- Email: [email protected]
Hydrodynamic interactions between particles in aggregation and flotation
Int. J. Miner. Process. 70 (2003) 157 – 170 www.elsevier.com/locate/ijminpro
Hydrodynamic interactions between particles in aggregation and flotation Yuehua Hu a, Guangzhou Qiu a, J.D. Miller b,* b
a Department of Mineral Engineering, Central South University, Changsha 410083, China Department of Metallurgical Engineering, College of Mines and Earth Sciences, University of Utah, 135 S. 1460 E. 412 William C. Browning Building, Salt Lake City, UT 84112, USA
Received 15 September 2000; received in revised form 23 October 2001; accepted 9 December 2002
Abstract The aggregation and flotation behavior of hematite and wolframite have been investigated through particle size analysis, flotation tests and measurement of energy input based on hydrodynamic interactions. In has been shown that when fine and coarse particles are mixed and conditioned in surfactant solution, the flocs with particle size greater than that of the coarse particle size and the flocs with particles size between that of the fine and coarse particle sizes are formed. The bigger size floc is attributed to the adhesion of fine particles onto coarse particles. The medium size floc may be the aggregation among fine particles themselves and detached flocs from the coarse substrate due to the shearing forces. Both cases depend on the state of turbulent flow of pulp and hydrodynamic conditions. The studies on the effect of particle size, agitating speed and time, and the structure of agitation tank on aggregation and flotation show the importance of hydrodynamic interactions in aggregation and flotation. D 2003 Elsevier Science B.V. All rights reserved. Keywords: hydrophobic aggregation; hydrodynamic interactions, flotation; hematite, wolframite; reynolds number, micro-size of turbulent flow; shearing stress
1. Introduction Besides surface forces, hydrodynamic interaction also plays a very important kinetic role in determining the collision efficiency between particles, the state of particulate suspension and flotation. The extent of hydrodynamic effect is determined by the character of the liquid * Corresponding author. Fax: +1-801-581-4937. E-mail address: [email protected] (J.D. Miller). 0301-7516/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-7516(03)00023-1
158
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
field flowing around the particles which, in turn, is dependent on the type of flow, i.e. the Reynolds number. Hydrodynamic forces influence the rate of aggregates growth and breakup in several ways (Valioulis and List, 1984; Derjaguin and Dukhin, 1979; Warren, 1984; Lafuma et al., 1991; Hu et al., 1994). Considering van der Waals attraction and electrostatic repulsion in DLVO theory, van de Ven and Mason (1975a,b, 1976) established that a suspension could be unstable at very low shear rate, due to aggregation in the DLVO secondary energy minimum, stable at intermediate shear rates, because hydrodynamic forces were large enough to push particles out of the shallow secondary minimum, and unstable at high shear rates, because the hydrodynamic forces were then large enough to overcome the DLVO energy barrier and allow the particles to aggregate in the primary energy minimum. However, it has been reported that if only taking into account DLVO forces the aggregation between particles with higher surface potential in surfactant solution may not occur even if at higher shearing rate. Based on the extended DLVO theory, if the particles are rendered hydrophobic in which the polar interfacial interaction energy of particles rSLAB>0, the aggregation occurs in the secondary energy minimum at low shear rates. At high shear rates, the stable hydrophobic flocs are formed in the primary energy minimum (Skvalar and Kmet, 1991; van Oss et al., 1990). It indicated that hydrodynamic forces have an effect in the process of floc growth and floc break-up. Particles size, the agitation condition and the structure of the agitation tank affect the character of the liquid field flowing around the particles, which influences the hydrodynamic interaction and flotation (Chia and Somasundaran, 1983; Raju et al., 1991; Liang and Shi, 1990; Subrahmanyam and Forssberg, 1990). The effect of these factors has been studied in this paper.
2. Experimental 2.1. Materials Pure wolframite and hematite were taken from Yaogangxian Mine and from Dong Anshan Mine in China, respectively. The handpicked pure lump samples were crushed, ground in a porcelain mill and screened to the desired size fractions. The coarser fractions of different size were used as carriers in the tests. The fraction of 5 Am obtained by sedimentation was used as ultra fine feed. Double distilled water was used in preparing all solutions. The sodium oleate used was grade purchased from Hunan Chemical. The styryl phosphoric acid was laboratory grade supplied by Changsha Research Institute of Mining and Metallurgy. All other reagents used for the pH adjustment were of analytical grade. 2.2. Methods In flotation, the 5Am mineral samples of 5 g were fully dispersed with distilled water agitating 30 min at 2150 rpm using a common impeller in a beaker. The dispersed pulp was transferred into a baffled tank made of organic glass with a volume of 200 ml. The collector was added after coarse particle addition and then the pH was adjusted. The pulp
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
159
was then conditioned for the required duration at desired speeds and the pH was measured. The conditioned pulp was then transferred to a micro-flotation cell with a volume of 100 ml, and floated at 1600 rpm for 5 min. Adsorption of styryl phosphoric acid (SPA) on wolframite was determined from the difference between the initial and equilibrium SPA concentrations. Preliminary kinetic studies showed that the adsorption of styryl phosphoric acid from the solution reaches equilibrium within 20 min. Therefore, 2 g of wolframite was stirred with 100 ml of a SPA solution at the desired initial concentration and pH in 200-ml beaker for 30 min. After equilibration, the suspension was centrifugalized. The supernatant was used for pH measurement and SPA concentration measurement, which was measured by a potential titration method.
3. Results and discussion 3.1. Collision rate between particles and flotation of fine particles The effects of conditioning speed and time on the flotation of 5Am wolframite are demonstrated in Fig. 1 using SPA as a collector and 25 + 38Am wolframite as carrier. The relative flotation recovery of 5Am wolframite is increased with the increase of conditioning time up to 60 min. The relative flotation recovery of 5Am wolframite is at first increased with the increase of conditioning speed up to 4000 rpm and then decreased when conditioning speed increases over 4000 rpm. The enhancement of fine mineral flotation requires the adhesion of fine particles onto mother particles, i.e. the aggregation between fine and coarse particles. On one hand the aggregation depends on the interaction forces between particles (Xu and Yoon, 1989; van
Fig. 1. Effects of conditioning time and speed on carrier flotation of 5Am wolframite in various speed.
