 Received 1 March 2001; received in revised form 15 June 2001; accepted 2 July 2001
Abstract In order to study the effect of frothers on the size of bubbles, experiments were carried out using single- and multi-hole spargers and a flotation cell. It was found that the size of bubbles strongly depends on frother concentration only when multi-hole spargers are utilized Žor when measured in a flotation cell.. At low frother concentrations Ž C - CCC., the bubble size is much larger, indicating coalescence as a main mechanism determining the size. Coalescence can be prevented at frother concentrations exceeding the critical coalescence concentration ŽCCC.. The foamability tests indicate that stability of foams under dynamic conditions is determined by bubble coalescence. q 2002 Elsevier Science B.V. All rights reserved. Keywords: flotation; frothers; bubbles; spargers; critical coalescence concentration; dynamic foamability index
1. Introduction Flotation kinetics involves a number of mass transfer processes with some taking place in the pulp phase Žparticle–bubble collision and attachment, transport of particle– bubble aggregate to the froth phase. and some in the froth phase Žrecovery of particle from the froth phase to concentrate launder.. All of these subprocesses depend strongly on bubble size and froth stability. In a flotation process, frothers are utilized to enhance generation of fine bubbles and to stabilize the froth. According to Leja–Schulman’s penetration theory, the interaction of frothers with a collector in the moment of the particle-to-bubble attachment is a vital step in the particle–bubble attachment. )
Corresponding author. E-mail address: [email protected] ŽJ.S. Laskowski..
0301-7516r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 Ž 0 1 . 0 0 0 6 4 - 3
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Y.S. Cho, J.S. Laskowskir Int. J. Miner. Process. 64 (2002) 69–80
It is known that pure liquids do not foam, but the presence of surface active molecules that preferentially adsorb at a liquidrgas interface changes this situation radically. Recent measurements of bubble size, dynamic foamability index and surface tension for a series of flotation frothers ŽFig. 1. showed a very good correlation between bubble size and dynamic foamability ŽSweet et al., 1997.. While the bubble size and dynamic foamability index were found to be sensitive to very low frother concentration changes, the surface tension was observed to be affected by the frother only at concentrations more than 10 times higher. Since the previously derived equations relate the size of generated bubbles to surface tension, and the surface tension does not seem to change much at very low frother concentrations, the question, therefore, arises why the bubble size depends on frother concentration. In order to answer such questions, we carried out a series of experiments in which specially designed spargers were used and the size of the bubbles was measured over a broad concentration range for different frothers. In concomitant experiments, the dynamic foamability index and the surface tension were measured for the same frothers. 2. Experimental procedures 2.1. Materials Experiments were performed using MIBC and four different hexanol isomersrderivatives kindly provided by the Condea Vista. MIBC Frother 1 Frother 2 Frother 3 Frother 4
Methyl isobutyl carbinol 1-hexanol Di ethoxy-mono propoxy hexanol Di ethoxy hexanol Mono propoxy-di ethoxy hexanol
wŽCH 3 . 2 CHCH 2 CHŽOH.CH 3 x wC 6 H 13 OHx wC 6 H 13 OHŽEO. 2 ŽPO.x wC 6 H 13 OHŽEO. 2 x wC 6 H 13 OHŽPO.ŽEO. 2 x
2.2. Methods 2.2.1. Bubble size measurements The UCT bubble size meter was employed to measure the bubble size as described by Tucker et al. Ž1994.. The bubbles were generated in a 3-l Plexiglas tank using distilled water. All experiments were conducted at 21 8C. Approximately 3000 bubbles were sampled during each run. Three runs were carried out for each concentration of tested surfactant, the average of three runs was reported and the experimental details were provided in another paper ŽCho and Laskowski, 2001.. Bubbles are commonly produced by sparging, that is pumping gas through a capillary or frit into the bulk liquid. In mechanical flotation cells, they are produced by cavitation at the trailing edge of the impeller blade, or if the air is supplied under pressure by breaking it into fine bubbles by shearing forces. The size of a bubble forming at an orifice under equilibrium conditions can be calculated using thermodynamic data which show clearly dependence on the surface tension. However, in most practical cases in which rapid bubble formation occurs, the equilibrium calculations are inadequate to predict the detachment volume ŽLubetkin, 1993.. To create the conditions as close to
Y.S. Cho, J.S. Laskowskir Int. J. Miner. Process. 64 (2002) 69–80
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equilibrium as possible, the bubbles in our experiments were generated at very low air flow rates of 2 cm3rmin and a Bel-Art Rite flowmeter was used. The sampler of the UCT bubble size analyzer was placed 50 mm above the sparger. A few different spargers were tested. A flexible latex sparger that contained two punctures made using a hypodermic syringe in a stretched latex sheet, far away from each other to eliminate coalescence, consistently produced bubbles of uniform size as shown in Fig. 2 Žstandard deviations of 0.057 and 0.029 mm.. However, probably because of the different hole dimensions, the size of the generated bubbles was observed to be very different Ž1.45 vs. 2.15 mm.. Since in the latex type spargers used by Rice et al. Ž1981., the punctured holes are not spherical, it is impossible to determine the exact hole