RESEARCH NOTE pubs.acs.org/IECR
A New Controlled Method to Eliminate the Influence of Micromixing on Particle Size Distribution for Reactive Crystallization Caihong Li,* Jinrong Liu,* Hongqiang Wang, Peipei Wang, and Haiyan Gong School of Chemical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China ABSTRACT: This paper analyzes the problem of particle size distribution of precipitation products resulting from inhomogeneous micromixing during reactive crystallization. A new idea is proposed to solve the problem of broader particle size distribution of the precipitation product. This idea comes from the fact that the nucleation induction time can be prolonged to meet tS < tind by selecting proper operating conditions in the precipitation process.
1. INTRODUCTION Reactive crystallization is the predominate method for solution crystallization to produce particulate material in the chemical industry. This method has been widely used in the lab for chemical analysis and industrial applications, such as in pharmaceuticals, food additives, and catalysts. During reactive crystallization, micromixing becomes the control step when the nucleation induction time scale is shorter than the time scale in which the liquid-phase reactants micromix uniformly. This result will markedly affect the particle size distribution of the product; an important quality evaluation index of the products. Therefore, finding a feasible method to decrease the micromixing effect on the particle size distribution of the product is an important research project in the field of reactive crystallization. We find that there is an inconsistency between the process investigated and the process involved in the micromixing concept by analyzing the theoretical research results on micromixing effects on the process of reactive crystallization. Micromixing is the mixing of reactants at the molecular level. Micromixing actually contains two processes because there is nucleation induction time in most research systems. The first process is a micromixing process of the reactants before the precipitation reaction. The second is supersaturation homogeneous distribution of the aim product after the precipitation reaction. Previous measures to decrease the micromixing effect on the particle size distribution include increasing the mixing intensity, such as increasing the stirring rate, taking jet mixing, or choosing the proper reactor feeding position to make the reactants mix in the large intensity turbulent region and then reducing the time scale of micromixing. Fang et al. established a scalable fabrication of lanthanide phosphate single crystals with very narrow size distributions with tunable aspect ratios using microfluids at room temperature. The mixing was achieved by feeding the reagents onto the center of a rapidly rotating disk or at the periphery of a rapidly rotating tube. The hydrodynamics of film flow over a rotating surface is important in dictating the micromixing environment for nanocrystal nucleation and growth.1 These enhancement measures, however, sometimes were limited because of the wide gap of the order of magnitudes between the time scale of precipitation reaction and the time scale of homogeneous micromixing. On the basis of a previous work, this paper analyzes the micromixing r 2011 American Chemical Society
concept and the enhancement measures of micromixing to make a micromixing concept more clear and provides a new idea to decrease the micromixing effect on the particle size distribution. As an experimental study, the preparation of strontium sulfate particles by means of reactive crystallization has been conducted to verify the conclusions.
2. MIXING DURING THE REACTIVE CRYSTALLIZATION PROCESS Materials mixing in the precipitation reactor can be classified as one of the following three processes: macromixing, mesomixing, or micromixing. Macromixing is a material homogeneous process on the scale of the vessel. Mesomixing refers to a uniform dispersion process of groups of microfluid caused by turbulence dispersion (usually 10100 μm). Micromixing occurs on the scale of molecular diffusion in stretching fluid lamellae.2,3 Mixing is the combination of three kinds of diffusion mechanisms, including bulk convection, eddy, and molecular diffusion. The influence scale of the mechanisms decreases one by one. Bulk convection diffusion can only mix the “bulk” of different materials, whereas eddy diffusion can reduce the inhomogeneity of the vortices at the “bulk” interface. Because the least vortex is much larger than a molecule, it is impossible to get completely homogeneous mixing at the molecular scale by bulk convection diffusion and eddy diffusion. Therefore, only molecular diffusion can provide micromixing. Macromixing and mesomixing can increase the surface area of molecular diffusion and decrease the diffusion distance and then indirectly increase the micromixing rate.46 Chemical reaction, nucleation, and crystal growth are all in molecular scale in the precipitation process, which are influenced directly by micromixing.7 Macromixing and mesomixing indirectly influence the process of reactive crystallization by determining the micromixing environment. Precipitation is generally composed of two steps. The first step is the generation of the supersaturated solution, which is the driving force for the aim product to be precipitated. The aim Received: June 21, 2011 Accepted: December 20, 2011 Revised: December 17, 2011 Published: December 20, 2011 576
dx.doi.org/10.1021/ie2025618 | Ind. Eng. Chem. Res. 2012, 51, 576–580
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Figure 1. Schematic diagram of precipitation process.