160
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Oss et al., 1990; Qiu et al., 1993; Veeramasuneni et al., 1997). When the interaction forces are repulsive, the aggregation among particles may not occur. When the interaction forces are attractive, the aggregation may be possible. In this case, the rate of aggregation will depend on the probability of collision from the hydrodynamic aspect. The rate of aggregation of particles depends on both the probability of collision and the probability of adhesion. For particles which collide by diffusion, Levich (1962) gives the collision rate: e 12 Jt ¼ 12pbR3 n20 ð1Þ m Where Jt is the collision rate per unit volume by turbulent diffusion mechanism, b is a constant, R is the radius of particles, n0 is the initial concentration of particles, e is the energy loss occurring in the flow per second per unit volume in J s 1 kg 1, m is the kinematic viscosity in m2 s 1. For collisions between particles of different size, R in Eq. (1) was substituted by (R1 + R2)/2 and n02 by n1 and n2, thus Jt ~ðR1 þ R2 Þ3 n1 n2
ð2Þ
Obviously, the collision rate between fine and coarse particles is much higher than that between the fine particles, providing a basis for coarse particles serving as carriers promoting the aggregation between particles. Expressing e0 in terms of the fluid flow velocity Vt, Levich showed that 3
R3 n20 Vt2 Jt ¼ pffiffiffiffiffiffi VL
ð3Þ
where L is the maximum scale of turbulence and approximately equal to the diameter of the stirring vessel. If the fluid flow velocity is directly proportional to the stirrer speed then the collision rate is proportional to the 3/2 power of the stirrer speed. There is an increase in collision rate with fluid velocity, which is enhanced by increasing stirrer speed. The decrease in flotation recovery at a very high conditioning speed of 4000 rpm may be attributed to shearing forces causing floc breakage . Fuerstenau et al. (1988) observed breakage of larger flocs at high shear rates in shear flocculation of fine hematite. That study used a lower speed (2000 rpm) than the condition speed used in this study. The agitation speeds thereby vary from system to system. 3.2. Energy dissipation of particles in the flow The kinetic energy of the particles in mixing can be estimated using the equation below Vk ¼
1 2 lu 2 r
ð4Þ
in which l is the reduced mass of interacting particles of mass m1 and m2 in kg and given by (Somasundaran, 1984). m1 m2 l¼ ð5Þ m1 þ m2 mr is the relative velocity of the particles.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
161
At R < k0, dissipative subrange of microturbulance (Delichatsios and Probstein, 1975) rffiffiffiffiffiffirffiffiffi rffiffiffiffiffiffiffiffi 1 e e ðR1 þ R2 Þ ¼ ð6Þ ðR1 þ R2 Þ ur ¼ 15 m 15m At R>k0, inertial subrange of microturbulence 1
1
lr ¼ 1:37e 3 ðR1 þ R2 Þ 3 k0 is turbulent microscale 3 14 m k0 ¼ e e¼
P m
ð7Þ
ð8Þ ð9Þ
here m is liquid mass and P is the power input (Schulze, 1984). The energy dissipation in the flow and the kinetic energy of the particles in the wolframite system of 5Am fine particles and 25 –38Am carrier particles are calculated in terms of Eqs. (4) – (9) and the results are presented in Fig. 2. e and VK are increased with the increase of conditioning speed. The energy dissipation in the flow and the kinetic energy of the particles in strong stirring may increase the collision between particles on one hand, and cause a rise in pulp temperature on the other hand (see Fig. 3), which can be expected to enhance collector adsorption on wolframite and hence enhance their hydrophobic aggregation and flotation recovery of fine particles (see Fig. 4). Fig. 3 shows that the pulp temperature is increased with the increase of conditioning speed and time. Fig. 4 shows that the adsorption of SPA on wolframite is increased and
Fig. 2. The energy dissipation e and the kinetic energy (Vk) of the particles in the flow vs. agitation speed.
162
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Fig. 3. Effect of conditioning speed and time on pulp temperature.
thereby relative flotation recovery of 5Am wolframite is increased with the increase of pulp temperature due to strong agitation. 3.3. Optimal size of coarse particles affecting the aggregation of fine particles As above, coarse particles can serve as carriers for fine particles because coarse particles have a greater collision rate with fine particles, and fine hematite and wolframite can
Fig. 4. Effect of pulp temperature on adsorption of styryl phosphoric acid at wolframite and on relative flotation recovery of 5Am wolframite.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
163
Table 1 The k0 values at different agitation speed Conditioning speed (rpm)
870
1200
1650
2050
2420
2900
k0 in Eq. (8) (Am) k0 in Eq. (10) (Am)
54.3 63.8
50.2 50.2
46.8 39.4
44.1 33.6
40.3 29.6
37.8 25.8
adhere onto hydrophobilized coarse substrates. What size is then best for coarse particles used as carriers, i.e. what carrier size is the optimal to make the carrier action maximum? On the basis of the theories on particle collision, mass transfer and concomitance, the collision rate between fine particles and coarse particles will reach a maximum, producing optimum carrier action, when the size of the coarse particle is comparable to the turbulent microscale of the vortex, k0. The value of k0 can be obtained either using Eq. (8) or using the equation below (Derjaguin et al., 1969) k0 ¼
L da2 n
ð10Þ
34
60m
where n is conditioning speed, L and da are, respectively, the diameter of stirring tank and impeller, L = 4.7 cm, da = 3.4 cm in the present work. The calculated k0 values in terms of Eqs. (8) and (10) from the data in Fig. 2 are given in Table 1. The reduced amount of the 5Am hematite by addition of various sizes dp of coarse particles at different conditioning speed is shown in Figs. 5 and 6. It can be seen that when k0 dp>0, i.e. the particle size of the coarse particles is less than the turbulent microscale k0, the reduced amount of 5Am hematite increases with the increase of the coarse particle size. When k0 dp < 0, i.e. the particle size of carrier is greater than the k0, the reduced
Fig. 5. The reduced amount of 5Am hematite vs. k0 dp.
