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Drop size distribution in a batch mixer under breakage conditions
Hydrometallurgy 63 (2002) 65 – 74 www.elsevier.com/locate/hydromet
Drop size distribution in a batch mixer under breakage conditions M.C. Ruiz*, P. Lermanda, R. Padilla Department of Metallurgical Engineering, University of Concepcio´n, Edmundo Larenas 270, Casilla 53-C, Concepcio´n, Chile Received 6 June 2001; received in revised form 10 October 2001; accepted 20 October 2001
Abstract The equilibrium size distribution, F0(v), of organic drops produced in a batch mixing vessel has been determined experimentally for very low dispersed phase fractions (0.006) in order to reduce the coalescence between drops to negligible values. The organic phase used was a 1:1 mixture of a salicylaldoxime (LIX 860N-IC) and a ketoxime (LIX 64-IC) in an aliphatic diluent (Escaid 103). The aqueous phase was a 0.25-M sodium sulfate solution. The results indicated that the system reaches an equilibrium drop size distribution in less than 30 min of stirring time. An increase in the stirring speed increased the tendency of the organic drops to break, shifting the drop size distribution toward the smaller drop sizes. An increase in temperature from 22 to 32 °C decreased the size of the organic drops, while a change in the concentration of the extractant in the organic phase from 7% to 20% by weight had little effect. Both effects can be attributed to changes in the physical properties of the system. A decrease in pH of the aqueous phase from 5.7 to 2.0 increased progressively the tendency of the organic drops to undergo breakage giving finer drop size distributions due to changes in the surface charge of the organic drops produced by the pH change. In all cases, the experimental drop size distributions could be accurately represented by a lognormal distribution. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Drop size distribution; Batch mixer; Breakage conditions
1. Introduction In many industrial operations, liquid – liquid dispersions are formed to enhance the mass and heat transfer between the phases or to enhance the rate of a chemical reaction. In the copper industry, the recovery of metal from dilute leaching solutions is carried out by solvent extraction, usually in mixer – settler units. In the mixer, dispersions are generated mainly by mechanical agitation to accomplish the extraction of the copper from the leaching solution into the organic phase
*
Corresponding author. Tel.: +56-41-204955; fax: +56-41243418. E-mail address: [email protected] (M.C. Ruiz).
for subsequent stripping of the organic into an electrowinning electrolyte. The drop size distribution produced in the mixer is critical for the performance of the solvent extraction reactor because it not only affects the rate of the extraction and stripping reactions but it also influences the subsequent phase separation in the settler. The organic losses by entrainment in the solvent extraction process are also intimately related to drop size distributions. In order to understand better the formation of dispersion in a solvent extraction process and how it is affected by the operating variables, this work focuses on the study of drop breakage in a batch mixer. The size distribution of drops produced in a mixer evolves as a result of two processes: drop breakage due to the turbulent field and coalescence due to
0304-386X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 6 X ( 0 1 ) 0 0 2 2 3 - 7
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collisions between drops. The kinetics of both rate processes must be known to predict and control the size distribution of drops in a mixer. However, since both rate processes occur simultaneously, it is extremely difficult to elucidate how the physical properties of the system and the operating variables affect each, unless the experimental conditions are chosen to minimize or completely eliminate one of the two processes. Two methods have been used to eliminate coalescence between drops: (i) the addition of surfactant substances to the system (Kumar et al., 1991) and (ii) the use of low dispersed phase fractions (Narsimham et al., 1980, 1984; Konno et al., 1980, 1993; Lagissety et al., 1986; Calabrese et al., 1986; Wang and Calabrese, 1986; Chatzi and Kiparissides, 1992; Sathyagal et al., 1996). It has been shown (Kosshy et al., 1988) that the addition of surfactants can produce local differences in interfacial tension when the drop deforms which affects the breakage process. Bearing this in mind, the technique selected in this research to obtain information on drop breakage was the use of very low dispersed phase fractions. Under this condition, due to the low number density of drops in the dispersion, the interactions between drops are reduced to negligible values and the resulting drop size distribution is due to breakage only. It is generally accepted that a drop in a turbulent field breaks mainly under the influence of inertial stresses arising from the turbulent pressure fluctuations, which tend to deform the drop. On the other hand, the elastic stress due to the interfacial tension and the viscous stress due to the internal flow tend to resist the deformation of the drop. As the size of the drop decreases, the deforming stress across it also decreases, whereas the restoring stresses increase. A size is finally reached where the deforming stress is unable to break the drop. This critical size is normally referred to as dmax, the diameter of the largest drop which can survive the flow field without further breakage. Numerous researchers have determined experimentally this maximum diameter in a stirred vessel and various correlations and models have been proposed to predict the value of dmax as a function of the characteristics of the flow field and the physical properties of the system (Kumar et al., 1991, 1992; Lagissety et al., 1986; Sprow, 1967; Lam et al., 1996). Shinnar (1961) derived the following equation for the
maximum stable drop diameter in a turbulent stirred vessel with a dilute dispersion. dmax ¼ C1 We0:6 D 2
ð1Þ 3
with We ¼ qc Nr D where We is the Weber number, D is the diameter of the impeller, N is the impeller speed, qc is the continuous phase viscosity, r is the interfacial tension and C1 is an experimentally determined constant which depends on the vessel geometry and impeller type. Eq. (1) neglects the viscous forces in the dispersed phase; consequently, it should only apply to dispersed phases of low viscosity. Recently, various models have been proposed taking into account the effect of the dispersed phase viscosity on the maximum stable drop size. Lagissety et al. (1986) proposed the following equation for Newtonian fluids 2
h
4 C2 We ¼
4 dmax 5=3
Re We
D
3
6 7 1 1 7 i1=2 tan 6 4h dmax 5=3 i1=2 5 1 1 4 C2 We D
dmax D
1=3 ð2Þ 2
with Re ¼ qc Nl D where ld is the viscosity of the d dispersed phase and the constant C2 is dependent on the geometry of the vessel and impeller. Calabrese et al. (1986) and Wang and Calabrese (1986) used a semi-empirical approach to develop various correlations for the maximum stable drop diameter for drops with a wide range of viscosity. The following equation was proposed for low to moderate dispersed phase viscosity " #3=5 dmax dmax 1=3 3=5 ¼ C3 We 1 þ C4 Vi D D
ð3Þ
1=2 with Vi ¼ ldrND qqc where Vi is a tank viscosity d group or capillary number representing the ratio of dispersed-phase viscous force to surface force, C3 and C4 are empirical constants, and qc and qd are the viscosities of the continuous and dispersed phases, respectively. In the limiting condition when the interfacial tension provides the dominant stabilizing stress
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of the drops (ld ! 0), both Eqs. (2) and (3) reduce to Eq. (1). The existence of a maximum stable drop size implies that the size distributions of drops in a batch mixing vessel will reach a steady state where all the drops will be smaller than the critical size. If the size distribution is produced by two competitive processes such as breakage and coalescence, this steady state is dynamic and it is the result of a balance between these opposite rate processes. The dynamic steady state should be independent of the earlier conditions of the system and, therefore, of the initial conditions. On the other hand, if only breakage occurs in the system, this steady state can be called static, in the sense that the drops smaller that the critical size undergo no further change and the drop size distribution could depend on the earlier conditions of the system. In spite of the widespread use of the solvent extraction process in the copper industry, very few studies on dispersions have dealt with organic phases containing copper specific extractants, or have used pump – mix impellers, widely used in solvent extraction plants. Consequently, the characteristics of the dispersions produced in such processes are little known. The objective of this work was to determine how the various operating variables, pertinent to solvent extraction plants, affect the drop breakage process and the resulting equilibrium drop size distribution in dispersions produced by mechanical agitation.
