(536b) Mathematical Modeling and Analysis of Cooling Crystallization within Dual-Impinging-Jet Mixers

In the pharmaceutical industry, good control of crystal size distribution (CSD) can improve process efficiency and formulation of drug product. An effective way to improve the control of CSD is through combining continuous seeding and growth with concentration control (Woo et al., 2011). To continuously produce small mono-disperse crystals, one well-studied approach is to combine solution and anti-solvent streams in a dual-impinging-jet (DIJ) mixer (e.g., Johnson and Prud'homme, 2003; Midler et al., 1994; Woo et al., 2011). The underlying principle is that, at appropriate flow rates, a DIJ mixer can generate high-intensity micro-mixing of fluids to quickly achieve a nearly homogeneous composition of high supersaturation before the onset of primary nucleation. Use of a DIJ mixer to generate crystals can sometimes remove the requirement of a milling step, which simplifies the overall manufacturing process and avoids the potential of generating an undesirable polymorphic transformation (Johnson and Prud'homme, 2003; Midler et al., 1994).

In past work, we experimentally demonstrated the use of a cooling DIJ mixer to combine hot and cold saturated solutions, rather than combining a solution with an anti-solvent, to generate seed crystals with a narrow size distribution for L-asparagine monohydrate (LAM) in aqueous solution (Jiang et al., 2012). The crystals were less than 10 microns in length, placing them in the correct size range for direct application in inhalers (Capstick and Clifton, 2012). Theoretically, if the mixing were perfect (that is, concentration and temperature were completely mixed at the molecular scale in the DIJ mixer), inspection of the phase diagram for the LAM-water system indicated that the supersaturation would not be high enough to nucleate crystals within a cooling DIJ mixer. The observed nucleation of crystals can be explained by the observation that the energy transfer rate at the interface between the impinging fluids is much faster than the mass transfer rate, so that the temperature of the hot solution near the interface can drop to the average temperature of the two solutions before its solution concentration can significantly change, resulting in the supersaturation in the hot fluid becoming sufficiently high to nucleate crystals.

While the ability to generate highly uniform-sized crystals of less than 10 microns using a cooling DIJ mixer would be a perfect technology for inhaler applications, this approach is not expected to be applicable to all combinations of pharmaceuticals and solvents. Currently, scientists/engineers have to assess whether any particular compound/solvent combination is suitable for use in a DIJ mixer by trial-and-error experimentation aided with experience (Tung et al., 2009). It would be useful at the early stage of research and development to be able to quickly identify compound-solvent combinations that cannot nucleate crystals within DIJ mixers, based on their physicochemical properties. This work answers this question for cooling jet DIJ mixers. We combine mathematical modeling of crystallization kinetics, thermodynamics, and transport with theoretical analysis to derive conditions in which a pharmaceutical/solvent combination is suitable for the nucleation of crystals within a cooling DIJ mixer. The mathematical models are in the form of partial differential equations that are simplified by exploiting symmetries and employing scaling analysis, to enable the derivation of analytical expressions that compare favorably with numerical simulations. The mathematical model and methodology are validated for the crystallization of LAM in aqueous solution.

References

Capstick, T. G. D., Clifton, I. J., 2012. Inhaler technique and training in people with chronic obstructive pulmonary disease and asthma, Expert Review of Respiratory Medicine 6(1), 91-103.

Jiang, M., Wong, M. H., Zhu, Z., Zhang, J., Zhou, L., Wang, K., Ford Versypt, A. N., Si, T., Hasenberg, L. M., Li, Y., Braatz, R. D., 2012. Towards achieving a flattop crystal size distribution by continuous seeding and controlled growth, Chemical Engineering Science 77, 2-9.

Johnson, B. K., Prud'homme, R. K., 2003. Chemical processing and micromixing in confined impinging jets, AIChE Journal 49(9), 2264-2282.

Midler, M., Jr., Paul, E. L., Whittington, E. F., Futran, M., Liu, P. D., Hsu, J., Pan, S. H., 1994. Crystallization method to improve crystal structure and size, U.S. Patent #5314506A, 11 pages.

Tung, H., Paul, E. L., Midler, M., McCauley, J. A., 2009. Crystallization of Pharmaceuticals: An Industrial Perspective. Hoboken, NJ: Wiley.

Woo, X. Y., Tan, R. B. H., Braatz, R. D., 2011. Precise tailoring of the crystal size distribution by controlled growth and continuous seeding from impinging jet crystallizers, CrystEngComm 13, 2006-2014.