164
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Fig. 6. The reduced amount of 5Am hematite vs. k0 dp.
amount of 5Am hematite decreases with the increase of coarse particle size. This shows that there exists an optimal coarse particle size, dp = k0. Using the particles with size dp = k0 as carriers, the carrier action of coarse particles and the reduced amount of 5Am hematite particles reach a maximum. Fig. 7 demonstrates the results of the flotation of 5Am hematite in carrier flotation at different stirring speed by adding different size of carrier. It further shows the optimum carrier action of coarse particles with dp = k0. The relative flotation recovery of 5Am hematite is maximum at dp = k0.
Fig. 7. The relative flotation recovery of 5Am hematite vs. (k0 dp).
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
165
The relative motion speed of coarse grain in turbulent flow is directly proportional to R2c at Rc V k0 and to R1/3 at Rc>k0 according to Samygin et al. (1968). Therefore, the relative motion speed of coarse particles, and thus the collision rate between fine particles and coarse particles, will be greatly increased with the increase of coarse particles size at Rc V k0. Whereas, the relative motion speed of coarse particles and hence the collision rate between fine particles and coarse particles will be decreased with the increase of coarse particle carrier size at Rc>k0. This suggests that the relative flotation recovery of fine particles will be enhanced with the enhancement of the carrier size at Rc V k0, and will be decreased with the increase of carrier size at Rc>k0 because the aggregates will be broken off due to intensifying of attrition action at Rc>k0. 3.4. Aggregation of fine particles in the vortices formed by movement of coarse particles Fig. 8 shows the particle size distribution before and after conditioning when 30– 40Am hematite was added to 5Am hematite pulp. Obviously, the content of 5Am particles is greatly decreased and the content of aggregates with size above the coarse size is increased after conditioning. It appeared that flocs with sizes between 5 and 30 Am, called middle size flocs, were produced. What is responsible for the formation of middle size flocs? There is a boundary layer between particles and fluids, the state of which varies with the Reynolds number of the particle because of the motion between the particle and fluid. The particle Reynolds number is given by dp us Rep ¼ ð11Þ m where us is the rate of sliding motion of particle, which can be obtained by the settling rate of particles. When Rep < 1, a boundary layer with laminar flow is formed between particle
Fig. 8. The distribution of hematite suspension by addition of 30 – 40 Am hematite into 5Am hematite pulp.
166
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
and fluid. When Rep>1, the boundary layer is transferred to turbulent flow. When Rep>10, the boundary layer breaks off. The flow lines near the coarse particle will curl up to form definite vortices. In this case, part of the kinetic energy of the particle motion is released in the form of heat owing to friction, and the rest of the kinetic energy is turned into work done producing turbulent wave. That is to say, the particles in motion will consume part of the turbulent energy, the other part of which will be consumed by turning big-sized vortices into small-sized vortices, bringing about changes in the frequency spectrum of turbulent motion. The eddy produced by coarse particle tailing trace is favorable for the aggregation of fine particles. This is the so-called ‘‘promoting aggregation action of coarse particles’’, which can be accessed using the particle Reynolds number. Fig. 9 shows that the content of newly produced middle size flocs increases with the increase in the particle Reynolds number when coarse particles are added into the pulp of fine hematite at different conditioning speeds. 3.5. Effect of shearing rate on aggregation of fine particles The behavior of fine particles will be different when adding coarse particles into the pulp with fine particles. The collision rate and thereby the adhesion of fine particles onto mother particle will increase. The higher collision rate between coarse particles in strong stirring may result in the detachment of already adhered fine flocs. This is especially true when the coarse particle size exceeds the microscale of turbulence, the aggregates break due to attrition and shear forces generated in the liquid. Lu and Spielman (1985) reported that the floc splitting frequency, fB, was directly proportional to the shear rate, e 12 ð12Þ fB ¼ KG ¼ K m where K is a constant.
Fig. 9. The amount of newly produced middle size floc vs. particle Reynolds number.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
167
Fig. 10. The content of newly produced middle size floc vs. particle size of coarse particle.
Figs. 10 and 11 show that the content of newly grown middle size flocs is increased with the increase in particle size of coarse particles and shear forces, which accounts for the intermedium-breakage action of coarse particles. 3.6. Effect of the structure of vessel on flow state and flotation of fine particles The turbulent flow state is very important to the collision and adhesion between fine particles and coarse particles in flotation, which is closely related not only to agitation
Fig. 11. The content of newly produced middle size floc vs. shear rate in the flow.
168
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Fig. 12. Effect of proportion of carrier on carrier flotation conditioning in unbaffled and baffled tank.
intensity and pulp property, but to cell geometry including the structure of the stirring vessels and the shape of impellers. Two vessels with and without baffles were tested in the present research. At high speed agitation the deeper swirl and vortex were formed and pulp moved along the inside wall of the tank, the moving speed of particles and hence the collision rate between fine
Fig. 13. The different types of impellers used.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
169
Table 2 The results of carrier flotation of 5 Am wolframite conditioning using various impellers Impeller types
1
2
3
4
Relative flotation recovery (%)
61.51
54.26
58.21
52.24
and coarse particles will be reduced due to the friction between the particles with various sizes. In the baffled tank, strong turbulent flow from top to bottom turnover will be produced, which will increase the collision rate between fine particles and coarse particles. The adhesion of fine particles onto coarse substrates is more effective and relative flotation recovery of fine particles by adding coarse particles into pulp is higher when the pulp is conditioned in the baffled cell than in the unbaffled cell (see Fig. 12). The effects of different impellers of various shapes (see Fig. 13) on fine flotation are also examined and the results are given in Table 2. It can be seen from Fig. 13 and Table 2 that when four different types of impellers are used for agitation, the flotation recovery of fine wolframite is in the order of types: 1>3>2>4, with the type 1 double-bladed paddle impeller being the best.