2. Experimental work The organic phase used in this study was a 1:1 mixture of a salicylaldoxime (LIX 860N-IC) and a ketoxime (LIX 84-IC) in an aliphatic diluent (ESCAID 103). This mixture of hydroxyoxime extractants is used in several copper solvent extraction plants for the recovery of copper from sulfate solutions. The concentration of the organic phase in most experiments was 7% by volume of extractant (3.5% of LIX 860NIC + 3.5% of LIX 84-IC). The aqueous phase was a 0.25-M sodium sulfate solution which was used instead of a copper sulfate solution mainly to eliminate mass transfer from the aqueous to the organic phase. Small amounts of sulfuric acid were added to regulate the pH when necessary.
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The experiments were carried out in a batch mixing vessel made of transparent acrylic. The mixer was a rectangular vessel of 25 25 26 cm. A pump – mix impeller, 15 cm in diameter, double shrouded and with eight curved blades, was used to generate the dispersion. The impeller was located in the center of the mixer, 4 cm above the bottom of the vessel, through a stainless steel shaft connected to a variable speed agitation system. All the experiments were carried out under aqueous continuity with a low organic phase fraction to reduce the coalescence of drops to negligible values. The procedure consisted of filling the mixer with 16 L of aqueous phase at the temperature specified for the experiment. Then, the stirring speed was incremented to the desired level and a small amount of organic phase, usually 100 cm3, was rapidly added to the vessel. The experiment was run for 30 min to achieve steady state, and dispersion samples were withdrawn from a point located 6 cm from the wall and 10 cm above the bottom of the vessel. The sampling technique consisted of siphoning a small amount of the dispersion into a Petri dish containing 7 – 8 cm3 of a gelatin solution (8% by weight) kept at about 35 °C. Subsequently, the Petri dish with the dispersion sample was cooled quickly in an ice bath. After setting of the gelatin, the sample was stored in a refrigerator until analyzed. To determine the size distribution of the embedded drops, digitized images of sectors of the sample were obtained by a microscope and a video camera Sony model HAD SSC-D50, connected to a personal computer. The drops were counted and sized by an image-analyzer software Omnimet Enterprise version 1.01 B002.
3. Results and discussion Experiments were carried out under various conditions to determine the effect of the operating variables on the equilibrium size distribution of the organic drops. The variables studied were stirring speed, pH of the aqueous phase, concentration of extractant in the organic phase, and temperature. The volume, v, was used as a characteristic size of the drops in the determination of the drop size distribution. However, for the maximum drop size, the diameter was used to facilitate comparison with data in the literature and to
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test the various correlations proposed for dmax. Since the method of analysis counted and sized individual drops, the size distribution obtained was a number distribution. Due to the wide range of drop sizes measured, and to facilitate the analysis of the experimental data, a logarithmic discretization scale was chosen for the size variable of the dispersion drops. In this way, the number of drops in each volume interval was determined. A minimum of 400 drops was considered to give a reliable drop size distribution, although in most cases samples with larger number of drops were measured. 3.1. Characterization of the organic and aqueous phases Interfacial tensions were determined using a du Nou¨y ring apparatus, the densities of aqueous and organic phases were determined through specific gravity measurements using hydrometers and the viscosities were determined by an Ostwald viscometer. Table 1 summarizes the density and viscosity values obtained for the various aqueous and organic phases used in this research, and Table 2 shows the values of the interfacial tension for the specified experimental conditions.
Table 1 Density and viscosity of the solutions
Aqueous phase 0.25 M Na2SO4, pH 5.7 0.25 M Na2SO4, pH 4.0 0.25 M Na2SO4, pH 2.0 0.25 M Na2SO4, pH 5.7 Organic phase 7% LIX 860N-IC + LIX 84-IC 7% LIX 860N-IC + LIX 84-IC 20% LIX 860N-IC + LIX 84-IC
Temperature, °C
Density, kg/m3
Viscosity, Pas
22
1030
1.052 10 3
22
1030
1.053 10 3
22
1030
1.054 10 3
32
1021
8.55 10 4
22
815
1.984 10 3
32
808
1.384 10 3
22
830
3.211 10 3
3.2. Reproducibility of the sampling and measuring technique In order to test the validity and reproducibility of the method used for the drop size characterization, particularly, the procedure used for sample withdrawal, duplicate experiments were carried out under identical experimental conditions and the drop size distributions were determined and compared. Fig. 1 shows the drop size distributions determined at 1 and 30 min of stirring time for duplicate experiments. The size distributions are presented in this figure as the cumulative number-percent, F0(v), versus the logarithm of the volume of the drops. It can be observed that the reproducibility of the technique used to determine the drops size distribution in the mixer is very good even for short stirring times. 3.3. Determination of the equilibrium conditions The time required for the dispersion drops to evolve to a constant or equilibrium drop size distribution in a batch mixer seems to vary widely for different liquid – liquid systems. In addition, the time to reach equilibrium has also been found to depend on the type of impeller used to produce the dispersion (Pacek et al., 1999) and on operating variables such as the stirring speed and the dispersed phase fraction. A faster approach to equilibrium has been observed when the stirring speed was increased or the dispersed phase fraction was decreased (Mackelprang et al., 1981). Many liquid – liquid dispersions have been reported to reach equilibrium conditions in about 1 h of mixing (Calabrese et al., 1986; Kosshy et al., 1988; Sprow, 1967; Kumar et al., 1991), while for some others systems, specially for dispersed phases of high viscosities, longer times were necessary (Chatzi and Kiparissides, 1992; Lam et al., 1996; Paceck et al., 1998). In the present study, it was found that a time of 30 min was enough for the system to reach a constant drop size distribution. This result is in agreement with the work of Mackelprang et al. (1981) who reported that 30 min of stirring time was enough for the dispersion to reach an equilibrium drop size distribution in a system containing an hydroxyoxime type copper specific extractant (LIX 64N), dispersed in a sodium sulfate solution. Fig. 2 shows the cumulative number distributions of drops obtained at stirring times of 16
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69
Table 2 Interfacial tension Aqueous phase 0.25 0.25 0.25 0.25 0.25
M M M M M
Na2SO4, Na2SO4, Na2SO4, Na2SO4, Na2SO4,
Organic phase pH pH pH pH pH