diameter. Therefore, we also employed rigid, bronze spargers. While the hole diameter can easily be determined for such spargers, it turned out to be impossible to obtain a steady stream of bubbles when using such spargers. Rice and Lakhani Ž1983. noticed that at superficial gas velocities of less than 5 cmrs, a rubber sparger produced a homogenous stream of bubbles as compared to the very unpredictable and irregular flow of bubbles varying in size when rigid spargers were employed. Since the only difference between the latex sparger and the rigid bronze plate sparger is the flexibility of the former and its ability to oscillate and deform as gas passes through, it was decided to vibrate the rigid sparger. The sparger tank was mounted on a Syntron Lapping–Polishing Machine and vibration was applied. As the frequency of the vibration increased stepwise, a small window of frequency was found in which the size of the generated bubbles became very uniform and consistent Žwithin 5%. over five runs of the bubble size measurements. This vibration frequency was, thus, set for the entire experiment. In the bubble size measurements in an open top Leeds flotation cell, the impeller speed was set at 1000 rpm and the air flow rate was 5 lrmin. The sampler of the bubble size analyzer was positioned 50 mm above the stator. 2.2.2. Sparger hole size determination Following published data ŽDobby and Finch, 1986; Diaz-Penafiel and Dobby, 1994., it was decided to work with bubbles of 1–2 mm in size, as they are most common for flotation systems. Using Eq. Ž4. below, the required size of the sparger opening was calculated to be within 0.1–0.15 mm, and drills of this size were used. 2.2.3. Dynamic foamability index Since this methodology employs a two-phase system consisting of liquid and dispersed air, we have decided to use the term foam instead of froth as used in the original publications by Malysa et al. Ž1978, 1981.. The foamability measurement in Malysa’s procedure defines the retention time, rt, as the slope of the linear part of the dependence of the total gas volume contained in the system Žsolutionq foam. on the gas flow rate. Values of the retention time are claimed to be independent of the gas flow rate and geometry of the measuring column. Physically, rt is the average lifetime of a bubble in the whole system, i.e. in both solution and foam. The dynamic foamability index ŽDFI. is defined as the limiting slope of rt vs. concentration for c ™ 0. Ert DFI s Ž 1. Ec cs 0
ž /
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Y.S. Cho, J.S. Laskowskir Int. J. Miner. Process. 64 (2002) 69–80
Alternatively, it is possible to fit an equation to the rt values vs. c data in order to alleviate the need to find the initial slope graphically. The equation takes the form of an inverse exponential, which when expanded into a power series gives: rt y 2.4 s DFI P c Ž 2. where DFI s rt` P k Ž 3. The quantity 2.4 was given by Malysa as the value of rt for distilled water, rt` is the limiting rt value for c ™ ` and k is a constant. In our tests, the frother aqueous solutions were placed in the column Ž45-mm diameter, 92-cm height.. Nitrogen was pumped through the sintered glass disk initially at a flow rate of 100 cm3rmin, which was then increased stepwise up to 2000 cm3rmin. After each change, the resulting steady state volume Žsolutionq foam. was recorded. The total volume was plotted vs. flow rate to obtain the slope Žretention time. via linear regression. 3. Results Fig. 1 compares the effect of concentration of two hexanol isomers on bubble size, retention time Žfoamability. and surface tension ŽSweet et al., 1997.. In order to facilitate comparisons, the results were plotted in a normalized form. The term AnormalizationB is used to describe the ratio of the parameter of interest to its value measured at zero surfactant concentration.
Fig. 1. Normalized retention time, Sauter mean bubble diameter and surface tension of n-hexanol and MIBC ŽSweet et al., 1997..
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As shown, the surface tension seems to be least sensitive to the surfactant concentration; both bubble size and retention time are affected by the frother at the concentrations at which the surface tension values are practically identical to that of distilled water. This figure reveals that bubble size is much more sensitive to the surfactant concentration than surface tension and perhaps could be used for analytical purposes to test the presence of surface active substances at very low concentrations. Similar plots for other frothers show the same trend. Discussion of these results was hindered by the fact that the bubble size and foamability in this project were measured in Cape Town tap water, while the surface tension data obtained using distilled water were quoted after other sources ŽSweet et al., 1997.. 3.1. Single-hole spargers Frothers did not show any effect on bubble size when bubbles were generated from a single-hole latex sparger. Fig. 2 shows quite uniform bubble sizes regardless of frother concentration. Eq. Ž4. quoted after Rubinstein Ž1995. shows that the bubble size depends only on inner capillary Žor sparger size. and surface tension of the solution. db s
ž
6 dc g g Ž r l y rg .
1r3
/
Ž 4.
where d b is the diameter of the bubble, g is the surface tension of the liquid, d c is the size of the capillary, r l is the density of the liquid and rg is the density of gas.
Fig. 2. Effect of frother concentration on bubble size using a latex sparger.
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Table 1 Comparison of calculated vs. measured bubble diameter sizes Capillary diameter Žmm.
Calculated bubble diameter sizes Žmm.
Average measured bubble diameter sizes"S.D. Žmm.