4. Conclusions The important variables influencing hydrodynamic interactions in fine flotation include, the intensity and time of agitation, the size of coarse particles, the structure of agitation vessel and shape of impeller, etc. Agitation intensity plays a major role in flotation. In turbulent flow, a bigger floc is formed due to the adhesion of fine particles onto a coarse particle substrate, and some middle size flocs with sizes between that of coarse and fine particles are also formed. Suitable intense agitation can increase the collision rate between fine and coarse particles, and can also enhance chemisorption of collector on the mineral surface, via the accompanying increase in the temperature of the flotation pulp, which makes the hydrophobic aggregation between fine particles increase. These effects enhance the flotation recovery of fine particles. There exists an optimal coarse particle size, at which the collision probability between fine and coarse particles increases, the formation of flocs (i.e. the reduced amount of 5Am particles ) and thus the flotation of fine particles are greatly increased. The baffled stirring tank and doublebladed paddle impeller cause stronger turbulent flow, which is useful for the collision and aggregation between particles, providing improved effectiveness for fine particle flotation.
Acknowledgements The authors would like to thank the China National Science Fund for Distinguished Young Scholars No. 59925412 and the National Key Fundamental Research Program G1999064901 for supporting this research.
170
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
References Chia, Y.H., Somasundaran, P., 1983. Carrier flotation of anatase from clay and its physicochemical mechanisms. In: Subhas, M.G. (Ed.), Ultrafine Grinding and Separation of Industrial Minerals. SME AIME, vol. 12, pp. 117 – 131. Delichatsios, M.A., Probstein, R.F., 1975. Coagulation in turbulent flow: theory and experiment. J. Colloid Interface Sci. 51 (3), 394 – 405. Derjaguin, B.V., Dukhin, S.S., 1979. Kinetic theory of the flotation of fine particles. 13th Inter. Miner. Process. Congr., Warsaw, Poland, Part A. Polish Scientific Publishers, pp. 21 – 60. Derjaguin, B.V., Livshits, A.K., Samygin, V.D., 1969. Aggregate stability of mineral suspensions in turbulent flow and the floatability of slurries. Int. Cong. Miner. Process., Leningrad, pp. 674 – 685. Fuerstenau, D.W., Li, C., Hanson, J.S., 1988. Shear flocculation and carrier flotation of fine hematite. In: Plumpton, A.J. (Ed.), Proc. Int. Symp. Production and Processing of Fine particles. Pergamon Press, New York, pp. 329 – 335. Hu, Y., Qiu, G., Wang, D., 1994. The studies of carrier flotation of ultrafine wolframite. Trans. Nonferr. Met. Soc. China 2, 44 – 48. Lafuma, F., Wong, K., Cabane, B., 1991. Bridging of colloidal particles through adsorbed polymers. J. Colloid Interface Sci. 143 (1), 9 – 21. Levich, V.G., 1962. Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ. 512 pp. Liang, R., Shi, D., 1990. Carrier flotation of ultrafine cassiterite particles and its mechanism. Nonferr. Met. 42 (3), 26 – 31. Lu, C.F., Spielman, L.A., 1985. Kinetics of flocculation breakage and aggregation in agitated liquid suspensions. J. Colloid Interface Sci. 103 (1), 95 – 105. Qiu, G., Hu, Y., Wang, D., 1993. Interactions Between Particles and Flotation of Fine Particles. CSUT Press, Changsha. 431 pp. (in Chinese). Raju, G.B., Subrahmanyam, T.V., Sun, Z., Forsling, W., 1991. Shear-flocculation of quartz. Int. J. Miner. Process. 32 (3/4), 283 – 294. Samygin, V.D., Barskii, A.A., Angelova, S.M., 1968. Mechanism of mutual flocculation of particles differing in size. Colloid J. 30, 435 – 439. Schulze, H.J., 1984. Physico-Chemical Elementary Processes in Flotation. Elsevier, Amsterdam, pp. 26 – 35. Skvalar, I., Kmet, S., 1991. Influence of wettability on the aggregation of fine minerals. Int. J. Miner. Process. 32, 111 – 131. Somasundaran, P., 1984. Role of surface phenomena in the beneficiation of fine particles. Min. Eng., Aug., 1177 – 1186. Subrahmanyam, T.V., Forssberg, K.S.E., 1990. Fine particles processing: shear-flocculation and carrier flotation—a review. Int. J. Miner. Process. 30 (3/4), 186 – 265. Valioulis, I.A., List, E.J., 1984. Collision efficiencies of diffusing spherical particles: hydrodynamic, van der Waals and electrostatic forces. Adv. Colloid Interface Sci. 20, 1 – 20. van de Ven, T.G.M., Mason, S.G., 1975a. The microrheology of colloidal dispersions: IV. Pairs of interacting spheres in shear flow. J. Colloid Interface Sci. 57 (3), 505 – 516. van de Ven, T.G.M., Mason, S.G., 1975b. The microrheology of colloidal dispersions: V. Primary and secondary double lets of spheres in shear flow. J. Colloid Interface Sci. 57 (3), 517 – 534. van de Ven, T.G.M., Mason, S.G., 1976. The microrheology of colloidal dispersions: IV. Pairs of interacting spheres in shear flow. J. Colloid Interface Sci. 57, 505 – 516. van Oss, C.J., Giese, R.F., Costanzo, P.M., 1990. DLVO and non-DLVO interactions in hectorite. Clays Clay Miner. 38 (2), 151 – 159. Veeramasuneni, S., Hu, Y., Yalamanchili, M.R., Miller, J.D., 1997. Interaction forces at high ionic strengths: the role of polar interfacial interactions. J. Colloid Interface Sci. 188, 473 – 480. Warren, L.J., 1984. Ultrafine particles in flotation. In: Jones, M.J., Woodcock, J.T. (Eds.), Principles of Mineral Flotation, The Wark Symposium, Australia. Aus/MM, Victoria, Australia, pp. 185 – 212. Xu, Z., Yoon, R.H., 1989. The role of hydrophobic interactions in coagulation. J. Colloid Interface Sci. 132 (2), 532 – 541.