5.7 4.0 2.0 5.7 5.7
7% 7% 7% 7% 20%
LIX LIX LIX LIX LIX
860N-IC + LIX 860N-IC + LIX 860N-IC + LIX 860N-IC + LIX 860N-IC + LIX
84-IC 84-IC 84-IC 84-IC 84-IC
Temperature, °C
Interfacial tension, N/m
22 22 22 32 22
2.39 10 2 2.39 10 2 2.38 10 2 1.33 10 2 1.80 10 2
and 30 min for a typical experiment. It can be observed in the figure that the size distributions for both times are nearly identical. Based on these results, 30 min of stirring time was used in subsequent tests to determine the equilibrium drop size distribution for different operating conditions. To assure that breakage was the dominant process controlling the drop size distribution, experiments were carried out using three volumetric fractions of organic phase: 0.006, 0.012 and 0.018. The resulting drop size distributions are shown in Fig. 3, and the values of the maximum drop diameter are presented in Table 3. We can observe in Fig. 3 that the equilibrium drop size distributions for the three dispersed phase fractions do not differ significantly. The slightly higher values at the lower dispersed phase fraction are probably due to experimental error since this result is the opposite of what could be expected if coalescence
were significant at the higher organic volumetric fractions. Consequently, even though it is not possible to assert a complete elimination of coalescence, specially between the smallest drops of the distribution, it can be concluded that within this range of dispersed phase fraction the coalescence between drops is negligible and breakage is essentially responsible for the obtained equilibrium distributions. In subsequent experiments, the volumetric fraction of organic phase used was 0.006.
Fig. 1. Drop size distributions at 1 and 30 min of stirring time for duplicate experiments. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm.
Fig. 2. Drop size distributions for various stirring times. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm.
3.4. Effect of the stirring speed For stirring speeds lower than 250 rpm an organic layer was observed at the top of the mixing vessel, and for stirring speeds higher than 350 rpm there was an increasing tendency to trap air. Therefore, mixing tests were carried out at stirring speeds of 250, 300 and 350 rpm, which produced good dispersion con-
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Fig. 3. Effect of the dispersed phase fraction on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; stirring speed 300 rpm; stirring time 30 min.
Fig. 4. Effect of the stirring speed on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring time 30 min.
ditions. The results are shown in Fig. 4 where we can observe that when the stirring speed increases in the range studied the drop size distribution shifts toward the smaller drops. The determined value of dmax also decreases with increasing stirring speed from 0.052 to 0.043 and 0.023 cm at 250, 300 and 350 rpm, respectively. The observed large effect of the stirring speed on the equilibrium drop size distribution is typical of dispersions in which drop breakage is the prevailing process. In this type of process an increase in the external inertial stress arising from the turbulent pressure fluctuations leads to a destabilization of the drops, consequently, the dmax decreases and the entire drop size distribution shifts toward the smaller drop sizes.
values of dmax were 0.043 and 0.037 cm, respectively. The drop size distribution obtained at 32 °C is significantly finer than that obtained at 22 °C. This result can be explained considering the data shown in Tables 1 and 2, where we can observe that an increase in temperature decreases the viscosity of the dispersed phase and the interfacial tension of the system. Since
3.5. Effect of the temperature Fig. 5 shows the drop size distributions obtained for temperatures of 22 and 32 °C. The corresponding Table 3 Values of dmax for the data on Fig. 3 Dispersed phase ratio
dmax, cm
0.006 0.012 0.018
0.043 0.038 0.037
Fig. 5. Effect of the temperature on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; dispersed phase fraction 0.006; stirring speed 300 rpm; stirring time 30 min.
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71
3.7. Effect of the pH
Fig. 6. Effect of the concentration of the extractant on the equilibrium drop size distribution. Aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 350 rpm; stirring time 30 min.
these changes produce a decrease on the two stabilizing forces of the drops, the equilibrium drop size distribution should shift to smaller drop sizes as seen in Fig. 5. Similar results have been found by other investigators working with various liquid –liquid systems (Lagissety et al., 1986; Sathyagal et al., 1996; Kosshy et al., 1988).
Tobin and Ramkrishna (1992) studied the effect of the pH of the aqueous phase on the coalescence rate of drops of benzene and carbon tetrachloride dispersed in water. They found that an increase in pH inhibited substantially the coalescence between drops, an effect that was attributed to the preferential adsorption of hydroxide ions onto the water organic interface. On the other hand, the effect of pH changes on the breakage rate of organic drops has not been studied. In this research, experiments were conducted to determine the drop size distribution for pH 5.7, 4.0 and 2.0. The corresponding values of dmax were 0.043, 0.040 and 0.033 cm. The pH value of 5.7 was the natural pH of the aqueous phase used in the experiments (0.25 M Na2SO4 solution) and to set the pH values 4.0 and 2.0 small amounts of sulfuric acid were added to the solution. The results shown in Fig. 7 indicate that by decreasing the pH finer drop size distributions are obtained. This behavior cannot be explained in terms of variations in the properties of the aqueous phase or the interfacial tension because, as shown in Tables 1 and 2, these physical properties varied very little with pH changes in the range considered. An alternative explanation can be given considering the surfactant properties and the acid – base
3.6. Effect of the concentration of the extractant The change in concentration of the extractant in the organic phase from 7% to 20% does not affect appreciably the equilibrium drop size distribution in the mixer as seen in Fig. 6, which compares the size distributions obtained for extractant concentrations of 7% and 20% by volume. The corresponding values of dmax determined were 0.022 and 0.028 cm, respectively. The change in extractant concentration from 7% to 20% produces a large increase in the viscosity of the organic phase, therefore, stabilizing the drops against breakage. On the other hand, the variation in the concentration of the extractant produces also a decrease in the interfacial tension, which would increase the tendency of the organic drops to break. The independence of the drop size distribution on the organic phase concentration observed here could be due to a balance between these two opposite effects.
Fig. 7. Effect of the pH on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm; stirring time 30 min.
