Crystallization Kinetics of Monosodium Aluminate Hydrate in

May 17, 2012 - Graduate University of Chinese Academy of Sciences, Beijing 100049, China ... Daniel L. Herting , Jacob G. Reynolds , and W. Blaine Bar...
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Crystallization Kinetics of Monosodium Aluminate Hydrate in Concentrated Sodium Aluminate Solutions Shaowei You,†,‡ Yifei Zhang,*,† Shaotao Cao,† Fangfang Chen,† and Yi Zhang† †

National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology and Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ Graduate University of Chinese Academy of Sciences, Beijing 100049, China S Supporting Information *

ABSTRACT: The nucleation, growth, and agglomeration of monosodium aluminate hydrate (MAH) crystallization in concentrated sodium aluminate solutions were investigated in a steady-state mixed-suspension−mixed-product-removal (MSMPR) crystallizer, and the mechanism was analyzed in detail. The crystal growth was diffusion- and surface-integration-controlled, and the secondary nucleation, as a result of crystal−agitator and crystal−crystallizer collisions, was determined further. The agglomeration kernel, expressed in terms of mean residence time, growth rate, and suspension density, was found to have a positive order of about 0.52 in the suspension density, indicating that the agglomeration kernel increased at higher frequencies of collisions between particles. The growth rate of MAH was found to be higher than that of gibbsite in active NaAl(OH)4− NaHCO3 systems, but the nucleation rate of MAH was lower than that of gibbsite in seeded-hydrolysis processes.

1. INTRODUCTION Sodium aluminate, a widespread inorganic chemical, is used mainly in purifying fresh water, preparing drilling mud for plug bore holes, producing waterproof concrete and aluminosilicate, and other fields.1 The crystallization of monosodium aluminate hydrate (MAH) is an important unit operation for the production of sodium aluminate,2 as well as for the hydrochemical process of alumina production.3 MAH is usually produced by the cooling crystallization of concentrated sodium aluminate solutions such as a postleaching solutions of bauxite.3 This process is quite different from the extensively investigated gibbsite precipitation,4−9 which is usually performed from dilute sodium aluminate solutions through carbonation decomposition in the sintering process for alumina production or seeded hydrolysis in the Bayer process. Little systematic investigation of the crystallization of MAH has been carried out. Sazhin reported the crystallization of MAH from synthesized solutions.2 Cao et al. presented the preparation, nucleation, and morphology of MAH from concentrated sodium aluminate solutions.3,10 It is well-known that reliable kinetics is necessary for the control and scaleup of the crystallization process. However, the kinetics of MAH crystallization, such as the crystal growth and agglomeration, in concentrated sodium aluminate solutions has not yet been presented. To understand the mechanism of MAH crystallization from concentrated sodium aluminate solutions, the nucleation, growth, and agglomeration of the crystallization should be investigated simultaneously.11 The traditional mixed-suspension−mixed-product-removal (MSMPR) crystallization technique has been proposed and applied extensively.12−21 Therefore, based on the measured particle size distribution (PSD) in a continuous MSMPR crystallizer in this research, the population balance model was used to systematically extract the values of parameters in the kinetic equations of MAH crystallization from concentrated sodium aluminate solutions. © 2012 American Chemical Society

Furthermore, in light of the obtained kinetic parameters, the crystallization mechanism was compared with that of gibbsite from seeded sodium aluminate solutions, as well as reactive NaAl(OH)4−NaHCO3 systems.

2. EXPERIMENTAL SECTION 2.1. Materials and Methods. The chemical reagents were sodium hydroxide (≥96% pure, carbonate ≤ 1.5%, silicate ≤ 0.01%, potassium ≤ 0.05%, calcium ≤ 0.01%; Shantou Xilong Chemical Industry Co Ltd.) and aluminum hydroxide (≥97% pure, sulfate ≤ 0.02%, alkali metal and alkaline earth metal ≤ 0.25%; Shanghai Meixing Chemical Industry Co Ltd.). Sodium aluminate solution feeds were made in a nickel vessel by heating a mixture of sodium hydroxide, aluminum hydroxide, and pure water in appropriate proportions. The prepared solutions were filtered to remove the insoluble impurities, so that the impurities would not affect the crystallization process. The experimental setup consisted of a jacketed stainless-steel crystallizer with a polyethylene lining and a three-blade marine-type propeller covered with polyethylene. The active volume of the crystallizer for all experiments was fixed at 200 mL, and the stirring rate was set at 300 rpm to provide full mixing of the suspension in the crystallizer. The solution temperature in the crystallizer was controlled by circulating heating oil from a thermostatted bath to the crystallizer jacket and kept precisely at 60 ± 0.5 °C. In each run, sodium aluminate solution was continuously fed into the crystallizer through a peristaltic pump. Withdrawal of product slurry was carried out with a peristaltic pump that worked intermittently at a relatively high outflow rate under isokinetic conditions to ensure no classification of the Received: Revised: Accepted: Published: 7736

