Solution crystallization produces materials with specific crystal shapes and size distributions. Both the crystal size and shape play an important role in deciding the processing rate of material in various downstream operations, namely filtration, washing, and drying. These also govern the storage and handling characteristics, the flow ability, and the extent of dust formation, dispersibility, and stability. Furthermore, crystals of different shapes have different bioavailability and compressibility, the properties that are important in tablet manufacturing. Thus, the significant impact of crystal size and shape demands for its tighter control. Hence the accurate prediction of crystal shape along with its distribution becomes essential.

The relative face specific growth rates have recently been used to predict the shape evolution of a growing convex crystal (Zhang et al., 2006). These predictions are obtained assuming constant relative face growth rates. Obviously, the assumption makes the population of the crystals to be described by one dimensional population balance model (Zhang and Doherty, 2004). It has been observed that there exists significantly different crystal shapes in a crystallizer (Weigler, 2005 and Yang et al., 2006). Furthermore, it has been reported in the literature (Joshi and Paul, 1974 and Mullin and Whiting, 1980) that the face specific growth rates have different dependencies on the supersaturation leading to relative face growth rates strongly varying with supersaturation. Thus the population of crystals at any instant will have widely varying crystal shapes and sizes depending upon the initial crystal shape and size distribution, face specific growth dependence on supersaturation as well as the supersaturation profile. Eventually these observations demand for the complex consideration of varying relative growth rates in accordance with the supersaturation while predicting the crystal shape and size distribution. The additional complexity can be well treated with the multidimensional population balance modeling (MDPBM) approach coupled with the supersaturation dynamics. It is this approach, which will be presented to show some interesting predictions of the evolution of the crystal size and shape distributions in industrially relevant batch and continuous crystallizers.

The proposed multidimensional population framework has the potential to model, optimize and control the evolution of desired crystal form based on fundamental understanding of crystal growth including effects of supersaturation and crystal-solvent interactions.

References

1. Joshi, M. S. and Paul, B. K. “Effect of Supersaturation and Fluid Shear on the Habit and Homogeneity of Potassium Dihydrogen Phosphate Crystals”, J. Cryst. Growth, 22, 321-327, 1974.

2. Mullin, J. W. and Whiting, M. J. L. “Succinic Acid Crystal Growth Rates in Aqueous Solution,” Ind. Eng. Chem. Fundam., 19, 117-121, 1980.

3. Weigler, F., Process investigations for Gold colloid production, Study Thesis, Magdeburg 2005.

4. Yang, G., Kubota, N. Sha, Z., Louhi-Kultanen, M. and Wang, J. “Crystal Shape Control by Manipulating Supersaturation in Batch Cooling Crystallization”, Crystal Growth and Design, 6, 2799 – 2803, 2006.

5. Zhang, Y. and Doherty, M. F. “Simultaneous Prediction of Crystal Shape and Size for Solution Crystallization”, AIChE J., 50, 2101-2112, 2004.

6. Zhang, Y., Sizemore, J. P. and Doherty, M. F. “Shape Evolution of 3-Dimensional Faceted Crystals”. AIChE J., 52, 1906-1915, 2006.