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characteristics of the chelating extractants present in the organic phase. All the hydroxyoxime extractants are interfacially active and tend to preferentially adsorb at the organic aqueous interface, although not to the extent of a true surface-active agent (Flett, 1977). It is also known that hydroxyoxime extractants tend to protonate at low pH values to give a positively charged species while at high pH values the hydroxyoxime molecule deprotonates to give an anionic species. Given the high interfacial concentration of the hydroxyoximes, it is believed that these two reactions could lead to a significant change in the surface charge of the organic drops with changes in pH. The fact that, as discussed by Al-Diwan et al. (1977), the value of the equilibrium constant for the interfacial hydroxyoxime deprotonation reaction can be much larger than the value of the equilibrium constant for the bulk aqueous phase hydroxyoxime deprotonation, further supports this argument. Therefore, changes in the surface charge of the organic drops would produce variations in the resistance to deformation (stiffness) of the drop surface due to electroviscous effects, which in turn will change the tendency of the drops to undergo breakage, thus explaining the effect of pH on the drop size distributions observed experimentally. 3.8. Drop size distribution function When the experimental data on drop sizes were plotted as the fraction of drops in each volume interval versus the logarithm of the average volume of the interval, a characteristic bell shaped form was observed. This suggested that the size distribution of the drops could be represented accurately by a lognormal distribution with density function given by (Hasting and Peacock, 1975) "
2 # ln mv 1 pffiffiffiffiffiffi exp f0 ðvÞ ¼ 2s2 v s 2p
ð4Þ
where s is the standard deviation of ln(v) and m is the median of the distribution. Fig. 8 shows a typical drop size distribution plotted as described. The fraction of drops in each size interval calculated using a lognormal density function whose parameters m and s were determined from the experimental data is also shown in the same figure. It can be observed that the agreement is excellent; con-
Fig. 8. Experimental and lognormal size distribution. Organic phase: 7% extractant; aqueous phase: pH 2.0; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm; stirring time 30 min.
sequently, the lognormal distribution can be used to represent accurately the drop size distribution data produced in a batch mixer operating under breakage conditions. Earlier studies with concentrated dispersions generated in a continuous mixer (Padilla et al., 1996) have also found that the lognormal distribution could represent well the drop size distribution data when the coalescence between drops is not negligible. Additionally, the values of dmax obtained in this research were correlated using the equation proposed by Shinnar, Eq. (1). A value of C1 equal to 0.353 was determined by minimization of the root mean square deviation, rrms, given by rrms
" #1=2 1 dmax E dmax P 2 ¼ 100 : dmax E n i
ð5Þ
The minimum value of the mean root deviation obtained for the experimental data was rrms = 15.1. Eq. (1) has been found by many investigators (Lagissety et al., 1986; Wang and Calabrese, 1986; Sathyagal et al., 1996) to predict well the dmax values for dilute dispersions of low viscosity fluids, and the C1 values were determined usually for cylindrical mixing vessels. For example, Lagissety et al. (1986) working with a cylindrical baffled vessel and a six bladed disk turbine suggested a value of C1 = 0.125, while the cor-
M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
relation obtained by Wang and Calabrese (1986) for a Rushton turbine impeller suggests a value of 0.088. Additional dmax data by Sathyagal et al. (1996) who also used a Rushton turbine impeller agreed well with C1 = 0.088. The larger value of C1 = 0.353 obtained here can be attributed to the different geometry of the mixing vessel and impeller which produces larger dispersion drops. Recently, Paceck et al. (1998) have demonstrated that the impeller type has a tremendous influence on the size of the generated dispersion drops, and differences of an order of magnitude in the mean drop sizes could be produced for different impeller geometries at constant mean energy dissipation rates. The Calabrese model, Eq. (3), was also tested for the experimental dmax data. The minimum rrms value obtained was when the constant C4 was equal to zero, for this condition the Calabrese model reduces to Shinnar’s Eq. (1). This was probably due to the fact that the additional term in this equation results in a weaker dependence of dmax with the stirring speed. The model of Lagisetty et al. (1986), Eq. (2), was not applicable to the experimental data, giving unreasonably high values for dmax.
4. Conclusions From the results of the experimental determination of the equilibrium size distribution of dispersion drops in the system LIX 860N-IC + LIX 84-IC in Escaid 100 – Na2SO4 solution, the following can be concluded. 1. 2.
3.
4.
The system reaches an equilibrium drop size distribution in less than 30 min of stirring time. An increase in the stirring speed increased the tendency of the organic drops to break, shifting the drop size distribution toward the smaller drop sizes. An increase in temperature from 22 to 32 °C decreased the size of the organic drops, while a change in the concentration of the extractant in the organic phase from 7% to 20% by weight did not affect the drop size distribution. A decrease in pH of the aqueous phase from 5.7 to 2.0 increased progressively the tendency of the organic drops to undergo breakage, giv-
5.
73
ing finer drop size distributions due to changes in the surface charge of the drops produced by the pH change. The experimental drop size distribution data was represented accurately by a lognormal distribution.
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imental study of the separation process. Hydrometallurgy 42, 267 – 279. Sathyagal, A.N., Ramkrishna, D., Narsimhan, G., 1996. Droplets breakage in stirred dispersions. Breakage functions from experimental drop-size distributions. Chem. Eng. Sci. 51 (9), 1377 – 1391. Shinnar, R., 1961. On the behavior of liquid dispersions in mixing vessels. J. Fluid Mech. 10, 259 – 275. Sprow, F.B., 1967. Distribution of drop sizes produced in turbulent liquid – liquid dispersions. Chem. Eng. Sci. 22, 435 – 442. Tobin, T., Ramkrishna, D., 1992. Coalescence of charged droplets in agitated liquid – liquid dispersions. AIChE J. 38 (8), 1199 – 1205. Wang, C.Y., Calabrese, R.V., 1986. Drop breakup in turbulent stirred-tank contactors: Part II. Relative influence of viscosity and interfacial tension. AIChE J. 32 (4), 667 – 676.
Drop size distribution in a batch mixer under breakage conditions M.C. Ruiz*, P. Lermanda, R. Padilla Department of Metallurgical Engineering, University of Concepcio´n, Edmundo Larenas 270, Casilla 53-C, Concepcio´n, Chile Received 6 June 2001; received in revised form 10 October 2001; accepted 20 October 2001
Abstract The equilibrium size distribution, F0(v), of organic drops produced in a batch mixing vessel has been determined experimentally for very low dispersed phase fractions (0.006) in order to reduce the coalescence between drops to negligible values. The organic phase used was a 1:1 mixture of a salicylaldoxime (LIX 860N-IC) and a ketoxime (LIX 64-IC) in an aliphatic diluent (Escaid 103). The aqueous phase was a 0.25-M sodium sulfate solution. The results indicated that the system reaches an equilibrium drop size distribution in less than 30 min of stirring time. An increase in the stirring speed increased the tendency of the organic drops to break, shifting the drop size distribution toward the smaller drop sizes. An increase in temperature from 22 to 32 °C decreased the size of the organic drops, while a change in the concentration of the extractant in the organic phase from 7% to 20% by weight had little effect. Both effects can be attributed to changes in the physical properties of the system. A decrease in pH of the aqueous phase from 5.7 to 2.0 increased progressively the tendency of the organic drops to undergo breakage giving finer drop size distributions due to changes in the surface charge of the organic drops produced by the pH change. In all cases, the experimental drop size distributions could be accurately represented by a lognormal distribution. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Drop size distribution; Batch mixer; Breakage conditions
1. Introduction In many industrial operations, liquid – liquid dispersions are formed to enhance the mass and heat transfer between the phases or to enhance the rate of a chemical reaction. In the copper industry, the recovery of metal from dilute leaching solutions is carried out by solvent extraction, usually in mixer – settler units. In the mixer, dispersions are generated mainly by mechanical agitation to accomplish the extraction of the copper from the leaching solution into the organic phase
*
Corresponding author. Tel.: +56-41-204955; fax: +56-41243418. E-mail address: [email protected] (M.C. Ruiz).