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suspended solids at withdrawal. Meanwhile, the suspension density and the particle shape and size distribution in the solution were steady. The crystallizer was operated to reach steady state, which generally occurred after 7−10 mean residence times from the start of an experiment. Slurry samples of a certain volume were withdrawn rapidly and then filtered immediately. A crystal sample of the whole cake was washed with anhydrous ethanol and air-desiccated at 70 °C for 12 h to determine the suspension density. PSDs of the produced crystals were measured using a Malvern Mastersizer Hydro 2000MU instrument; measurements were performed at least three times with good consistency in peak position, height, and half-width. The morphologies and habits of the crystals were analyzed by scanning electron microscopy (JEOL JSM-6700F). The operating experimental conditions are listed in Table 1.

β=

parameter

value(s) 200 3000−5400 300 60 480 116.6−255.1 2.2−6.0

where Gv is the volume-average growth rate (m /s); τ is the mean residence time (s); B0 is the nucleation rate [number/ (m3 s)]; β is the agglomeration kernel [m3/(number s)]; and μj is the jth moment, which is defined as μj =

2 1 ⎛ μ2 μ0 ⎞ ⎜⎜ 2 ⎟⎟ 2τ ⎝ μ1 ⎠

∫0

∞

n(v)v j dv

(4)

where v is the crystal volume (m3) and n(v) is the crystal population density function expressed as a function of the crystal volume [number/(m3 L)]. Based on the method of moment transformation, eqs 1−3 were used to determine the rates of nucleation and growth and the agglomeration kernel from the moments of the measured population density data at steady state. The nucleation and growth rates and the agglomeration kernels obtained by calculation from a series of experiments were further correlated using empirical power-law kinetic correlations15,21−23 Gv = kgσ g

(5)

B0 = kR Gv iM T j

(6)

β = kβGv hB0 pτ q

(7)

where kg, kR, and kβ are rate coefficients; g, i, j, h, p, and q are kinetic orders; and MT is the suspension density (g/L). The relative supersaturation, σ, for MAH crystallization from sodium aluminate solution is defined as σ = (C − Ceq)/Ceq, where C is the actual concentration and Ceq is the equilibrium concentration of alumina in a Na2O−Al2O3−H2O system. The equilibrium data on the Na2O−Al2O3−H2O system at 60 °C were obtained from the literature.24

2.2. Determination of the Rates of Growth and Nucleation and the Agglomeration Kernel. In a steadystate MSMPR crystallizer, full mixing of the solution, no classification at withdrawal, negligible crystal breakage, sizeindependent growth, and crystals with the same shape factor were assumed in this research. Therefore, according to the agglomeration population balance model based on the PSDs of crystals from the MSMPR crystallizer, the kinetic parameters of MAH crystallization were calculated by the following expressions15,21,23 1 μ1 Gv = τ μ0 (1) B0 =

(3) 3

Table 1. Conditions of MAH Crystallization in an MSMPR Crystallizer crystallization volume (mL) residence time (s) agitation speed (rpm) temperature (°C) Na2O concentration (g/L) Al2O3 concentration (g/L) relative supersaturation

1 ⎛ μ2 2⎞ ⎜⎜ 2 − ⎟⎟ τ ⎝ μ1 μ0 ⎠

3. RESULTS AND DISCUSSION 3.1. Crystal Morphology. As shown in Figure 1, the MAH crystal particles from the standard steady-state MSMPR crystallizer used in this research were homogeneous in size and had regular morphologies and structures. The crystal particles had the same crystal habit, and most crystals were in the form of spherelike agglomerates with uneven surfaces and clear corner angles. There were no fines or large crystals, confirming the assumption of size-independent growth. The agglomerates and

(2)