product is obtained from the homogeneous phase chemical reaction of reactants contacting at the molecular level. The second step is the crystallization process, including the aim product nucleation and crystal growth, which are influenced by the supersaturation degree and its distribution.2,3 The process mentioned above is shown in Figure 1. Characteristic times to describe the rate of processes as shown in Figure 1 are as follows: (1) The characteristic time of reactants micromixing tM: the time characterizing reactants A and B to reach homogeneous micromixing. (2) The characteristic time of chemical reaction tR: the time required for the stoichiometric reactants A and B to translate into product C at the initial reaction rate. (3) Nucleation induction time tind: the sum of time from the generation of supersaturated solution of the aim product to the appearance of detectable change of physical features of the system. Through further analysis of the precipitation process (Figure 1), we find that micromixing refers only to the homogeneous distribution process of reactants A and B at the molecular scale. Because the nucleation induction period exists for the precipitation process of sparingly soluble species, after the precipitation reaction is over and before the nucleation process occurs there exists a process conducting homogeneous distribution of the aim product C. Therefore, to completely describe the precipitation process, we introduce tS, the characteristic time for supersaturation homogeneous distribution of aim product C. This time constant characterizes the rate from supersaturated solution formation to homogeneous distribution in the whole crystallizer. Its value depends on the degree of micromixing of reactants A and B and the diffusion rate of the product C. In many cases, tM + tS > tM, that is, tS > 0. For analyzing the effect of micromixing on the precipitation process, it is helpful to separate the supersaturation homogeneous distribution process from the dim micromixing process.
Figure 2. Schematic diagram of characteristic time for micromixing and precipitation process in fast reaction precipitation system.
which causes an inhomogeneous distribution of the initial supersaturation. In view of controlling the particle size distribution of crystallization products, the starting point should be to ensure that the nucleation and crystal growth process takes place under the homogeneous supersaturation distribution condition. The conventional approach is to make the reactants micromix completely before the precipitation reaction occurs. Then, after the precipitation reaction, the supersaturation distribution of the product is homogeneous, and the nucleation and crystal growth rate are simultaneously homogeneous in the whole crystallizer. Therefore, the resultant crystal particle size distribution should show good monodispersity. Previous results on improving particle size distribution have also focused on intensifying the reactants’ micromixing. Increasing the mixing intensity could shorten the scale of tM, and accelerate the molecular diffusion of the aim product, which increases the supersaturation homogeneous degree. However, because of the difference in the order of magnitude between the micromixing rate and the chemical reaction rate, increasing the mixing intensity could not perfectly intensify the mixing degree, as is expected. Additionally, the efficiency of intensification micromixing is restricted for systems with shorter induction times. After introducing the concept of characteristic time for supersaturation homogeneous distribution tS, we can analyze the influence of micromixing on the precipitation product’s particle size distribution from a new angle. When the micromixing of reactants is not complete, the influence of micromixing on the precipitation products’ particle size distribution will depend on the relative magnitudes of tS and tind, as shown in Figure 2. When tS > tind (Figure 2b), before the supersaturation distribution of the aim product is homogeneous, the crystal nucleation has already taken place and then the reactants’ insufficient micromixing will affect the crystal particle size distribution. In contrast, when tS < tind (Figure 2a), even though the initial supersaturation distribution of the aim product is not homogeneous, the induction time allows the aim product’s supersaturation to distribute homogeneously by means of molecular diffusion mass transfer. Therefore, the crystal nucleation occurs under the condition of the aim product’s supersaturation homogeneous distribution. As a result, insufficient micromixing of the reactants will not influence the crystal particle size distribution. To eliminate the effects of insufficient micromixing on the crystal product properties, tS < tind should be met. One way is to shorten tS. Previous research suggests that some methods, such as increasing the stirring intensity and choosing proper feeding positions, could increase the turbulence level of the fluid to promote
3. INFLUENCE OF MICROMIXING ON PARTICLE SIZE DISTRIBUTION (PSD) AND THE CONTROL OF PSD According to the micromixing theory, tM can be calculated as follows:8,9 1=2 υm tM ¼ km ð1Þ εm where, km is a constant, which varies with the crystallizer, νm is kinematic viscosity, for which the value is 1 106 m2/s for aqueous solution,10 and εm is the energy dissipation rate per unit mass. The constant, εm, is about 1 103100 103 kJ/(kg s) for the conventional stirred-tank reactor, km is about 10 for the static mixer,11 and tM is 5 103 to 50 103 s, calculated by eq 1. Because the precipitation reaction is very rapid, the chemical reaction is finished as soon as A is in contact with B, and C is formed. Compared with tM, tR is negligible.12 Therefore, the precipitation reaction occurs when micromixing is uneven, 577
dx.doi.org/10.1021/ie2025618 |Ind. Eng. Chem. Res. 2012, 51, 576–580
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Figure 4. SEM images of SrSO4.