for subsequent stripping of the organic into an electrowinning electrolyte. The drop size distribution produced in the mixer is critical for the performance of the solvent extraction reactor because it not only affects the rate of the extraction and stripping reactions but it also influences the subsequent phase separation in the settler. The organic losses by entrainment in the solvent extraction process are also intimately related to drop size distributions. In order to understand better the formation of dispersion in a solvent extraction process and how it is affected by the operating variables, this work focuses on the study of drop breakage in a batch mixer. The size distribution of drops produced in a mixer evolves as a result of two processes: drop breakage due to the turbulent field and coalescence due to
0304-386X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 6 X ( 0 1 ) 0 0 2 2 3 - 7
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collisions between drops. The kinetics of both rate processes must be known to predict and control the size distribution of drops in a mixer. However, since both rate processes occur simultaneously, it is extremely difficult to elucidate how the physical properties of the system and the operating variables affect each, unless the experimental conditions are chosen to minimize or completely eliminate one of the two processes. Two methods have been used to eliminate coalescence between drops: (i) the addition of surfactant substances to the system (Kumar et al., 1991) and (ii) the use of low dispersed phase fractions (Narsimham et al., 1980, 1984; Konno et al., 1980, 1993; Lagissety et al., 1986; Calabrese et al., 1986; Wang and Calabrese, 1986; Chatzi and Kiparissides, 1992; Sathyagal et al., 1996). It has been shown (Kosshy et al., 1988) that the addition of surfactants can produce local differences in interfacial tension when the drop deforms which affects the breakage process. Bearing this in mind, the technique selected in this research to obtain information on drop breakage was the use of very low dispersed phase fractions. Under this condition, due to the low number density of drops in the dispersion, the interactions between drops are reduced to negligible values and the resulting drop size distribution is due to breakage only. It is generally accepted that a drop in a turbulent field breaks mainly under the influence of inertial stresses arising from the turbulent pressure fluctuations, which tend to deform the drop. On the other hand, the elastic stress due to the interfacial tension and the viscous stress due to the internal flow tend to resist the deformation of the drop. As the size of the drop decreases, the deforming stress across it also decreases, whereas the restoring stresses increase. A size is finally reached where the deforming stress is unable to break the drop. This critical size is normally referred to as dmax, the diameter of the largest drop which can survive the flow field without further breakage. Numerous researchers have determined experimentally this maximum diameter in a stirred vessel and various correlations and models have been proposed to predict the value of dmax as a function of the characteristics of the flow field and the physical properties of the system (Kumar et al., 1991, 1992; Lagissety et al., 1986; Sprow, 1967; Lam et al., 1996). Shinnar (1961) derived the following equation for the
maximum stable drop diameter in a turbulent stirred vessel with a dilute dispersion. dmax ¼ C1 We0:6 D 2
ð1Þ 3
with We ¼ qc Nr D where We is the Weber number, D is the diameter of the impeller, N is the impeller speed, qc is the continuous phase viscosity, r is the interfacial tension and C1 is an experimentally determined constant which depends on the vessel geometry and impeller type. Eq. (1) neglects the viscous forces in the dispersed phase; consequently, it should only apply to dispersed phases of low viscosity. Recently, various models have been proposed taking into account the effect of the dispersed phase viscosity on the maximum stable drop size. Lagissety et al. (1986) proposed the following equation for Newtonian fluids 2
h
4 C2 We ¼
4 dmax 5=3
Re We
D
3
6 7 1 1 7 i1=2 tan 6 4h dmax 5=3 i1=2 5 1 1 4 C2 We D
dmax D
1=3 ð2Þ 2
with Re ¼ qc Nl D where ld is the viscosity of the d dispersed phase and the constant C2 is dependent on the geometry of the vessel and impeller. Calabrese et al. (1986) and Wang and Calabrese (1986) used a semi-empirical approach to develop various correlations for the maximum stable drop diameter for drops with a wide range of viscosity. The following equation was proposed for low to moderate dispersed phase viscosity " #3=5 dmax dmax 1=3 3=5 ¼ C3 We 1 þ C4 Vi D D
ð3Þ
1=2 with Vi ¼ ldrND qqc where Vi is a tank viscosity d group or capillary number representing the ratio of dispersed-phase viscous force to surface force, C3 and C4 are empirical constants, and qc and qd are the viscosities of the continuous and dispersed phases, respectively. In the limiting condition when the interfacial tension provides the dominant stabilizing stress
M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
of the drops (ld ! 0), both Eqs. (2) and (3) reduce to Eq. (1). The existence of a maximum stable drop size implies that the size distributions of drops in a batch mixing vessel will reach a steady state where all the drops will be smaller than the critical size. If the size distribution is produced by two competitive processes such as breakage and coalescence, this steady state is dynamic and it is the result of a balance between these opposite rate processes. The dynamic steady state should be independent of the earlier conditions of the system and, therefore, of the initial conditions. On the other hand, if only breakage occurs in the system, this steady state can be called static, in the sense that the drops smaller that the critical size undergo no further change and the drop size distribution could depend on the earlier conditions of the system. In spite of the widespread use of the solvent extraction process in the copper industry, very few studies on dispersions have dealt with organic phases containing copper specific extractants, or have used pump – mix impellers, widely used in solvent extraction plants. Consequently, the characteristics of the dispersions produced in such processes are little known. The objective of this work was to determine how the various operating variables, pertinent to solvent extraction plants, affect the drop breakage process and the resulting equilibrium drop size distribution in dispersions produced by mechanical agitation.