Figure 1. Scanning electron microscopy images of MAH crystals. 7737

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supersaturation was correlated using the linear least-squares technique for minimizing the sum of squared residuals, as shown in Figure 3. The correlation was linearized by taking

individual crystals followed similar growth mechanisms. The spherical agglomerates comprised a large number of smaller truncated quadrangular orthopyramid and octagonal plate-shape crystals woven together or growing into each other (i.e., twinned crystals), and this is different from aluminum hydroxide aggregated through welding or cementing.15 Moreover, no broken particles were found in the scanning electron microscopy images, which implies that the breakage in MAH crystals was negligible in this research. 3.2. Population Density Distribution of Crystals. A unimodal PSD of MAH crystals was obtained from the MSMPR crystallizer in this research. A typical population density distribution curve of MAH crystals is shown in Figure 2. The curve

Figure 3. Growth rate correlation.

logarithms, and then, the parameters were fitted. The regressed correlation can be expressed as Gv = 2.57 × 10−20σ 1.19

exhibits two distinct parts: a sharp downward curve over the small size range, followed by a downward beeline. The sharp downward curve is mainly ascribed to agglomeration in the crystallization process, whereas other phenomena, such as breakage, classification effects, and size-dependent growth, can be neglected. This was verified by experiments. 3.3. Simulation of the Kinetic Parameters. The kinetic parameters were calculated from the moments of the measured population density data. Then, the growth and nucleation rates and the agglomeration kernel for the MAH crystallization system were correlated according to empirical power-law expressions. The values and standard errors of all parameters are listed in Table 2. Table 2. Parameter Values and Standard Errors value

kg g KR i j kβ h p q

2.57 × 10−20 1.19 3.05 × 10−18 −1.15 1.06 9.65 × 10−39 0.92 0.49 1.25

standard error 0.48 0.11 0.75 0.56 0.13 0.13 0.21 0.16 0.25

× 10−20 × × × ×

(8)

The exponent 1.19 in the range of 1−2 for the relative supersaturation indicates that the crystal growth has a diffusionand surface-integration-controlled mechanism.25 During the crystallization process, units of the crystallizing substance arrive at the crystal surface from the bulk solution by diffusion and then migrate over the crystal surface and further link into the lattice in positions, enlarging the crystal.26 The growth of the lateral face and {001} basal face basically determined the size and morphology of the crystals, and the greater growth rate of lateral face resulted in the formation of MAH crystals with clear corner angles (Figure 1). The calculated growth rates ranged from 4.79 × 10−20 to 2.11 × 10−19 m3/s, that is, 2−3 orders of magnitude higher than the growth rates of gibbsite precipitated from active NaAl(OH)4−NaHCO3 systems in MSMPR crystallizers.15 This implies quite different growth mechanisms between MAH and gibbsite. Gibbsite crystal growth from both seeded sodium aluminate solutions and active NaAl(OH)4−NaHCO3 systems has a second-order supersaturation dependence, which indicates a spiral growth mechanism.15,27,28 3.3.2. Nucleation Rate. The nucleation rates for MSMPR experiments are usually correlated as a function of suspension density and growth rate (eq 6) by means of nonlinear regression. The exponents were estimated with reasonable confidence as listed in Table 3. The regression result shown in Figure 4 are expressed by the equation

Figure 2. Typical population density distribution of MAH crystals.

parameter

R2 = 0.942

10−22 10−6 10−5 10−35

B0 = 3.05 × 10−18Gv −1.15M T1.06

R2 = 0.946

(9)

Table 3. 95% Confidence Intervals

3.3.1. Growth Rate. According to eq 5, the relationship of the crystal volume-average growth rate and the relative 7738

variable

value

lower limit

upper limit

kR i j

3.04985 × 10−18 −1.15000104 1.060000833

3.04968 × 10−18 −1.150002293 1.05999804

3.05001 × 10−18 −1.149999788 1.060003625

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indicate that solution supersaturation has a significant impact on the agglomeration kernel. The positive exponent of 1.25 for the mean residence time τ implies that the agglomeration rate increases with increasing contact time between particles. With long residence times, particles have sufficient time to cling together and form agglomerates.18 Substituting eq 9 into eq 10 gives β = 16.69 × 10−48Gv 0.33M T 0.52τ1.25

(11)

Indirectly, through the nucleation rate, the suspension density shows positive effects, indicating that agglomeration is promoted by increasingly frequent collisions between particles; this results from the possibility that two colliding particles cohere to form an aggregate.21,31,32 In addition, the agglomeration kernel of MAH crystallization was found to range from 3.96 × 10−48 to 1.16 × 10−47 m3/(number s), which is much smaller than the agglomeration kernels of (4.3 × 10−15)−(5.8 × 10−14) m3/(number s) for aluminum hydroxide in dilute sodium aluminate solution.33 This implies that particle agglomeration is not as important as growth for crystal enlargement in MAH crystallization, unlike the case for the extensively investigated gibbsite crystallization. 3.4. Effects of Supersaturation on Suspension Density and Mean Crystal Size. The suspension density increased with increasing supersaturation, but the mean crystal size decreased (Figure 6). The increase in suspension density shows

Figure 4. Nucleation rate correlation.