0.10 0.15
1.65 1.88
1.65"0.029 1.89"0.017
Since the surface tension was practically constant throughout the tested frother concentrations ŽCho and Laskowski, 2001., the size of bubbles was expected to be uniform for the same spargers. As shown in Fig. 2, the results are consistent with published Eq. Ž4.. The tests carried out using the bronze sparger gave similar results. Calculated Sauter mean diameters of the bubbles generated from 0.1 and 0.15 mm spargers were 1.65 and 1.88 mm, respectively. The average bubble sizes actually produced from the bronze spargers were in perfect agreement with the calculated sizes as shown in Table 1 and Fig. 3. Indeed, the bubble size did not change with frother concentration. 3.2. Three-hole sparger (0.1 mm) and flotation cell tests Since the frothers do not affect the size of bubbles generated using a single-hole sparger, the only possible mechanism to change the bubble size when a multi-hole sparger Žor a flotation cell. is utilized would be by coalescence andror breakage of the bubbles. The measured bubble sizes were much smaller than the critical size subjected to breakage ŽPrince and Blanch, 1990. and, therefore, bubble breakage should be ruled out
Fig. 3. Effect of frother concentration on bubble size using a bronze single-hole sparger.
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Fig. 4. Effect of frother concentration on bubble size using 0.1-mm diameter three-hole bronze sparger.
as a possible mechanism for the bubble size changes. This leaves bubble coalescence as the only possible mechanism responsible for bubble size changes in our multi-hole sparger experiment. Taking 1.65 mm Žfrom Table 1. as the average diameter of the bubble generated from 0.1-mm sparger, three 1.65-mm bubbles when coalescing should give a larger bubble of 2.38 mm in diameter. This is again in a perfect agreement with the measured bubble diameters without frothers ŽFig. 4.. As the concentration of frothers increased in the solution, the degree of coalescence decreased. More powerful frothers Žfrothers 2 and 4. prevented the bubble coalescence at lower frother concentrations. As the measurements of surface tension revealed ŽCho and Laskowski, 2001., frothers 2 and 4 turned out to be more surface active than frother 3, hexanol and MIBC. The obvious difference between these two groups is the presence of propylene oxide group in frothers 2 and 4.
4. Discussion It is commonly believed that the bubble size decreases with an increase in the frother concentration owing to a decrease in the surface tension induced by the addition of surfactants. By the way, this was one of the conclusions drawn in a very recent paper ŽAldrich and Feng, 2000.. As the results presented in our paper Žand in another paper by Cho and Laskowski Ž2001. demonstrate, at frother concentrations typical for the froth flotation systems, the bubble size is not affected at all by a frother if the bubbles cannot collide with each other. The results obtained by Sweet et al. Ž1997. already hinted that
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Fig. 5. Effect of frother concentration on bubble size measured in an open-top Leeds flotation cell.
there is a poor correlation between bubble size and surface tension. Figs. 2–5 explain why. As these figures reveal, in the experiments in which one-hole spargers were utilized Žin other words, when the bubbles could not collide with each other., there was no effect of frother concentration on the bubble size. If the experiments were carried out using multi-hole spargers, or were carried out in a flotation cell, the size of bubbles was substantially larger at low frother concentrations.
Fig. 6. Effect of frother concentration on bubble size Žschematic..
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Table 2 Comparison of CCC values obtained using a three-hole sparger and an open-top Leeds flotation cell Frothers
Three-hole sparger CCC values Žmolrl.
Open-top flotation cell CCC values Žmolrl.
MIBC Frother 1 Frother 2 Frother 3 Frother 4
0.000079 0.000079 0.000013 0.000031 0.000016
0.000083 0.000083 0.000015 0.000037 0.000015
It is obvious that with increasing frother concentration, the degree of bubble coalescence decreases and at a particular concentration Žcritical coalescence concentration., the coalescence of the bubbles is completely prevented ŽFig. 6.. The stronger frothers reach the CCC point at a lower concentration. The values of CCC seem to characterize frothers very well. At concentrations higher than CCC, the coalescence does not occur. The three-hole sparger experiment, which was conducted in a controlled environment, provided CCC values that were identical to those obtained in a flotation cell. This implies that the CCC values obtained for a given frother in a small-scale laboratory experiment Ži.e. three-hole sparger. do not depend on a type of flotation cell. As seen from Table 2, the five tested frothers are characterized by unique CCC values. As shown in another paper ŽCho and Laskowski, 2001., the CCC values could also be obtained from Tucker et al.’s Ž1994. data who measured the size of bubbles in a flotation cell using DIBK Ždi-isobutyl ketone., TEB Žtriethoxybutane. and MIBC frothers. Fig. 7 shows the interrelation between CCC and DFI and demonstrates that the foamability of aqueous solutions measured under dynamic conditions is determined by
Fig. 7. Relationship between DFI and critical coalescence concentration for the tested frothers.
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Table 3 DFI values for various commercial frothers using Cape Town tap water ŽSweet et al., 1997. Frothers
rt` Žs.
k Ždm3 rmol.
DFI Žs dm3 rmol.
n-Butanol 2-Butanol t-Butanol n-Pentanol n-Hexanol n-Heptanol n-Octanol n-Octanol 2-Ethyl-hexanol MIBC a-Terpineol Texanol TEB DowFroth400 DIBK n-Butanola
20.5 12.7 10.8 22.6 62.6 82.5 87.3 61.1 68.3 55.0 27.1 31.2 34.7 72.8 21.5 20.8
65.3 65.0 146.6 243.7 539.6 495.6 908.5 2313.3 2066.8 672.2 5093.9 10,392.7 7279.4 11,025.7 3589.6 61.0
1339 826 1588 5517 33,779 40,867 79,338 141,226 141,147 36,991 138,171 323,901 252,589 802,142 77,019 1271
a
Test conducted in distilled water.
bubble coalescence. More surface active frothers are characterized by lower CCC and higher DFI values. The DFI values determined for various frothers using Cape Town tap water are shown in Table 3 ŽSweet et al., 1997.. It seems to be possible to predict the CCC values for these frothers from this data.