2. Experimental work The organic phase used in this study was a 1:1 mixture of a salicylaldoxime (LIX 860N-IC) and a ketoxime (LIX 84-IC) in an aliphatic diluent (ESCAID 103). This mixture of hydroxyoxime extractants is used in several copper solvent extraction plants for the recovery of copper from sulfate solutions. The concentration of the organic phase in most experiments was 7% by volume of extractant (3.5% of LIX 860NIC + 3.5% of LIX 84-IC). The aqueous phase was a 0.25-M sodium sulfate solution which was used instead of a copper sulfate solution mainly to eliminate mass transfer from the aqueous to the organic phase. Small amounts of sulfuric acid were added to regulate the pH when necessary.
67
The experiments were carried out in a batch mixing vessel made of transparent acrylic. The mixer was a rectangular vessel of 25 25 26 cm. A pump – mix impeller, 15 cm in diameter, double shrouded and with eight curved blades, was used to generate the dispersion. The impeller was located in the center of the mixer, 4 cm above the bottom of the vessel, through a stainless steel shaft connected to a variable speed agitation system. All the experiments were carried out under aqueous continuity with a low organic phase fraction to reduce the coalescence of drops to negligible values. The procedure consisted of filling the mixer with 16 L of aqueous phase at the temperature specified for the experiment. Then, the stirring speed was incremented to the desired level and a small amount of organic phase, usually 100 cm3, was rapidly added to the vessel. The experiment was run for 30 min to achieve steady state, and dispersion samples were withdrawn from a point located 6 cm from the wall and 10 cm above the bottom of the vessel. The sampling technique consisted of siphoning a small amount of the dispersion into a Petri dish containing 7 – 8 cm3 of a gelatin solution (8% by weight) kept at about 35 °C. Subsequently, the Petri dish with the dispersion sample was cooled quickly in an ice bath. After setting of the gelatin, the sample was stored in a refrigerator until analyzed. To determine the size distribution of the embedded drops, digitized images of sectors of the sample were obtained by a microscope and a video camera Sony model HAD SSC-D50, connected to a personal computer. The drops were counted and sized by an image-analyzer software Omnimet Enterprise version 1.01 B002.
3. Results and discussion Experiments were carried out under various conditions to determine the effect of the operating variables on the equilibrium size distribution of the organic drops. The variables studied were stirring speed, pH of the aqueous phase, concentration of extractant in the organic phase, and temperature. The volume, v, was used as a characteristic size of the drops in the determination of the drop size distribution. However, for the maximum drop size, the diameter was used to facilitate comparison with data in the literature and to
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test the various correlations proposed for dmax. Since the method of analysis counted and sized individual drops, the size distribution obtained was a number distribution. Due to the wide range of drop sizes measured, and to facilitate the analysis of the experimental data, a logarithmic discretization scale was chosen for the size variable of the dispersion drops. In this way, the number of drops in each volume interval was determined. A minimum of 400 drops was considered to give a reliable drop size distribution, although in most cases samples with larger number of drops were measured. 3.1. Characterization of the organic and aqueous phases Interfacial tensions were determined using a du Nou¨y ring apparatus, the densities of aqueous and organic phases were determined through specific gravity measurements using hydrometers and the viscosities were determined by an Ostwald viscometer. Table 1 summarizes the density and viscosity values obtained for the various aqueous and organic phases used in this research, and Table 2 shows the values of the interfacial tension for the specified experimental conditions.
Table 1 Density and viscosity of the solutions
Aqueous phase 0.25 M Na2SO4, pH 5.7 0.25 M Na2SO4, pH 4.0 0.25 M Na2SO4, pH 2.0 0.25 M Na2SO4, pH 5.7 Organic phase 7% LIX 860N-IC + LIX 84-IC 7% LIX 860N-IC + LIX 84-IC 20% LIX 860N-IC + LIX 84-IC
Temperature, °C
Density, kg/m3
Viscosity, Pas
22
1030
1.052 10 3
22
1030
1.053 10 3
22
1030
1.054 10 3
32
1021
8.55 10 4
22
815
1.984 10 3
32
808
1.384 10 3
22
830
3.211 10 3
3.2. Reproducibility of the sampling and measuring technique In order to test the validity and reproducibility of the method used for the drop size characterization, particularly, the procedure used for sample withdrawal, duplicate experiments were carried out under identical experimental conditions and the drop size distributions were determined and compared. Fig. 1 shows the drop size distributions determined at 1 and 30 min of stirring time for duplicate experiments. The size distributions are presented in this figure as the cumulative number-percent, F0(v), versus the logarithm of the volume of the drops. It can be observed that the reproducibility of the technique used to determine the drops size distribution in the mixer is very good even for short stirring times. 3.3. Determination of the equilibrium conditions The time required for the dispersion drops to evolve to a constant or equilibrium drop size distribution in a batch mixer seems to vary widely for different liquid – liquid systems. In addition, the time to reach equilibrium has also been found to depend on the type of impeller used to produce the dispersion (Pacek et al., 1999) and on operating variables such as the stirring speed and the dispersed phase fraction. A faster approach to equilibrium has been observed when the stirring speed was increased or the dispersed phase fraction was decreased (Mackelprang et al., 1981). Many liquid – liquid dispersions have been reported to reach equilibrium conditions in about 1 h of mixing (Calabrese et al., 1986; Kosshy et al., 1988; Sprow, 1967; Kumar et al., 1991), while for some others systems, specially for dispersed phases of high viscosities, longer times were necessary (Chatzi and Kiparissides, 1992; Lam et al., 1996; Paceck et al., 1998). In the present study, it was found that a time of 30 min was enough for the system to reach a constant drop size distribution. This result is in agreement with the work of Mackelprang et al. (1981) who reported that 30 min of stirring time was enough for the dispersion to reach an equilibrium drop size distribution in a system containing an hydroxyoxime type copper specific extractant (LIX 64N), dispersed in a sodium sulfate solution. Fig. 2 shows the cumulative number distributions of drops obtained at stirring times of 16
M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
69
Table 2 Interfacial tension Aqueous phase 0.25 0.25 0.25 0.25 0.25
M M M M M
Na2SO4, Na2SO4, Na2SO4, Na2SO4, Na2SO4,
Organic phase pH pH pH pH pH
5.7 4.0 2.0 5.7 5.7
7% 7% 7% 7% 20%
LIX LIX LIX LIX LIX
860N-IC + LIX 860N-IC + LIX 860N-IC + LIX 860N-IC + LIX 860N-IC + LIX
84-IC 84-IC 84-IC 84-IC 84-IC
Temperature, °C
Interfacial tension, N/m
22 22 22 32 22
2.39 10 2 2.39 10 2 2.38 10 2 1.33 10 2 1.80 10 2
and 30 min for a typical experiment. It can be observed in the figure that the size distributions for both times are nearly identical. Based on these results, 30 min of stirring time was used in subsequent tests to determine the equilibrium drop size distribution for different operating conditions. To assure that breakage was the dominant process controlling the drop size distribution, experiments were carried out using three volumetric fractions of organic phase: 0.006, 0.012 and 0.018. The resulting drop size distributions are shown in Fig. 3, and the values of the maximum drop diameter are presented in Table 3. We can observe in Fig. 3 that the equilibrium drop size distributions for the three dispersed phase fractions do not differ significantly. The slightly higher values at the lower dispersed phase fraction are probably due to experimental error since this result is the opposite of what could be expected if coalescence
were significant at the higher organic volumetric fractions. Consequently, even though it is not possible to assert a complete elimination of coalescence, specially between the smallest drops of the distribution, it can be concluded that within this range of dispersed phase fraction the coalescence between drops is negligible and breakage is essentially responsible for the obtained equilibrium distributions. In subsequent experiments, the volumetric fraction of organic phase used was 0.006.