Hydrodynamic interactions between particles in aggregation and flotation Yuehua Hu a, Guangzhou Qiu a, J.D. Miller b,* b
a Department of Mineral Engineering, Central South University, Changsha 410083, China Department of Metallurgical Engineering, College of Mines and Earth Sciences, University of Utah, 135 S. 1460 E. 412 William C. Browning Building, Salt Lake City, UT 84112, USA
Received 15 September 2000; received in revised form 23 October 2001; accepted 9 December 2002
Abstract The aggregation and flotation behavior of hematite and wolframite have been investigated through particle size analysis, flotation tests and measurement of energy input based on hydrodynamic interactions. In has been shown that when fine and coarse particles are mixed and conditioned in surfactant solution, the flocs with particle size greater than that of the coarse particle size and the flocs with particles size between that of the fine and coarse particle sizes are formed. The bigger size floc is attributed to the adhesion of fine particles onto coarse particles. The medium size floc may be the aggregation among fine particles themselves and detached flocs from the coarse substrate due to the shearing forces. Both cases depend on the state of turbulent flow of pulp and hydrodynamic conditions. The studies on the effect of particle size, agitating speed and time, and the structure of agitation tank on aggregation and flotation show the importance of hydrodynamic interactions in aggregation and flotation. D 2003 Elsevier Science B.V. All rights reserved. Keywords: hydrophobic aggregation; hydrodynamic interactions, flotation; hematite, wolframite; reynolds number, micro-size of turbulent flow; shearing stress
1. Introduction Besides surface forces, hydrodynamic interaction also plays a very important kinetic role in determining the collision efficiency between particles, the state of particulate suspension and flotation. The extent of hydrodynamic effect is determined by the character of the liquid * Corresponding author. Fax: +1-801-581-4937. E-mail address: [email protected] (J.D. Miller). 0301-7516/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-7516(03)00023-1
158
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
field flowing around the particles which, in turn, is dependent on the type of flow, i.e. the Reynolds number. Hydrodynamic forces influence the rate of aggregates growth and breakup in several ways (Valioulis and List, 1984; Derjaguin and Dukhin, 1979; Warren, 1984; Lafuma et al., 1991; Hu et al., 1994). Considering van der Waals attraction and electrostatic repulsion in DLVO theory, van de Ven and Mason (1975a,b, 1976) established that a suspension could be unstable at very low shear rate, due to aggregation in the DLVO secondary energy minimum, stable at intermediate shear rates, because hydrodynamic forces were large enough to push particles out of the shallow secondary minimum, and unstable at high shear rates, because the hydrodynamic forces were then large enough to overcome the DLVO energy barrier and allow the particles to aggregate in the primary energy minimum. However, it has been reported that if only taking into account DLVO forces the aggregation between particles with higher surface potential in surfactant solution may not occur even if at higher shearing rate. Based on the extended DLVO theory, if the particles are rendered hydrophobic in which the polar interfacial interaction energy of particles rSLAB>0, the aggregation occurs in the secondary energy minimum at low shear rates. At high shear rates, the stable hydrophobic flocs are formed in the primary energy minimum (Skvalar and Kmet, 1991; van Oss et al., 1990). It indicated that hydrodynamic forces have an effect in the process of floc growth and floc break-up. Particles size, the agitation condition and the structure of the agitation tank affect the character of the liquid field flowing around the particles, which influences the hydrodynamic interaction and flotation (Chia and Somasundaran, 1983; Raju et al., 1991; Liang and Shi, 1990; Subrahmanyam and Forssberg, 1990). The effect of these factors has been studied in this paper.
2. Experimental 2.1. Materials Pure wolframite and hematite were taken from Yaogangxian Mine and from Dong Anshan Mine in China, respectively. The handpicked pure lump samples were crushed, ground in a porcelain mill and screened to the desired size fractions. The coarser fractions of different size were used as carriers in the tests. The fraction of 5 Am obtained by sedimentation was used as ultra fine feed. Double distilled water was used in preparing all solutions. The sodium oleate used was grade purchased from Hunan Chemical. The styryl phosphoric acid was laboratory grade supplied by Changsha Research Institute of Mining and Metallurgy. All other reagents used for the pH adjustment were of analytical grade. 2.2. Methods In flotation, the 5Am mineral samples of 5 g were fully dispersed with distilled water agitating 30 min at 2150 rpm using a common impeller in a beaker. The dispersed pulp was transferred into a baffled tank made of organic glass with a volume of 200 ml. The collector was added after coarse particle addition and then the pH was adjusted. The pulp
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
159
was then conditioned for the required duration at desired speeds and the pH was measured. The conditioned pulp was then transferred to a micro-flotation cell with a volume of 100 ml, and floated at 1600 rpm for 5 min. Adsorption of styryl phosphoric acid (SPA) on wolframite was determined from the difference between the initial and equilibrium SPA concentrations. Preliminary kinetic studies showed that the adsorption of styryl phosphoric acid from the solution reaches equilibrium within 20 min. Therefore, 2 g of wolframite was stirred with 100 ml of a SPA solution at the desired initial concentration and pH in 200-ml beaker for 30 min. After equilibration, the suspension was centrifugalized. The supernatant was used for pH measurement and SPA concentration measurement, which was measured by a potential titration method.
3. Results and discussion 3.1. Collision rate between particles and flotation of fine particles The effects of conditioning speed and time on the flotation of 5Am wolframite are demonstrated in Fig. 1 using SPA as a collector and 25 + 38Am wolframite as carrier. The relative flotation recovery of 5Am wolframite is increased with the increase of conditioning time up to 60 min. The relative flotation recovery of 5Am wolframite is at first increased with the increase of conditioning speed up to 4000 rpm and then decreased when conditioning speed increases over 4000 rpm. The enhancement of fine mineral flotation requires the adhesion of fine particles onto mother particles, i.e. the aggregation between fine and coarse particles. On one hand the aggregation depends on the interaction forces between particles (Xu and Yoon, 1989; van
Fig. 1. Effects of conditioning time and speed on carrier flotation of 5Am wolframite in various speed.