Fig. 8. Effect of concentration of tested n-alcohols on the normalized Sauter mean bubble diameter ŽSweet et al., 1997..
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Fig. 9. Relationship between DFI and C0.6 ŽSweet et al., 1997., dashed line, and DFI and CCC Žfrom Fig. 7., continuous line.
In the paper by Sweet et al. Ž1997., an empirical coefficient that did not have any physical meaning, the C0.6 concentration defined as the frother concentration at which the Sauter mean bubble diameter is reduced to 0.6 of its original value in water Žat zero surfactant concentration. was selected to discuss the obtained results. Fig. 8 shows how the C0.6 values were obtained from the experiments. Because—as Fig. 8 indicates—it is obvious that the C0.6 frother concentration is pretty close to the critical coalescence concentration ŽCCC., Fig. 7 provides an entirely different physical meaning for the correlations discussed by Sweet et al. Ž1997.. This is shown in Fig. 9. Only because the experimental C0.6 values happen to be close to the CCC values, our DFI s f ŽCCC. plot Žcontinuous bold line. that has a well defined physical meaning is not very different from the empirical relation DFI s f Ž C0.6 . obtained by Sweet et al. Ž1997. for two series of frothers. 5. Summary The experiments described herein indicate that the frothers control the size of bubbles in flotation systems by controlling bubble coalescence. At frother concentrations C lower than CCC, the bubble size mainly results from coalescence. The ability of frothers
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to prevent bubble coalescence is well characterized by the critical coalescence concentration ŽCCC.. At frother concentrations that exceed CCC, the bubble size is no longer determined by coalescence and will then strongly depend on sparger’s geometry and hydrodynamic conditions. Thus, efficiency of different spargers can be compared only when the experiments are carried out at frother concentrations exceeding CCC. Flotation experiments carried out using small-scale flotation devices Že.g. Hallimond tube. equipped with either single capillary or a porous frit may be very difficult to compare. They may give different flotation kinetics because of bubble coalescence in the latter case at C - CCC, hence, resulting in much larger bubble sizes. Such results should be more consistent at frother concentrations C ) CCC. Foam stability measured under dynamic conditions is determined by bubble coalescence. Acknowledgements The authors would like to thank CONDEA Vista for supplying reagents for this investigation. References Aldrich, C., Feng, D., 2000. The effect of frothers on bubble size distributions in flotation pulp phases and surface froths. Miner. Eng. 13, 1049–1057. Cho, Y.S., Laskowski, J.S., 2001. Bubble coalescence and its effect on dynamic foam stability. Can. J. Chem. Eng., Submitted. Diaz-Penafiel, P., Dobby, G.S., 1994. Kinetic studies in flotation columns: bubble size effect. Miner. Eng. 7, 465–478. Dobby, G.S., Finch, J.A., 1986. Particle collection in columns—gas rate and bubble size effects. Can. Metall. Q. 25, 9–13. Lubetkin, S.D., 1993. Bubble nucleation and growth. In: Wedlock, D.J. ŽEd.., Controlled Particle, Droplet and Bubble Formation. Butterworths, Oxford, pp. 159–190. Malysa, K., Czubak-Pawlikowska, J., Pomianowski, A., 1978. Frothing properties of solutions and their influence on the floatability. Proc. 7th Int. Congress Surface Active Substances ŽMoscow, 1976., vol. 3, Gordon and Breach, London, pp. 513–520. Malysa, K., Lunkenheimer, K., Miller, R., Hartenstein, C., 1981. Surface elasticity and frothability of n-octanol and n-octanoic acid solutions. Colloids Surf. 3, 329–338. Prince, M., Blanch, H.W., 1990. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 36, 1485–1499. Rice, R.G., Lakhani, N.B., 1983. Bubble formation at a puncture in a submerged rubber membrane. Chem. Eng. Commun. 24, 215–234. Rice, R.G., Tupperainen, J.M.I., Hedge, R.M., 1981. Dispersion and hold-up in bubble columns, comparison of rigid and flexible spargers. Can. J. Chem. Eng. 59, 677–687. Rubinstein, J.B., 1995. Column flotation-processes, designs and practices. Gordon and Breach, New York, pp. 36–42. Sweet, C., van Hoogstraten, J., Harris, M., Laskowski, J.S., 1997. The effect of frothers on bubble size and frothability of aqueous solutions. In: Finch, J.A., Rao, S.R., Holubec, I. ŽEds.., Processing of Complex Ores—Proc. 2nd UBC-McGill Int. Symp. Metallurgical Society of CIM, Montreal, pp. 235–245. Tucker, J.P., Deglon, D.A., Franzidis, J.P., Harris, M.C., O’Connor, C.T., 1994. An evaluation of a direct method of bubble size distribution measurement in a laboratory batch flotation cell. Miner. Eng. 7, 667–680.