Fig. 1. Drop size distributions at 1 and 30 min of stirring time for duplicate experiments. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm.
Fig. 2. Drop size distributions for various stirring times. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm.
3.4. Effect of the stirring speed For stirring speeds lower than 250 rpm an organic layer was observed at the top of the mixing vessel, and for stirring speeds higher than 350 rpm there was an increasing tendency to trap air. Therefore, mixing tests were carried out at stirring speeds of 250, 300 and 350 rpm, which produced good dispersion con-
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M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
Fig. 3. Effect of the dispersed phase fraction on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; stirring speed 300 rpm; stirring time 30 min.
Fig. 4. Effect of the stirring speed on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring time 30 min.
ditions. The results are shown in Fig. 4 where we can observe that when the stirring speed increases in the range studied the drop size distribution shifts toward the smaller drops. The determined value of dmax also decreases with increasing stirring speed from 0.052 to 0.043 and 0.023 cm at 250, 300 and 350 rpm, respectively. The observed large effect of the stirring speed on the equilibrium drop size distribution is typical of dispersions in which drop breakage is the prevailing process. In this type of process an increase in the external inertial stress arising from the turbulent pressure fluctuations leads to a destabilization of the drops, consequently, the dmax decreases and the entire drop size distribution shifts toward the smaller drop sizes.
values of dmax were 0.043 and 0.037 cm, respectively. The drop size distribution obtained at 32 °C is significantly finer than that obtained at 22 °C. This result can be explained considering the data shown in Tables 1 and 2, where we can observe that an increase in temperature decreases the viscosity of the dispersed phase and the interfacial tension of the system. Since
3.5. Effect of the temperature Fig. 5 shows the drop size distributions obtained for temperatures of 22 and 32 °C. The corresponding Table 3 Values of dmax for the data on Fig. 3 Dispersed phase ratio
dmax, cm
0.006 0.012 0.018
0.043 0.038 0.037
Fig. 5. Effect of the temperature on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4 and pH 5.7; dispersed phase fraction 0.006; stirring speed 300 rpm; stirring time 30 min.
M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
71
3.7. Effect of the pH
Fig. 6. Effect of the concentration of the extractant on the equilibrium drop size distribution. Aqueous phase: 0.25 M Na2SO4 and pH 5.7; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 350 rpm; stirring time 30 min.
these changes produce a decrease on the two stabilizing forces of the drops, the equilibrium drop size distribution should shift to smaller drop sizes as seen in Fig. 5. Similar results have been found by other investigators working with various liquid –liquid systems (Lagissety et al., 1986; Sathyagal et al., 1996; Kosshy et al., 1988).
Tobin and Ramkrishna (1992) studied the effect of the pH of the aqueous phase on the coalescence rate of drops of benzene and carbon tetrachloride dispersed in water. They found that an increase in pH inhibited substantially the coalescence between drops, an effect that was attributed to the preferential adsorption of hydroxide ions onto the water organic interface. On the other hand, the effect of pH changes on the breakage rate of organic drops has not been studied. In this research, experiments were conducted to determine the drop size distribution for pH 5.7, 4.0 and 2.0. The corresponding values of dmax were 0.043, 0.040 and 0.033 cm. The pH value of 5.7 was the natural pH of the aqueous phase used in the experiments (0.25 M Na2SO4 solution) and to set the pH values 4.0 and 2.0 small amounts of sulfuric acid were added to the solution. The results shown in Fig. 7 indicate that by decreasing the pH finer drop size distributions are obtained. This behavior cannot be explained in terms of variations in the properties of the aqueous phase or the interfacial tension because, as shown in Tables 1 and 2, these physical properties varied very little with pH changes in the range considered. An alternative explanation can be given considering the surfactant properties and the acid – base
3.6. Effect of the concentration of the extractant The change in concentration of the extractant in the organic phase from 7% to 20% does not affect appreciably the equilibrium drop size distribution in the mixer as seen in Fig. 6, which compares the size distributions obtained for extractant concentrations of 7% and 20% by volume. The corresponding values of dmax determined were 0.022 and 0.028 cm, respectively. The change in extractant concentration from 7% to 20% produces a large increase in the viscosity of the organic phase, therefore, stabilizing the drops against breakage. On the other hand, the variation in the concentration of the extractant produces also a decrease in the interfacial tension, which would increase the tendency of the organic drops to break. The independence of the drop size distribution on the organic phase concentration observed here could be due to a balance between these two opposite effects.
Fig. 7. Effect of the pH on the equilibrium drop size distribution. Organic phase: 7% extractant; aqueous phase: 0.25 M Na2SO4; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm; stirring time 30 min.
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M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
characteristics of the chelating extractants present in the organic phase. All the hydroxyoxime extractants are interfacially active and tend to preferentially adsorb at the organic aqueous interface, although not to the extent of a true surface-active agent (Flett, 1977). It is also known that hydroxyoxime extractants tend to protonate at low pH values to give a positively charged species while at high pH values the hydroxyoxime molecule deprotonates to give an anionic species. Given the high interfacial concentration of the hydroxyoximes, it is believed that these two reactions could lead to a significant change in the surface charge of the organic drops with changes in pH. The fact that, as discussed by Al-Diwan et al. (1977), the value of the equilibrium constant for the interfacial hydroxyoxime deprotonation reaction can be much larger than the value of the equilibrium constant for the bulk aqueous phase hydroxyoxime deprotonation, further supports this argument. Therefore, changes in the surface charge of the organic drops would produce variations in the resistance to deformation (stiffness) of the drop surface due to electroviscous effects, which in turn will change the tendency of the drops to undergo breakage, thus explaining the effect of pH on the drop size distributions observed experimentally. 3.8. Drop size distribution function When the experimental data on drop sizes were plotted as the fraction of drops in each volume interval versus the logarithm of the average volume of the interval, a characteristic bell shaped form was observed. This suggested that the size distribution of the drops could be represented accurately by a lognormal distribution with density function given by (Hasting and Peacock, 1975) "
2 # ln mv 1 pffiffiffiffiffiffi exp f0 ðvÞ ¼ 2s2 v s 2p
ð4Þ
where s is the standard deviation of ln(v) and m is the median of the distribution. Fig. 8 shows a typical drop size distribution plotted as described. The fraction of drops in each size interval calculated using a lognormal density function whose parameters m and s were determined from the experimental data is also shown in the same figure. It can be observed that the agreement is excellent; con-
Fig. 8. Experimental and lognormal size distribution. Organic phase: 7% extractant; aqueous phase: pH 2.0; temperature 22 °C; dispersed phase fraction 0.006; stirring speed 300 rpm; stirring time 30 min.