160
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Oss et al., 1990; Qiu et al., 1993; Veeramasuneni et al., 1997). When the interaction forces are repulsive, the aggregation among particles may not occur. When the interaction forces are attractive, the aggregation may be possible. In this case, the rate of aggregation will depend on the probability of collision from the hydrodynamic aspect. The rate of aggregation of particles depends on both the probability of collision and the probability of adhesion. For particles which collide by diffusion, Levich (1962) gives the collision rate: e 12 Jt ¼ 12pbR3 n20 ð1Þ m Where Jt is the collision rate per unit volume by turbulent diffusion mechanism, b is a constant, R is the radius of particles, n0 is the initial concentration of particles, e is the energy loss occurring in the flow per second per unit volume in J s 1 kg 1, m is the kinematic viscosity in m2 s 1. For collisions between particles of different size, R in Eq. (1) was substituted by (R1 + R2)/2 and n02 by n1 and n2, thus Jt ~ðR1 þ R2 Þ3 n1 n2
ð2Þ
Obviously, the collision rate between fine and coarse particles is much higher than that between the fine particles, providing a basis for coarse particles serving as carriers promoting the aggregation between particles. Expressing e0 in terms of the fluid flow velocity Vt, Levich showed that 3
R3 n20 Vt2 Jt ¼ pffiffiffiffiffiffi VL
ð3Þ
where L is the maximum scale of turbulence and approximately equal to the diameter of the stirring vessel. If the fluid flow velocity is directly proportional to the stirrer speed then the collision rate is proportional to the 3/2 power of the stirrer speed. There is an increase in collision rate with fluid velocity, which is enhanced by increasing stirrer speed. The decrease in flotation recovery at a very high conditioning speed of 4000 rpm may be attributed to shearing forces causing floc breakage . Fuerstenau et al. (1988) observed breakage of larger flocs at high shear rates in shear flocculation of fine hematite. That study used a lower speed (2000 rpm) than the condition speed used in this study. The agitation speeds thereby vary from system to system. 3.2. Energy dissipation of particles in the flow The kinetic energy of the particles in mixing can be estimated using the equation below Vk ¼
1 2 lu 2 r
ð4Þ
in which l is the reduced mass of interacting particles of mass m1 and m2 in kg and given by (Somasundaran, 1984). m1 m2 l¼ ð5Þ m1 þ m2 mr is the relative velocity of the particles.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
161
At R < k0, dissipative subrange of microturbulance (Delichatsios and Probstein, 1975) rffiffiffiffiffiffirffiffiffi rffiffiffiffiffiffiffiffi 1 e e ðR1 þ R2 Þ ¼ ð6Þ ðR1 þ R2 Þ ur ¼ 15 m 15m At R>k0, inertial subrange of microturbulence 1
1
lr ¼ 1:37e 3 ðR1 þ R2 Þ 3 k0 is turbulent microscale 3 14 m k0 ¼ e e¼
P m
ð7Þ
ð8Þ ð9Þ
here m is liquid mass and P is the power input (Schulze, 1984). The energy dissipation in the flow and the kinetic energy of the particles in the wolframite system of 5Am fine particles and 25 –38Am carrier particles are calculated in terms of Eqs. (4) – (9) and the results are presented in Fig. 2. e and VK are increased with the increase of conditioning speed. The energy dissipation in the flow and the kinetic energy of the particles in strong stirring may increase the collision between particles on one hand, and cause a rise in pulp temperature on the other hand (see Fig. 3), which can be expected to enhance collector adsorption on wolframite and hence enhance their hydrophobic aggregation and flotation recovery of fine particles (see Fig. 4). Fig. 3 shows that the pulp temperature is increased with the increase of conditioning speed and time. Fig. 4 shows that the adsorption of SPA on wolframite is increased and
Fig. 2. The energy dissipation e and the kinetic energy (Vk) of the particles in the flow vs. agitation speed.
162
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Fig. 3. Effect of conditioning speed and time on pulp temperature.
thereby relative flotation recovery of 5Am wolframite is increased with the increase of pulp temperature due to strong agitation. 3.3. Optimal size of coarse particles affecting the aggregation of fine particles As above, coarse particles can serve as carriers for fine particles because coarse particles have a greater collision rate with fine particles, and fine hematite and wolframite can
Fig. 4. Effect of pulp temperature on adsorption of styryl phosphoric acid at wolframite and on relative flotation recovery of 5Am wolframite.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
163
Table 1 The k0 values at different agitation speed Conditioning speed (rpm)
870
1200
1650
2050
2420
2900
k0 in Eq. (8) (Am) k0 in Eq. (10) (Am)
54.3 63.8
50.2 50.2
46.8 39.4
44.1 33.6
40.3 29.6
37.8 25.8
adhere onto hydrophobilized coarse substrates. What size is then best for coarse particles used as carriers, i.e. what carrier size is the optimal to make the carrier action maximum? On the basis of the theories on particle collision, mass transfer and concomitance, the collision rate between fine particles and coarse particles will reach a maximum, producing optimum carrier action, when the size of the coarse particle is comparable to the turbulent microscale of the vortex, k0. The value of k0 can be obtained either using Eq. (8) or using the equation below (Derjaguin et al., 1969) k0 ¼
L da2 n
ð10Þ
34
60m
where n is conditioning speed, L and da are, respectively, the diameter of stirring tank and impeller, L = 4.7 cm, da = 3.4 cm in the present work. The calculated k0 values in terms of Eqs. (8) and (10) from the data in Fig. 2 are given in Table 1. The reduced amount of the 5Am hematite by addition of various sizes dp of coarse particles at different conditioning speed is shown in Figs. 5 and 6. It can be seen that when k0 dp>0, i.e. the particle size of the coarse particles is less than the turbulent microscale k0, the reduced amount of 5Am hematite increases with the increase of the coarse particle size. When k0 dp < 0, i.e. the particle size of carrier is greater than the k0, the reduced
Fig. 5. The reduced amount of 5Am hematite vs. k0 dp.