Effect of flotation frothers on bubble size and foam stability Y.S. Cho, J.S. Laskowski ) Department of Mining and Mineral Process Engineering, UniÕersity of British Columbia, 6350 Stores Road, VancouÕer, B.C., Canada V6T 1Z4 Received 1 March 2001; received in revised form 15 June 2001; accepted 2 July 2001
Abstract In order to study the effect of frothers on the size of bubbles, experiments were carried out using single- and multi-hole spargers and a flotation cell. It was found that the size of bubbles strongly depends on frother concentration only when multi-hole spargers are utilized Žor when measured in a flotation cell.. At low frother concentrations Ž C - CCC., the bubble size is much larger, indicating coalescence as a main mechanism determining the size. Coalescence can be prevented at frother concentrations exceeding the critical coalescence concentration ŽCCC.. The foamability tests indicate that stability of foams under dynamic conditions is determined by bubble coalescence. q 2002 Elsevier Science B.V. All rights reserved. Keywords: flotation; frothers; bubbles; spargers; critical coalescence concentration; dynamic foamability index
1. Introduction Flotation kinetics involves a number of mass transfer processes with some taking place in the pulp phase Žparticle–bubble collision and attachment, transport of particle– bubble aggregate to the froth phase. and some in the froth phase Žrecovery of particle from the froth phase to concentrate launder.. All of these subprocesses depend strongly on bubble size and froth stability. In a flotation process, frothers are utilized to enhance generation of fine bubbles and to stabilize the froth. According to Leja–Schulman’s penetration theory, the interaction of frothers with a collector in the moment of the particle-to-bubble attachment is a vital step in the particle–bubble attachment. )
Corresponding author. E-mail address: [email protected] ŽJ.S. Laskowski..
0301-7516r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 Ž 0 1 . 0 0 0 6 4 - 3
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Y.S. Cho, J.S. Laskowskir Int. J. Miner. Process. 64 (2002) 69–80
It is known that pure liquids do not foam, but the presence of surface active molecules that preferentially adsorb at a liquidrgas interface changes this situation radically. Recent measurements of bubble size, dynamic foamability index and surface tension for a series of flotation frothers ŽFig. 1. showed a very good correlation between bubble size and dynamic foamability ŽSweet et al., 1997.. While the bubble size and dynamic foamability index were found to be sensitive to very low frother concentration changes, the surface tension was observed to be affected by the frother only at concentrations more than 10 times higher. Since the previously derived equations relate the size of generated bubbles to surface tension, and the surface tension does not seem to change much at very low frother concentrations, the question, therefore, arises why the bubble size depends on frother concentration. In order to answer such questions, we carried out a series of experiments in which specially designed spargers were used and the size of the bubbles was measured over a broad concentration range for different frothers. In concomitant experiments, the dynamic foamability index and the surface tension were measured for the same frothers. 2. Experimental procedures 2.1. Materials Experiments were performed using MIBC and four different hexanol isomersrderivatives kindly provided by the Condea Vista. MIBC Frother 1 Frother 2 Frother 3 Frother 4
Methyl isobutyl carbinol 1-hexanol Di ethoxy-mono propoxy hexanol Di ethoxy hexanol Mono propoxy-di ethoxy hexanol
wŽCH 3 . 2 CHCH 2 CHŽOH.CH 3 x wC 6 H 13 OHx wC 6 H 13 OHŽEO. 2 ŽPO.x wC 6 H 13 OHŽEO. 2 x wC 6 H 13 OHŽPO.ŽEO. 2 x
2.2. Methods 2.2.1. Bubble size measurements The UCT bubble size meter was employed to measure the bubble size as described by Tucker et al. Ž1994.. The bubbles were generated in a 3-l Plexiglas tank using distilled water. All experiments were conducted at 21 8C. Approximately 3000 bubbles were sampled during each run. Three runs were carried out for each concentration of tested surfactant, the average of three runs was reported and the experimental details were provided in another paper ŽCho and Laskowski, 2001.. Bubbles are commonly produced by sparging, that is pumping gas through a capillary or frit into the bulk liquid. In mechanical flotation cells, they are produced by cavitation at the trailing edge of the impeller blade, or if the air is supplied under pressure by breaking it into fine bubbles by shearing forces. The size of a bubble forming at an orifice under equilibrium conditions can be calculated using thermodynamic data which show clearly dependence on the surface tension. However, in most practical cases in which rapid bubble formation occurs, the equilibrium calculations are inadequate to predict the detachment volume ŽLubetkin, 1993.. To create the conditions as close to
Y.S. Cho, J.S. Laskowskir Int. J. Miner. Process. 64 (2002) 69–80