Figure 3. XRD patterns of SrSO4 (A,B, sample patterns; C, SrSO4 standard patterns).
reactant micromixing. At the same time, the same methods can increase the aim product’s diffusion mass transfer rate, and as a result, tS is shortened. However, from the point of view of crystallization kinetics, increasing the turbulence level will also increase the rate of nucleation and crystal growth. Therefore, tind is shortened and it is hard to get the case as shown in Figure 2a. As a result, the existing methods for enhancing micromixing are limited in decreasing the effect of micromixing on the precipitation process. Another method is to prolong the induction time, tind. There is an obvious induction time for most supersaturation solution systems in the metastable state, which is affected by many factors, such as degree of supersaturation, temperature, stirring intensity, and impurities added. The induction time may be extended or shortened.1316 The main factors to prolong the induction time can be determined through experiments for the precipitation system given. The induction time will provide enough time for aim product’s supersaturation distribution to reach a homogeneous state, which is undoubtedly a new idea in decreasing the effect of micromixing on the reactive crystallization process.
Figure 5. TEM images of SrSO4.
of EDTA were added into the mixture. The remaining experimental procedure was the same as experiment A. The samples produced by experiment A and B were characterized by X-ray diffraction (XRD, D8-Advance, Bruker Company, Germany), and morphology, particle size, and particle size distribution studies for strontium sulfate were done by scanning electron microscopy (SEM, S-3400N, Hitachi Ltd. Japan), transmission electron microscopy (TEM, JEM-2010, JEOL, Ltd., Japan), and dynamic light scattering of laser particle size analyzer (DLS, Zetasizer Nano ZS90, Malvern Instruments Ltd., France). 4.2. Results and Discussion. The XRD patterns show that the samples produced by experiment A and B are both SrSO4 (Figure 3). However, from the results of Figure 4, Figure 5, and Figure 6, it was found that the two crystallization products prepared with different controlling methods show different PSD and crystal sizes. Sample A has a narrow PSD and uniform morphology with smaller particle size, while sample B has a wide PSD and uneven morphology with larger particle size. In this example, the controlling method to prolong the induction time tind was performed by adding EDTA into the system before the precipitation reaction took place in experiment A and a desired result was obtained. The comparison of PSD between experiment A and B was obvious. In experiment A, we created a system with an 8 s induction time by adding EDTA into the Sr(NO3)2 solution. Ethanol was added into the supersaturated SrSO4 solution after SrSO4 supersaturation was distributed homogeneously. As a result, there were no insufficient micromixing effects on the crystal product properties under the condition tS < tind. On the contrary, in experiment B, because EDTA was added into the system after the precipitation reaction was conducted, EDTA cannot inhibit the nucleation process of SrSO4 even though EDTA was then added into the system. Therefore, the induction time of SrSO4 was zero at the selected reactant concentration and the feeding orders in experiment B, and tS > tind, which resulted in the effects of initial insufficiency micromixing of reactants on the crystal product properties under the other same conditions with
4. APPLICATION EXAMPLE Thus far, we have discussed micromixing in the crystallization process and its influence on PSD. We have also presented a new thought on avoiding the influence of uneven micromixing on the crystallization process. Here, we also provide a crystallization process of SrSO4 as an application of our idea. 4.1. Experimental Methods. Experiment A: 0.28 g EDTA was added to 50 mL of 0.1 M Sr(NO3)2, and the pH was adjusted to 8 with 0.1 M NaOH. Then, 50 mL of 0.1 M Na2SO4 was added into the Sr(NO3)2 solution with constant stirring at 25 °C. The induction time was measured to be 8 s using the conductivity method with conductivity meter (DDSJ-308A, Leici Company, China).16,17 After the mixed solution was stirred for 5 s at a speed of 300 rpm before SrSO4 precipitation created, 15 mL of ethanol was then added to the mixed solution. The resulting suspension was filtered. The cake was washed several times with distilled water and absolute ethanol. The product was dried at 60 °C for 8 h in a vacuum dryer. The final product was a white powder. Experiment B: 50 mL of 0.1 M Na2SO4 and 50 mL of 0.1 M Sr(NO3)2 were mixed together. Then, 15 mL of ethanol and 0.28 g 578