164
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Fig. 6. The reduced amount of 5Am hematite vs. k0 dp.
amount of 5Am hematite decreases with the increase of coarse particle size. This shows that there exists an optimal coarse particle size, dp = k0. Using the particles with size dp = k0 as carriers, the carrier action of coarse particles and the reduced amount of 5Am hematite particles reach a maximum. Fig. 7 demonstrates the results of the flotation of 5Am hematite in carrier flotation at different stirring speed by adding different size of carrier. It further shows the optimum carrier action of coarse particles with dp = k0. The relative flotation recovery of 5Am hematite is maximum at dp = k0.
Fig. 7. The relative flotation recovery of 5Am hematite vs. (k0 dp).
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
165
The relative motion speed of coarse grain in turbulent flow is directly proportional to R2c at Rc V k0 and to R1/3 at Rc>k0 according to Samygin et al. (1968). Therefore, the relative motion speed of coarse particles, and thus the collision rate between fine particles and coarse particles, will be greatly increased with the increase of coarse particles size at Rc V k0. Whereas, the relative motion speed of coarse particles and hence the collision rate between fine particles and coarse particles will be decreased with the increase of coarse particle carrier size at Rc>k0. This suggests that the relative flotation recovery of fine particles will be enhanced with the enhancement of the carrier size at Rc V k0, and will be decreased with the increase of carrier size at Rc>k0 because the aggregates will be broken off due to intensifying of attrition action at Rc>k0. 3.4. Aggregation of fine particles in the vortices formed by movement of coarse particles Fig. 8 shows the particle size distribution before and after conditioning when 30– 40Am hematite was added to 5Am hematite pulp. Obviously, the content of 5Am particles is greatly decreased and the content of aggregates with size above the coarse size is increased after conditioning. It appeared that flocs with sizes between 5 and 30 Am, called middle size flocs, were produced. What is responsible for the formation of middle size flocs? There is a boundary layer between particles and fluids, the state of which varies with the Reynolds number of the particle because of the motion between the particle and fluid. The particle Reynolds number is given by dp us Rep ¼ ð11Þ m where us is the rate of sliding motion of particle, which can be obtained by the settling rate of particles. When Rep < 1, a boundary layer with laminar flow is formed between particle
Fig. 8. The distribution of hematite suspension by addition of 30 – 40 Am hematite into 5Am hematite pulp.
166
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
and fluid. When Rep>1, the boundary layer is transferred to turbulent flow. When Rep>10, the boundary layer breaks off. The flow lines near the coarse particle will curl up to form definite vortices. In this case, part of the kinetic energy of the particle motion is released in the form of heat owing to friction, and the rest of the kinetic energy is turned into work done producing turbulent wave. That is to say, the particles in motion will consume part of the turbulent energy, the other part of which will be consumed by turning big-sized vortices into small-sized vortices, bringing about changes in the frequency spectrum of turbulent motion. The eddy produced by coarse particle tailing trace is favorable for the aggregation of fine particles. This is the so-called ‘‘promoting aggregation action of coarse particles’’, which can be accessed using the particle Reynolds number. Fig. 9 shows that the content of newly produced middle size flocs increases with the increase in the particle Reynolds number when coarse particles are added into the pulp of fine hematite at different conditioning speeds. 3.5. Effect of shearing rate on aggregation of fine particles The behavior of fine particles will be different when adding coarse particles into the pulp with fine particles. The collision rate and thereby the adhesion of fine particles onto mother particle will increase. The higher collision rate between coarse particles in strong stirring may result in the detachment of already adhered fine flocs. This is especially true when the coarse particle size exceeds the microscale of turbulence, the aggregates break due to attrition and shear forces generated in the liquid. Lu and Spielman (1985) reported that the floc splitting frequency, fB, was directly proportional to the shear rate, e 12 ð12Þ fB ¼ KG ¼ K m where K is a constant.
Fig. 9. The amount of newly produced middle size floc vs. particle Reynolds number.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
167
Fig. 10. The content of newly produced middle size floc vs. particle size of coarse particle.
Figs. 10 and 11 show that the content of newly grown middle size flocs is increased with the increase in particle size of coarse particles and shear forces, which accounts for the intermedium-breakage action of coarse particles. 3.6. Effect of the structure of vessel on flow state and flotation of fine particles The turbulent flow state is very important to the collision and adhesion between fine particles and coarse particles in flotation, which is closely related not only to agitation
Fig. 11. The content of newly produced middle size floc vs. shear rate in the flow.
168
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
Fig. 12. Effect of proportion of carrier on carrier flotation conditioning in unbaffled and baffled tank.
intensity and pulp property, but to cell geometry including the structure of the stirring vessels and the shape of impellers. Two vessels with and without baffles were tested in the present research. At high speed agitation the deeper swirl and vortex were formed and pulp moved along the inside wall of the tank, the moving speed of particles and hence the collision rate between fine
Fig. 13. The different types of impellers used.
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
169
Table 2 The results of carrier flotation of 5 Am wolframite conditioning using various impellers Impeller types
1
2
3
4
Relative flotation recovery (%)
61.51
54.26
58.21
52.24
and coarse particles will be reduced due to the friction between the particles with various sizes. In the baffled tank, strong turbulent flow from top to bottom turnover will be produced, which will increase the collision rate between fine particles and coarse particles. The adhesion of fine particles onto coarse substrates is more effective and relative flotation recovery of fine particles by adding coarse particles into pulp is higher when the pulp is conditioned in the baffled cell than in the unbaffled cell (see Fig. 12). The effects of different impellers of various shapes (see Fig. 13) on fine flotation are also examined and the results are given in Table 2. It can be seen from Fig. 13 and Table 2 that when four different types of impellers are used for agitation, the flotation recovery of fine wolframite is in the order of types: 1>3>2>4, with the type 1 double-bladed paddle impeller being the best.
