(579b) Cooling Crystallization within Micromixers: Mathematical Modeling, Theoretical Analysis, and Experimental Validation

A key objective in crystallization is to control crystal size distribution (CSD), to improve product quality (e.g., pharmaceutical and biopharmaceutical) and process efficiency. Micromixers have been an effective technology to enhance the control of nucleation, which is the key step towards final product CSD in continuous [1] and semi-continuous crystallization processes [2]. Common micromixers combine solution and anti-solvent streams such as in a dual-impinging-jet (DIJ) micromixer (e.g., [3]â??[5]).

Rather than anti-solvent crystallization as commonly used, a DIJ mixer has been demonstrated to combine hot and cold saturated solutions of the same solute/solvent to generate small uniform seed crystals [2], which appears to be the first reported cooling DIJ nucleation. The product crystals were less than 10 microns in length, placing them in the correct size range for direct application in inhalers [6]. Theoretically, if the mixing was perfect (that is, concentration and temperature were completely mixed at the molecular scale in the mixer), the average supersaturation level would be too low to nucleate crystals in a cooling DIJ mixer. The surprising result of nucleating crystals by combining hot and cold saturated solutions in a DIJ mixer motivated the theoretical analysis of the system, which showed that nucleation was enabled by the much faster energy transfer than mass transfer rates near the interface. This difference in rates enabled the temperature of the hot solution to drop to approximately the average temperature of the two solutions before its solution concentration had significantly changed, resulting in a supersaturation sufficiently high to nucleate crystals.

The theoretical analysis is supported with process simulations. The two-dimensional energy and solute mass balances are solved using COMSOL input with an analytical solution for the velocity field, to generate spatial distributions of temperature, concentration, and supersaturation near the hot-cold interface within a cooling DIJ mixer. In the most important spatial region of importance for characterization of nucleation, the two-dimensional fields are shown to be very close to analytical solutions derived from a one-dimensional approximation of the energy and molar balances. This simplification applied the derivation of design criteria to facilitate quick assessment of whether any particular pharmaceutical-solute combination will nucleate crystals in a cooling DIJ mixer, based on the physicochemical properties. These criteria could save time and material by avoiding or reducing trial-and-error experiments, which is helpful at the early stage of pharmaceutical process development. The process simulations are then expanded to include the full solution of the spatially-varying population balance model [5] to calculate the crystal size distributions throughout the spatial domain. The mathematical models and methodologies are validated for the crystallization of L-asparagine monohydrate (LAM) in aqueous solution.

References

[1] M. Jiang, Z. Zhu, E. Jimenez, C. D. Papageorgiou, J. Waetzig, A. Hardy, M. Langston, and R. D. Braatz, â??Continuous-flow tubular crystallization in slugs spontaneously induced by hydrodynamics,â? Cryst. Growth Des., vol. 14, no. 2, pp. 851â??860, 2014.

[2] M. Jiang, M. H. Wong, Z. Zhu, J. Zhang, L. Zhou, K. Wang, A. N. Ford Versypt, T. Si, L. M. Hasenberg, Y. E. Li, and R. D. Braatz, â??Towards achieving a flattop crystal size distribution by continuous seeding and controlled growth,â? Chem. Eng. Sci., vol. 77, pp. 2â??9, 2012.

[3] B. K. Johnson and R. K. Prudâ??homme, â??Chemical Processing and Micromixing in Confined Impinging Jets,â? AIChE J., vol. 49, no. 9, pp. 2264â??2282, 2003.

[4] M. Midler Jr., E. L. Paul, E. F. Whittington, M. Futran, P. D. Liu, J. Hsu, and S. H. Pan, â??Crystallization method to improve crystal structure and size,â? US5314506 A, 24-May-1994.

[5] X. Y. Woo, R. B. H. Tan, and R. D. Braatz, â??Precise tailoring of the crystal size distribution by controlled growth and continuous seeding from impinging jet crystallizers,â? CrystEngComm, vol. 13, no. 6, pp. 2006â??2014, 2011.

[6] T. G. D. Capstick and I. J. Clifton, â??Inhaler technique and training in people with chronic obstructive pulmonary disease and asthma,â? Expert Rev. Respir. Med., vol. 6, no. 1, pp. 91â??103, Feb. 2012.