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’ ACKNOWLEDGMENT We acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 50862006) and the Natural Science Foundation of Inner Mongolia (Grant No. 20080404MS0211). ’ NOTATION tS = characteristic time for supersaturation homogeneous distribution of aim product, s tind = nucleation induction time, s tM = characteristic time of reactants micromixing, s tR = characteristic time of chemical reaction, s tN = characteristic time of nucleation, s tG = characteristic time of crystal growth, s km = a constant, m2 s kJ/kg νm = kinetic viscosity, m2/s Greek Letters
εm = energy dissipation rate per unit mass, kJ/(kg s) Abbreviations
PSD = particle size distribution
’ REFERENCES (1) Fang, J.; Guo, Y.; Lu, G.; Raston, C. L.; Iyer, K. Swaminathan. Instantaneous Crystallization of Ultrathin One-Dimensional Fuorescent Rhabdophane Nanowires at Room Temperature. Green Chem. 2011, 13, 817–819. (2) Baldyga, J.; Podgorska, W.; Pohorecki, R. Mixing-Precipitation Model with Application to Double Feed Semibatch Precipitation. Chem. Eng. Sci. 1995, 50, 1281–1300. (3) Fourcade, E.; Hoefsloot, H. C. J.; Vliet, G.; Bunge, W.; Mutsers, S. M. P.; Iedema, P. D. The Influence of Micromixing on Molecular Weight Distribution During Controlled Polypropylene Degradation in a Static Mixer Reactor. Chem. Eng. Sci. 2001, 56, 6589–6603. (4) Khang, S. J.; Levenspiel, O. New Scale-up and Design Method for Stirrer Agitated Batch Mixing Vessels. Chem. Eng. Sci. 1976, 31, 567– 571. (5) Brodkey, R. S. Turbulence in Mixing Operations; Academic Press: New York, 1975. (6) Biggs, R. D. Mixing Rates in Stirred Tanks. AIChE J. 1963, 9, 636. (7) Bruno, M; David, R. Experimental Evidence for Prediction of Micromixing Effects in Precipitation. AIChE J. 1991, 37, 1698–1710. (8) Fournier, M. C; Falk, L; Villermaux, J. A New Parallel Competing Reaction System for Assessing Micromixing Efficiency Determination of Micromixing Time by a Simple Mixing Model. Chem. Eng. Sci. 1996, 51, 5187–5196. (9) Baldyga, J.; Bourne, J. R. Comparison of the Engulfment and the Interaction by Exchange with the Mean Micromixing Model. Chem. Eng. J 1990, 45, 25. (10) Yang, H.-J.; Chu, G.-W.; Zhang, J.-W.; Shen, Z.-G.; Chen, J.-F. Micromixing Efficiency in a Rotating Packed Bed: Experiments and Simulation. Ind. Eng. Chem. Res. 2005, 44, 7730–7737. (11) Fang, J. Z.; Lee, D. J. Micromixing Efficiency in Static Mixer. Chem. Eng. Sci. 2001, 56, 3797–3802. (12) Dai, G.; Chen, M. Fluid Mechanics in Chemical Engineering; Chemical Industry Press: Beijing, 1988. (13) Amjad, Z. Calcium Sulfate Dihydrate Scale Formation on Heat Exchanger Surfaces: The Influence of Scale Inhibitors. J. Colloid Interface Sci. 1988, 123, 523–536. (14) Randolph, A. D.; Larson, M. A. Theory of Particulate Processes; Academic Press: New York, 1988. (15) Guerbuez, H.; Oezdemir, B. Experimental Determination of the Metastable Zone Width of Borax Decahydrate by Ultrasonic Velocity Measurement. J. Cryst. Growth 2003, 252, 343–349.
Figure 6. Particle size distribution of SrSO4.
experiment A. The results show that prolonging the induction time of the supersaturated solution to meet tS < tind was effective in avoiding the unwelcome influence of micromixing on PSD.
5. CONCLUSIONS The concept of micromixing is clearly explained by distinguishing the rate of micromixing, the precipitation reaction, and the nucleation process. The introduction of the characteristic time of the supersaturation homogeneous distribution, tS, and the comparison of the relative magnitudes of tS and tind allowed us to determine whether the inhomogeneous micromixing of the reactants influences the quality of precipitation product. While promoting the reactants micromixing has little effect on improving the bad influence of micromixing on PSD, the method for prolonging the induction time, tind, might be promising in solving the problem of micromixing heterogeneity. This measure was conducted in our application example and proved that prolonging the induction time can obtain the resultant product with more uniform PSD compared with the contrast condition. ’ AUTHOR INFORMATION Corresponding Author
*Tel.: +86-471-6575722. Fax: +86-471-6575722. E-mail:
[email protected]. 579
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(16) Nathalie, L.; Fabienne, E.; Olivier, L.; Jacques, S. Effect of Ultrasound on the Induction Time and the Metastable Zone Widths of Potassium Sulphate. Chem. Eng. Sci. 2002, 86 (3), 233–241. (17) Amathieu, L.; Boistelle, R. Crystallization Kinetics of Gypsum from Dense Suspension of Hemihydrate in Water. J. Cryst. Growth. 1988, 88, 183–186.
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