4. Conclusions The important variables influencing hydrodynamic interactions in fine flotation include, the intensity and time of agitation, the size of coarse particles, the structure of agitation vessel and shape of impeller, etc. Agitation intensity plays a major role in flotation. In turbulent flow, a bigger floc is formed due to the adhesion of fine particles onto a coarse particle substrate, and some middle size flocs with sizes between that of coarse and fine particles are also formed. Suitable intense agitation can increase the collision rate between fine and coarse particles, and can also enhance chemisorption of collector on the mineral surface, via the accompanying increase in the temperature of the flotation pulp, which makes the hydrophobic aggregation between fine particles increase. These effects enhance the flotation recovery of fine particles. There exists an optimal coarse particle size, at which the collision probability between fine and coarse particles increases, the formation of flocs (i.e. the reduced amount of 5Am particles ) and thus the flotation of fine particles are greatly increased. The baffled stirring tank and doublebladed paddle impeller cause stronger turbulent flow, which is useful for the collision and aggregation between particles, providing improved effectiveness for fine particle flotation.
Acknowledgements The authors would like to thank the China National Science Fund for Distinguished Young Scholars No. 59925412 and the National Key Fundamental Research Program G1999064901 for supporting this research.
170
Y. Hu et al. / Int. J. Miner. Process. 70 (2003) 157–170
References Chia, Y.H., Somasundaran, P., 1983. Carrier flotation of anatase from clay and its physicochemical mechanisms. In: Subhas, M.G. (Ed.), Ultrafine Grinding and Separation of Industrial Minerals. SME AIME, vol. 12, pp. 117 – 131. Delichatsios, M.A., Probstein, R.F., 1975. Coagulation in turbulent flow: theory and experiment. J. Colloid Interface Sci. 51 (3), 394 – 405. Derjaguin, B.V., Dukhin, S.S., 1979. Kinetic theory of the flotation of fine particles. 13th Inter. Miner. Process. Congr., Warsaw, Poland, Part A. Polish Scientific Publishers, pp. 21 – 60. Derjaguin, B.V., Livshits, A.K., Samygin, V.D., 1969. Aggregate stability of mineral suspensions in turbulent flow and the floatability of slurries. Int. Cong. Miner. Process., Leningrad, pp. 674 – 685. Fuerstenau, D.W., Li, C., Hanson, J.S., 1988. Shear flocculation and carrier flotation of fine hematite. In: Plumpton, A.J. (Ed.), Proc. Int. Symp. Production and Processing of Fine particles. Pergamon Press, New York, pp. 329 – 335. Hu, Y., Qiu, G., Wang, D., 1994. The studies of carrier flotation of ultrafine wolframite. Trans. Nonferr. Met. Soc. China 2, 44 – 48. Lafuma, F., Wong, K., Cabane, B., 1991. Bridging of colloidal particles through adsorbed polymers. J. Colloid Interface Sci. 143 (1), 9 – 21. Levich, V.G., 1962. Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ. 512 pp. Liang, R., Shi, D., 1990. Carrier flotation of ultrafine cassiterite particles and its mechanism. Nonferr. Met. 42 (3), 26 – 31. Lu, C.F., Spielman, L.A., 1985. Kinetics of flocculation breakage and aggregation in agitated liquid suspensions. J. Colloid Interface Sci. 103 (1), 95 – 105. Qiu, G., Hu, Y., Wang, D., 1993. Interactions Between Particles and Flotation of Fine Particles. CSUT Press, Changsha. 431 pp. (in Chinese). Raju, G.B., Subrahmanyam, T.V., Sun, Z., Forsling, W., 1991. Shear-flocculation of quartz. Int. J. Miner. Process. 32 (3/4), 283 – 294. Samygin, V.D., Barskii, A.A., Angelova, S.M., 1968. Mechanism of mutual flocculation of particles differing in size. Colloid J. 30, 435 – 439. Schulze, H.J., 1984. Physico-Chemical Elementary Processes in Flotation. Elsevier, Amsterdam, pp. 26 – 35. Skvalar, I., Kmet, S., 1991. Influence of wettability on the aggregation of fine minerals. Int. J. Miner. Process. 32, 111 – 131. Somasundaran, P., 1984. Role of surface phenomena in the beneficiation of fine particles. Min. Eng., Aug., 1177 – 1186. Subrahmanyam, T.V., Forssberg, K.S.E., 1990. Fine particles processing: shear-flocculation and carrier flotation—a review. Int. J. Miner. Process. 30 (3/4), 186 – 265. Valioulis, I.A., List, E.J., 1984. Collision efficiencies of diffusing spherical particles: hydrodynamic, van der Waals and electrostatic forces. Adv. Colloid Interface Sci. 20, 1 – 20. van de Ven, T.G.M., Mason, S.G., 1975a. The microrheology of colloidal dispersions: IV. Pairs of interacting spheres in shear flow. J. Colloid Interface Sci. 57 (3), 505 – 516. van de Ven, T.G.M., Mason, S.G., 1975b. The microrheology of colloidal dispersions: V. Primary and secondary double lets of spheres in shear flow. J. Colloid Interface Sci. 57 (3), 517 – 534. van de Ven, T.G.M., Mason, S.G., 1976. The microrheology of colloidal dispersions: IV. Pairs of interacting spheres in shear flow. J. Colloid Interface Sci. 57, 505 – 516. van Oss, C.J., Giese, R.F., Costanzo, P.M., 1990. DLVO and non-DLVO interactions in hectorite. Clays Clay Miner. 38 (2), 151 – 159. Veeramasuneni, S., Hu, Y., Yalamanchili, M.R., Miller, J.D., 1997. Interaction forces at high ionic strengths: the role of polar interfacial interactions. J. Colloid Interface Sci. 188, 473 – 480. Warren, L.J., 1984. Ultrafine particles in flotation. In: Jones, M.J., Woodcock, J.T. (Eds.), Principles of Mineral Flotation, The Wark Symposium, Australia. Aus/MM, Victoria, Australia, pp. 185 – 212. Xu, Z., Yoon, R.H., 1989. The role of hydrophobic interactions in coagulation. J. Colloid Interface Sci. 132 (2), 532 – 541.