The near-unity exponent 1.06 for the suspension density in eq 9 implies the possibility of a secondary nucleation mechanism, mainly induced by crystal−agitator and crystal−crystallizer collisions rather than by crystal−crystal collisions.13,15,21 The negative order of −1.15 indicates that the nucleation of MAH in an MSMPR crystallizer is particle-size-limiting.25 The nucleation rates of MAH ranged from 1.26 × 105 to 2.33 × 108 number/(m3 s), which is lower than the nucleation rate of gibbsite in a seeded-hydrolysis process.29 This is probably because the viscosity of concentrated sodium aluminate solutions is much greater than that of dilute sodium aluminate solutions.24 An increase in the viscosity of the solution reduces the solution fluidity, which lowers the frequencies of crystal−agitator and crystal−crystallizer collisions. Moreover, no seeds were added during MAH crystallization. 3.3.3. Agglomeration Kernel. According to the empirical power-law equation (eq 7), the regression results for the agglomeration kernels are shown in Figure 5. The correlation expression is

Figure 6. Effects of supersaturation on suspension density and mean crystal size.

that the MAH crystallization conversion ratio increased. In solutions with high supersaturation, nucleation was fast and dominant, and large numbers of primary nuclei formed, which favored the generation of large numbers of small crystals. In solutions with relatively low supersaturation, however, growth was predominant and favored the formation of fewer, but larger, crystals. An increase in solution supersaturation increased the suspension density, which promoted collisions between particles to generate aggregates and further increase the crystal size. However, the mean crystal size decreased (Figure 6). This therefore indicates that crystal growth, rather than agglomeration, was responsible for crystal enlargement, in accordance with the inference regarding the agglomeration kernel. The high growth rate of MAH crystals also resulted in negligible breakage during MAH crystallization. However, in the case of

Figure 5. Agglomeration kernel correlation.

β = 9.65 × 10−39Gv 0.92B0 0.49τ1.25

R2 = 0.939

(10)

The volume-average growth rate, Gv, can be considered to be a measure of solution supersaturation,30 and τ represents the mean length of time for which a particle stays within the MSMPR crystallizer. The positive kinetic orders of Gv and B0 7739

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gibbsite precipitated from seeded sodium aluminate solutions or from active NaAl(OH)4−NaHCO3 solutions, agglomeration is an important factor in crystal size enhancement.15,27,34,35

4. CONCLUSIONS The kinetic equations of MAH crystallization were systematically acquired using the population balance model in a steadystate MSMPR crystallizer. The MAH crystal growth mechanism was found to be controlled by diffusion and surface integration, as well as nucleation, mainly secondary nucleation resulting from crystal−agitator and crystal−crystallizer collisions rather than from crystal−crystal collisions. The agglomeration kernel was proportional to the residence time, growth rate, and suspension density. The positive order of the agglomeration kernel with respect to the suspension density indicates that the agglomeration of MAH particles in the MSMPR crystallizer was promoted by frequent collisions between particles. Compared to the quite rapid growth during MAH crystallization, agglomeration was less important for crystal enlargement. Furthermore, the growth rate of MAH was greater than that of gibbsite in active NaAl(OH)4−NaHCO3 systems, but the nucleation rate of MAH was smaller than that of gibbsite in seeded-hydrolysis processes.