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equilibrium as possible, the bubbles in our experiments were generated at very low air flow rates of 2 cm3rmin and a Bel-Art Rite flowmeter was used. The sampler of the UCT bubble size analyzer was placed 50 mm above the sparger. A few different spargers were tested. A flexible latex sparger that contained two punctures made using a hypodermic syringe in a stretched latex sheet, far away from each other to eliminate coalescence, consistently produced bubbles of uniform size as shown in Fig. 2 Žstandard deviations of 0.057 and 0.029 mm.. However, probably because of the different hole dimensions, the size of the generated bubbles was observed to be very different Ž1.45 vs. 2.15 mm.. Since in the latex type spargers used by Rice et al. Ž1981., the punctured holes are not spherical, it is impossible to determine the exact hole diameter. Therefore, we also employed rigid, bronze spargers. While the hole diameter can easily be determined for such spargers, it turned out to be impossible to obtain a steady stream of bubbles when using such spargers. Rice and Lakhani Ž1983. noticed that at superficial gas velocities of less than 5 cmrs, a rubber sparger produced a homogenous stream of bubbles as compared to the very unpredictable and irregular flow of bubbles varying in size when rigid spargers were employed. Since the only difference between the latex sparger and the rigid bronze plate sparger is the flexibility of the former and its ability to oscillate and deform as gas passes through, it was decided to vibrate the rigid sparger. The sparger tank was mounted on a Syntron Lapping–Polishing Machine and vibration was applied. As the frequency of the vibration increased stepwise, a small window of frequency was found in which the size of the generated bubbles became very uniform and consistent Žwithin 5%. over five runs of the bubble size measurements. This vibration frequency was, thus, set for the entire experiment. In the bubble size measurements in an open top Leeds flotation cell, the impeller speed was set at 1000 rpm and the air flow rate was 5 lrmin. The sampler of the bubble size analyzer was positioned 50 mm above the stator. 2.2.2. Sparger hole size determination Following published data ŽDobby and Finch, 1986; Diaz-Penafiel and Dobby, 1994., it was decided to work with bubbles of 1–2 mm in size, as they are most common for flotation systems. Using Eq. Ž4. below, the required size of the sparger opening was calculated to be within 0.1–0.15 mm, and drills of this size were used. 2.2.3. Dynamic foamability index Since this methodology employs a two-phase system consisting of liquid and dispersed air, we have decided to use the term foam instead of froth as used in the original publications by Malysa et al. Ž1978, 1981.. The foamability measurement in Malysa’s procedure defines the retention time, rt, as the slope of the linear part of the dependence of the total gas volume contained in the system Žsolutionq foam. on the gas flow rate. Values of the retention time are claimed to be independent of the gas flow rate and geometry of the measuring column. Physically, rt is the average lifetime of a bubble in the whole system, i.e. in both solution and foam. The dynamic foamability index ŽDFI. is defined as the limiting slope of rt vs. concentration for c ™ 0. Ert DFI s Ž 1. Ec cs 0
ž /
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Alternatively, it is possible to fit an equation to the rt values vs. c data in order to alleviate the need to find the initial slope graphically. The equation takes the form of an inverse exponential, which when expanded into a power series gives: rt y 2.4 s DFI P c Ž 2. where DFI s rt` P k Ž 3. The quantity 2.4 was given by Malysa as the value of rt for distilled water, rt` is the limiting rt value for c ™ ` and k is a constant. In our tests, the frother aqueous solutions were placed in the column Ž45-mm diameter, 92-cm height.. Nitrogen was pumped through the sintered glass disk initially at a flow rate of 100 cm3rmin, which was then increased stepwise up to 2000 cm3rmin. After each change, the resulting steady state volume Žsolutionq foam. was recorded. The total volume was plotted vs. flow rate to obtain the slope Žretention time. via linear regression. 3. Results Fig. 1 compares the effect of concentration of two hexanol isomers on bubble size, retention time Žfoamability. and surface tension ŽSweet et al., 1997.. In order to facilitate comparisons, the results were plotted in a normalized form. The term AnormalizationB is used to describe the ratio of the parameter of interest to its value measured at zero surfactant concentration.
Fig. 1. Normalized retention time, Sauter mean bubble diameter and surface tension of n-hexanol and MIBC ŽSweet et al., 1997..
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As shown, the surface tension seems to be least sensitive to the surfactant concentration; both bubble size and retention time are affected by the frother at the concentrations at which the surface tension values are practically identical to that of distilled water. This figure reveals that bubble size is much more sensitive to the surfactant concentration than surface tension and perhaps could be used for analytical purposes to test the presence of surface active substances at very low concentrations. Similar plots for other frothers show the same trend. Discussion of these results was hindered by the fact that the bubble size and foamability in this project were measured in Cape Town tap water, while the surface tension data obtained using distilled water were quoted after other sources ŽSweet et al., 1997.. 3.1. Single-hole spargers Frothers did not show any effect on bubble size when bubbles were generated from a single-hole latex sparger. Fig. 2 shows quite uniform bubble sizes regardless of frother concentration. Eq. Ž4. quoted after Rubinstein Ž1995. shows that the bubble size depends only on inner capillary Žor sparger size. and surface tension of the solution. db s
ž
6 dc g g Ž r l y rg .
1r3
/
Ž 4.
where d b is the diameter of the bubble, g is the surface tension of the liquid, d c is the size of the capillary, r l is the density of the liquid and rg is the density of gas.
Fig. 2. Effect of frother concentration on bubble size using a latex sparger.
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Table 1 Comparison of calculated vs. measured bubble diameter sizes Capillary diameter Žmm.
Calculated bubble diameter sizes Žmm.
Average measured bubble diameter sizes"S.D. Žmm.