sequently, the lognormal distribution can be used to represent accurately the drop size distribution data produced in a batch mixer operating under breakage conditions. Earlier studies with concentrated dispersions generated in a continuous mixer (Padilla et al., 1996) have also found that the lognormal distribution could represent well the drop size distribution data when the coalescence between drops is not negligible. Additionally, the values of dmax obtained in this research were correlated using the equation proposed by Shinnar, Eq. (1). A value of C1 equal to 0.353 was determined by minimization of the root mean square deviation, rrms, given by rrms
" #1=2 1 dmax E dmax P 2 ¼ 100 : dmax E n i
ð5Þ
The minimum value of the mean root deviation obtained for the experimental data was rrms = 15.1. Eq. (1) has been found by many investigators (Lagissety et al., 1986; Wang and Calabrese, 1986; Sathyagal et al., 1996) to predict well the dmax values for dilute dispersions of low viscosity fluids, and the C1 values were determined usually for cylindrical mixing vessels. For example, Lagissety et al. (1986) working with a cylindrical baffled vessel and a six bladed disk turbine suggested a value of C1 = 0.125, while the cor-
M.C. Ruiz et al. / Hydrometallurgy 63 (2002) 65–74
relation obtained by Wang and Calabrese (1986) for a Rushton turbine impeller suggests a value of 0.088. Additional dmax data by Sathyagal et al. (1996) who also used a Rushton turbine impeller agreed well with C1 = 0.088. The larger value of C1 = 0.353 obtained here can be attributed to the different geometry of the mixing vessel and impeller which produces larger dispersion drops. Recently, Paceck et al. (1998) have demonstrated that the impeller type has a tremendous influence on the size of the generated dispersion drops, and differences of an order of magnitude in the mean drop sizes could be produced for different impeller geometries at constant mean energy dissipation rates. The Calabrese model, Eq. (3), was also tested for the experimental dmax data. The minimum rrms value obtained was when the constant C4 was equal to zero, for this condition the Calabrese model reduces to Shinnar’s Eq. (1). This was probably due to the fact that the additional term in this equation results in a weaker dependence of dmax with the stirring speed. The model of Lagisetty et al. (1986), Eq. (2), was not applicable to the experimental data, giving unreasonably high values for dmax.
4. Conclusions From the results of the experimental determination of the equilibrium size distribution of dispersion drops in the system LIX 860N-IC + LIX 84-IC in Escaid 100 – Na2SO4 solution, the following can be concluded. 1. 2.
3.
4.
The system reaches an equilibrium drop size distribution in less than 30 min of stirring time. An increase in the stirring speed increased the tendency of the organic drops to break, shifting the drop size distribution toward the smaller drop sizes. An increase in temperature from 22 to 32 °C decreased the size of the organic drops, while a change in the concentration of the extractant in the organic phase from 7% to 20% by weight did not affect the drop size distribution. A decrease in pH of the aqueous phase from 5.7 to 2.0 increased progressively the tendency of the organic drops to undergo breakage, giv-
5.
73
ing finer drop size distributions due to changes in the surface charge of the drops produced by the pH change. The experimental drop size distribution data was represented accurately by a lognormal distribution.
Acknowledgements Support from the Fondo Nacional de Ciencia y Tecnologı´a (FONDECYT) of Chile, through the Project No. 1980473 is gratefully acknowledged. References Al-Diwan, T.A.B., Hughes, M.A., Whewell, R.J., 1977. Behaviour of interfacial tension in systems involving hydroxyoxime extractans for copper. J. Inorg. Nucl. Chem. 39, 1419 – 1424. Calabrese, R.V., Chang, T.P.K., Dang, P.T., 1986. Drop breakup in turbulent stirred-tank contactors. Part I: Effect of dispersedphase viscosity. AIChE J. 32, 657 – 666. Chatzi, E.G., Kiparissides, C., 1992. Dynamic simulation of bimodal drop size distributions in low-coalescence batch dispersion systems. Chem. Eng. Sci. 47 (2), 445 – 456. Flett, D.S., 1977. Chemical kinetics, mechanisms in solvent extraction of copper chelates. Acc. Chem. Res. 10, 99 – 104. Hasting, N.A.J., Peacock, J.B., 1975. Statistical distributions. A Handbook for Students and Practitioners. Wiley, New York. Konno, M., Matsunaga, Y., Arai, K., Saito, S., 1980. Simulation model for breakup process in an agitated tank. J. Chem. Eng. Jpn. 13 (1), 67 – 73. Konno, M., Kosaka, N., Saito, S., 1993. Correlation of transient drop sizes in breakup process in liquid – liquid agitation. J. Chem. Eng. Jpn. 26 (1), 37 – 40. Kosshy, A., Das, T.R., Kumar, R., 1988. Effect of surfactants on drop breakage in turbulent liquid dispersions. Chem. Eng. Sci. 43 (3), 649 – 654. Kumar, S., Kumar, R., Gandhi, K.S., 1991. Alternative mechanism of drop breakage in stirred vessels. Chem. Eng. Sci. 46 (10), 2483 – 2489. Kumar, S., Kumar, R., Gandhi, K.S., 1992. A multistage model for drop breakage in stirred vessels. Chem. Eng. Sci. 47 (5), 971 – 980. Lagissety, J.S., Das, P.K., Kumar, R., Gandhi, K.S., 1986. Breakage of viscous and non-Newtonian drops in stirred dispersions. Chem. Eng. Sci. 41 (1), 65 – 72. Lam, A., Sathyagal, A.N., Kumar, S., Ramkrishna, D., 1996. Maximum stable drop diameter in stirred dispersions. AIChE J. 42 (6), 1547 – 1552. Mackelprang, R., Herbst, J.A., Miller, J.D., 1981. Factors affecting droplet size distributions produced in dispersed phase mixers. In: Kuhn, M.C. (Ed.), Process and Fundamental Considerations of Selected Hydrometallurgical Systems. Soc. Mining Engineers of AIME, Warrendale, PA, pp. 269 – 280, Chap. 23.
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