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REFERENCES

(1) Rayzman, V.; Filipovich, I.; Nisse, L.; Vlasenko, Y. Sodium aluminate from alumina-bearing intermediates and wastes. JOM 1998, 50, 32−37. (2) Sazhin, V. S. The crystallization of sodium aluminate. In Alumina Chemistry and Technology; Liu, W. Q., Ed.; China Industry Press: Beijing, 1964. (3) Cao, S. T.; Zhang, Y. F.; Zhang, Y. Preparation of sodium aluminate from the leach liquor of diasporic bauxite in concentrated NaOH solution. Hydrometallurgy 2009, 98, 298−303. (4) Bekker, A. V.; Livk, I. An implicit FEM solution of a PBE model of gibbsite crystallization with constant and nonlinear kinetics. Ind. Eng. Chem. Res. 2011, 50, 4641−4652. (5) Freij, S. J.; Parkinson, G. M. Surface morphology and crystal growth mechanism of gibbsite in industrial Bayer liquors. Hydrometallurgy 2005, 78, 246−255. (6) Li, H. X.; Addai-Mensah, J.; Thomas, J. C.; Gerson, A. R. The crystallization mechanism of Al(OH)3 from sodium aluminate solutions. J. Cryst. Growth 2005, 279, 508−520. (7) Zhou, Q. S.; Peng, D. J.; Peng, Z. H.; Liu, G. H.; Liu, X. B. Agglomeration of gibbsite particles from carbonation process of sodium aluminate solution. Hydrometallurgy 2009, 99, 163−169. (8) Muhr, H.; Leclerc, J. P.; Plasari, E.; Novel-Cattin, F. A rapid method for the determination of growth rate kinetic constants: Application to the precipitation of aluminum trihydroxide. Ind. Eng. Chem. Res. 1997, 36, 675−681. (9) Bekker, A. V.; Livk, I. Agglomeration process modeling based on a PDE approximation of the Safronov agglomeration equation. Ind. Eng. Chem. Res. 2011, 50, 3464−3474. (10) Cao, S. T.; Zhang, Y. F.; Zhang, Y. Nucleation and morphology of monosodium aluminate hydrate from concentration sodium aluminate solutions. Cryst. Growth Des. 2010, 10, 1605−1610. (11) Tai, C. Y.; Chen, P. C. Nucleation, agglomeration and crystal morphology of calcium carbonate. AIChE J. 1995, 41, 68−77. (12) Randolph, A. D.; Larson, M. A. Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization, 2nd ed.; Academic Press: London, 1988. (13) Chemaly, Z.; Muhr, H.; Fick, M. Crystallization kinetics of calcium lactate in a mixed-suspension-mixed-product removal crystallizer. Ind. Eng. Chem. Res. 1999, 38, 2803−2808. (14) Jarmer, D. J.; Lengsfeld, C. S.; Randolph, T. W. Nucleation and growth rates of poly(L-lactic acid) microparticles during precipitation with a compressed-fluid antisolvent. Langmuir 2004, 20, 7254−7264. (15) Li, Y.; Zhang, Y. F.; Yang, C.; Chen, L. B.; Zhang, Y. Crystallization of aluminium hydroxide from the reactive NaAl(OH)4−NaHCO3 solution: Experiment and modeling. Chem. Eng. Sci. 2010, 65, 4906−4912. (16) Wierzbowska, B.; Hutnik, N.; Piotrowski, K.; Matynia, A. Continuous mass crystallization of vitamin C in L(+)-ascorbic acid− ethanol−water system: Size-independent growth kinetic model approach. Cryst. Growth Des. 2011, 11, 1557−1565.

ASSOCIATED CONTENT

S Supporting Information *

Three measurements of PSDs of produced crystals (Figure S1), 99% confidence intervals of nucleation rate correlation (Table S1). This material is available free of charge via the Internet at http:// pubs.acs.org.

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kg = growth rate coefficient kR = nucleation rate coefficient kβ = agglomeration kernel coefficient MT = suspension density (g/L) n = crystal population density function [number/(m3 L)] p = exponent of the nucleation rate in the agglomeration kernel correlation q = exponent of the residence time in the agglomeration kernel correlation R = regression correlation coefficient v = crystal volume (m3) β = agglomeration kernel [m3/(number s)] μj = jth moment σ = relative supersaturation τ = mean residence time (s)

AUTHOR INFORMATION

Corresponding Author

*Address: National Engineering Laboratory for Hydrometallurgical Cleaner Production, Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, No. 1, Beiertiao, Zhongguancun, Beijing 100190, P.R. China. Tel./Fax: +86 10 82544826. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support from the National High Technology Research and Development Program of China (863 Program, 2011AA060701), the National Natural Science Foundation of China (21101159), and the Knowledge Innovation Project of Chinese Academy of Sciences (KGCX2-YW-321-2).