0.10 0.15
1.65 1.88
1.65"0.029 1.89"0.017
Since the surface tension was practically constant throughout the tested frother concentrations ŽCho and Laskowski, 2001., the size of bubbles was expected to be uniform for the same spargers. As shown in Fig. 2, the results are consistent with published Eq. Ž4.. The tests carried out using the bronze sparger gave similar results. Calculated Sauter mean diameters of the bubbles generated from 0.1 and 0.15 mm spargers were 1.65 and 1.88 mm, respectively. The average bubble sizes actually produced from the bronze spargers were in perfect agreement with the calculated sizes as shown in Table 1 and Fig. 3. Indeed, the bubble size did not change with frother concentration. 3.2. Three-hole sparger (0.1 mm) and flotation cell tests Since the frothers do not affect the size of bubbles generated using a single-hole sparger, the only possible mechanism to change the bubble size when a multi-hole sparger Žor a flotation cell. is utilized would be by coalescence andror breakage of the bubbles. The measured bubble sizes were much smaller than the critical size subjected to breakage ŽPrince and Blanch, 1990. and, therefore, bubble breakage should be ruled out
Fig. 3. Effect of frother concentration on bubble size using a bronze single-hole sparger.
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Fig. 4. Effect of frother concentration on bubble size using 0.1-mm diameter three-hole bronze sparger.
as a possible mechanism for the bubble size changes. This leaves bubble coalescence as the only possible mechanism responsible for bubble size changes in our multi-hole sparger experiment. Taking 1.65 mm Žfrom Table 1. as the average diameter of the bubble generated from 0.1-mm sparger, three 1.65-mm bubbles when coalescing should give a larger bubble of 2.38 mm in diameter. This is again in a perfect agreement with the measured bubble diameters without frothers ŽFig. 4.. As the concentration of frothers increased in the solution, the degree of coalescence decreased. More powerful frothers Žfrothers 2 and 4. prevented the bubble coalescence at lower frother concentrations. As the measurements of surface tension revealed ŽCho and Laskowski, 2001., frothers 2 and 4 turned out to be more surface active than frother 3, hexanol and MIBC. The obvious difference between these two groups is the presence of propylene oxide group in frothers 2 and 4.
4. Discussion It is commonly believed that the bubble size decreases with an increase in the frother concentration owing to a decrease in the surface tension induced by the addition of surfactants. By the way, this was one of the conclusions drawn in a very recent paper ŽAldrich and Feng, 2000.. As the results presented in our paper Žand in another paper by Cho and Laskowski Ž2001. demonstrate, at frother concentrations typical for the froth flotation systems, the bubble size is not affected at all by a frother if the bubbles cannot collide with each other. The results obtained by Sweet et al. Ž1997. already hinted that
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Fig. 5. Effect of frother concentration on bubble size measured in an open-top Leeds flotation cell.
there is a poor correlation between bubble size and surface tension. Figs. 2–5 explain why. As these figures reveal, in the experiments in which one-hole spargers were utilized Žin other words, when the bubbles could not collide with each other., there was no effect of frother concentration on the bubble size. If the experiments were carried out using multi-hole spargers, or were carried out in a flotation cell, the size of bubbles was substantially larger at low frother concentrations.
Fig. 6. Effect of frother concentration on bubble size Žschematic..
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Table 2 Comparison of CCC values obtained using a three-hole sparger and an open-top Leeds flotation cell Frothers
Three-hole sparger CCC values Žmolrl.
Open-top flotation cell CCC values Žmolrl.
MIBC Frother 1 Frother 2 Frother 3 Frother 4
0.000079 0.000079 0.000013 0.000031 0.000016
0.000083 0.000083 0.000015 0.000037 0.000015
It is obvious that with increasing frother concentration, the degree of bubble coalescence decreases and at a particular concentration Žcritical coalescence concentration., the coalescence of the bubbles is completely prevented ŽFig. 6.. The stronger frothers reach the CCC point at a lower concentration. The values of CCC seem to characterize frothers very well. At concentrations higher than CCC, the coalescence does not occur. The three-hole sparger experiment, which was conducted in a controlled environment, provided CCC values that were identical to those obtained in a flotation cell. This implies that the CCC values obtained for a given frother in a small-scale laboratory experiment Ži.e. three-hole sparger. do not depend on a type of flotation cell. As seen from Table 2, the five tested frothers are characterized by unique CCC values. As shown in another paper ŽCho and Laskowski, 2001., the CCC values could also be obtained from Tucker et al.’s Ž1994. data who measured the size of bubbles in a flotation cell using DIBK Ždi-isobutyl ketone., TEB Žtriethoxybutane. and MIBC frothers. Fig. 7 shows the interrelation between CCC and DFI and demonstrates that the foamability of aqueous solutions measured under dynamic conditions is determined by
Fig. 7. Relationship between DFI and critical coalescence concentration for the tested frothers.
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Table 3 DFI values for various commercial frothers using Cape Town tap water ŽSweet et al., 1997. Frothers
rt` Žs.
k Ždm3 rmol.
DFI Žs dm3 rmol.
n-Butanol 2-Butanol t-Butanol n-Pentanol n-Hexanol n-Heptanol n-Octanol n-Octanol 2-Ethyl-hexanol MIBC a-Terpineol Texanol TEB DowFroth400 DIBK n-Butanola
20.5 12.7 10.8 22.6 62.6 82.5 87.3 61.1 68.3 55.0 27.1 31.2 34.7 72.8 21.5 20.8
65.3 65.0 146.6 243.7 539.6 495.6 908.5 2313.3 2066.8 672.2 5093.9 10,392.7 7279.4 11,025.7 3589.6 61.0
1339 826 1588 5517 33,779 40,867 79,338 141,226 141,147 36,991 138,171 323,901 252,589 802,142 77,019 1271
a
Test conducted in distilled water.
bubble coalescence. More surface active frothers are characterized by lower CCC and higher DFI values. The DFI values determined for various frothers using Cape Town tap water are shown in Table 3 ŽSweet et al., 1997.. It seems to be possible to predict the CCC values for these frothers from this data.
Fig. 8. Effect of concentration of tested n-alcohols on the normalized Sauter mean bubble diameter ŽSweet et al., 1997..
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Fig. 9. Relationship between DFI and C0.6 ŽSweet et al., 1997., dashed line, and DFI and CCC Žfrom Fig. 7., continuous line.
In the paper by Sweet et al. Ž1997., an empirical coefficient that did not have any physical meaning, the C0.6 concentration defined as the frother concentration at which the Sauter mean bubble diameter is reduced to 0.6 of its original value in water Žat zero surfactant concentration. was selected to discuss the obtained results. Fig. 8 shows how the C0.6 values were obtained from the experiments. Because—as Fig. 8 indicates—it is obvious that the C0.6 frother concentration is pretty close to the critical coalescence concentration ŽCCC., Fig. 7 provides an entirely different physical meaning for the correlations discussed by Sweet et al. Ž1997.. This is shown in Fig. 9. Only because the experimental C0.6 values happen to be close to the CCC values, our DFI s f ŽCCC. plot Žcontinuous bold line. that has a well defined physical meaning is not very different from the empirical relation DFI s f Ž C0.6 . obtained by Sweet et al. Ž1997. for two series of frothers. 5. Summary The experiments described herein indicate that the frothers control the size of bubbles in flotation systems by controlling bubble coalescence. At frother concentrations C lower than CCC, the bubble size mainly results from coalescence. The ability of frothers
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to prevent bubble coalescence is well characterized by the critical coalescence concentration ŽCCC.. At frother concentrations that exceed CCC, the bubble size is no longer determined by coalescence and will then strongly depend on sparger’s geometry and hydrodynamic conditions. Thus, efficiency of different spargers can be compared only when the experiments are carried out at frother concentrations exceeding CCC. Flotation experiments carried out using small-scale flotation devices Že.g. Hallimond tube. equipped with either single capillary or a porous frit may be very difficult to compare. They may give different flotation kinetics because of bubble coalescence in the latter case at C - CCC, hence, resulting in much larger bubble sizes. Such results should be more consistent at frother concentrations C ) CCC. Foam stability measured under dynamic conditions is determined by bubble coalescence. Acknowledgements The authors would like to thank CONDEA Vista for supplying reagents for this investigation. References Aldrich, C., Feng, D., 2000. The effect of frothers on bubble size distributions in flotation pulp phases and surface froths. Miner. Eng. 13, 1049–1057. Cho, Y.S., Laskowski, J.S., 2001. Bubble coalescence and its effect on dynamic foam stability. Can. J. Chem. Eng., Submitted. Diaz-Penafiel, P., Dobby, G.S., 1994. Kinetic studies in flotation columns: bubble size effect. Miner. Eng. 7, 465–478. Dobby, G.S., Finch, J.A., 1986. Particle collection in columns—gas rate and bubble size effects. Can. Metall. Q. 25, 9–13. Lubetkin, S.D., 1993. Bubble nucleation and growth. In: Wedlock, D.J. ŽEd.., Controlled Particle, Droplet and Bubble Formation. Butterworths, Oxford, pp. 159–190. Malysa, K., Czubak-Pawlikowska, J., Pomianowski, A., 1978. Frothing properties of solutions and their influence on the floatability. Proc. 7th Int. Congress Surface Active Substances ŽMoscow, 1976., vol. 3, Gordon and Breach, London, pp. 513–520. Malysa, K., Lunkenheimer, K., Miller, R., Hartenstein, C., 1981. Surface elasticity and frothability of n-octanol and n-octanoic acid solutions. Colloids Surf. 3, 329–338. Prince, M., Blanch, H.W., 1990. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 36, 1485–1499. Rice, R.G., Lakhani, N.B., 1983. Bubble formation at a puncture in a submerged rubber membrane. Chem. Eng. Commun. 24, 215–234. Rice, R.G., Tupperainen, J.M.I., Hedge, R.M., 1981. Dispersion and hold-up in bubble columns, comparison of rigid and flexible spargers. Can. J. Chem. Eng. 59, 677–687. Rubinstein, J.B., 1995. Column flotation-processes, designs and practices. Gordon and Breach, New York, pp. 36–42. Sweet, C., van Hoogstraten, J., Harris, M., Laskowski, J.S., 1997. The effect of frothers on bubble size and frothability of aqueous solutions. In: Finch, J.A., Rao, S.R., Holubec, I. ŽEds.., Processing of Complex Ores—Proc. 2nd UBC-McGill Int. Symp. Metallurgical Society of CIM, Montreal, pp. 235–245. Tucker, J.P., Deglon, D.A., Franzidis, J.P., Harris, M.C., O’Connor, C.T., 1994. An evaluation of a direct method of bubble size distribution measurement in a laboratory batch flotation cell. Miner. Eng. 7, 667–680.