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NOMENCLATURE B0 = nucleation rate [number/(m3 s)] C = concentration (g/L) Ceq = equilibrium concentration (g/L) g = exponent of relative supersaturation in the growth rate correlation Gv = volume-average growth rate (m3/s) h = exponent of the growth rate in the agglomeration kernel correlation i = exponent of the growth rate in the nucleation rate correlation j = exponent of the suspension density in the nucleation rate correlation 7740

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(17) Wong, S. Y.; Bund, R. K.; Connelly, R. K.; Hartel, R. W. Modeling the crystallization kinetic rates of lactose via artificial neural network. Cryst. Growth Des. 2010, 10, 2620−2628. (18) Zauner, R.; Jones, A. G. Determination of nucleation, growth, agglomeration and disruption kinetics from experimental precipitation data: The calcium oxalate system. Chem. Eng. Sci. 2000, 55, 4219− 4232. (19) Wu, J. F.; Tai, C. Y.; Yang, W. K.; Leu, L. P. Temperature effects on the crystallization kinetics of size-dependent systems in a continuous mixed-suspension mixed-product removal crystallizer. Ind. Eng. Chem. Res. 1991, 30, 2226−2233. (20) Alvarez, A. J.; Singh, A.; Myerson, A. S. Crystallization of cyclosporine in a multistage continuous MSMPR crystallizer. Cryst. Growth Des. 2011, 11, 4392−4400. (21) Tavare, N. S.; Patwardhan, A. V. Agglomeration in a continuous MSMPR crystallizer. AIChE J. 1992, 38, 377−384. (22) Garside, J.; Shah, M. B. Crystallization kinetics from MSMPR crystallizers. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 509−514. (23) Morales, J. G.; Burgues, J. T.; Clemente, R. R. Crystal size distribution of hydroxyapatite precipitated in a MSMPR reactor. Cryst. Res. Technol. 2001, 36, 1065−1074. (24) A Manual of Alumina Production; Metallurgical Industry Press: Beijing, 1974. (25) Chen, P. C.; Chen, C. C.; Fun, M. H.; Liao, O. Y.; Jiang, J. J.; Wang, Y. S.; Chen, C. S. Mixing and crystallization kinetics in gas− liquid reactive crystallization. Chem. Eng. Technol. 2004, 27, 519−528. (26) Mullin, J. W. Crystallization, 4th ed.; Butterworth Heinemann: London, 2001. (27) Ilievski, D.; White, E. T. Agglomeration during precipitation: Agglomeration mechanism identification for Al(OH)3 crystals in stirred caustic aluminate solutions. Chem. Eng. Sci. 1994, 49, 3227− 3239. (28) Li, T. S.; Livk, I.; Ilievski, D. Supersaturation and temperature dependency of gibbsite growth in laminar and turbulent flows. J. Cryst. Growth 2003, 258, 409−419. (29) Li, J.; Prestidge, C. A.; Addai-Mensah, J. Secondary nucleation of gibbsite crystals from synthetic Bayer liquors: Effect of alkali metal ions. J. Cryst. Growth 2000, 219, 451−464. (30) Tavare, N. S.; Shah, M. B.; Garside, J. Crystallization and agglomeration kinetics of nickel ammonium sulphate in an MSMPR crystallizer. Powder Technol. 1985, 44, 13−18. (31) Alopaeus, V.; Laakkonen, M.; Aittamaa, J. Solution of population balances with breakage and agglomeration by high-order moment-conserving method of classes. Chem. Eng. Sci. 2006, 61, 6732−6752. (32) Ilievski, D.; Livk, I. An agglomeration efficiency model for gibbsite precipitation in a turbulently stirred vessel. Chem. Eng. Sci. 2006, 61, 2010−2022. (33) Li, T. S.; Livk, I.; Ilievski, D. Influence of the estimation procedure on the accuracy and precision of aluminum trihydroxide crystallization kinetics from dynamic data. Ind. Eng. Chem. Res. 2001, 40, 5005−5013. (34) Seyssiecq, I.; Veesler, S.; Boistelle, R.; Lamérant, J. M. Agglomeration of gibbsite Al(OH)3 crystals in Bayer liquors. Influence of the process parameters. Chem. Eng. Sci. 1998, 53, 2177−2185. (35) Livk, I.; Ilievski, D. A macroscopic agglomeration kernel model for gibbsite precipitation in turbulent and laminar flows. Chem. Eng. Sci. 2007, 62, 3787−3797.

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