On the prediction of crystal shape distributions in a steady-state continuous crystallizer

Zhang and Doherty [2004. Simultaneous prediction of crystal shape and size for solution crystallization. A.I.Ch.E. journal 50, 2101-2112] have provided a one-dimensional analysis of crystallization based on the assumption that the relative face-specific growth rates of a (2-D) crystal are independent of supersaturation and hence invariant with time. Subsequent work by these authors [Zhang, Y., Sizemore, J.P., Doherty, M.F., 2006. Shape evolution of 3-dimensional faceted crystals. A.I.Ch.E. journal 52, 1906-1915) consider shape evolution of single three-dimensional crystals with morphological changes. In this work, we present a multidimensional population balance approach accounting for dependence of the relative face-specific growth rates on supersaturation, a situation more commonly encountered. For example, Joshi and Paul [1974. Effect of supersaturation and fluid shear on habit and homogeneity of potassium dihydrogen phosphate crystals. journal of Crystal Growth 22, 321-327] and Mullin and Whiting [1980. Succinic acid crystal-growth rates in aqueous solution. Industrial & Engineering Chemistry Fundamentals 19, 117-121] report face-specific growth rates with different dependence on the supersaturation. Thus it has been observed that there exists significantly different crystal shapes in a crystallizer [Yang, G., Kubota, N., Sha, Z., Louhi-Kultanen, M. Wang, J., 2006. Crystal shape control by manipulating supersaturation in batch cooling crystallization. Crystal Growth and Design 6, 2799-2803]. Consequently, the population of crystals at any instant will have widely varying crystal shapes and sizes depending upon the initial crystal shape and size distribution. Computations are presented for the shape distributions of the crystal population emerging from a steady-state continuous crystallizer for two cases: (1) feed without crystals including nucleation for the formation of new crystals, and (2) feed with seed crystals of known shape, with suppressed nucleation. In the range of mean residence times investigated, the calculated crystal volume distributions for the first case show geometrically dissimilar shapes without morphological variations. However, in the second case, because the feed crystals of the chosen shape were susceptible to morphological changes, the volume distributions display this feature with shape and size distributions for each of a number of different morphologies. By varying operating conditions such as the flow rate, the inlet supersaturation, and the shapes of feed crystals, the proposed model can clearly be used to manipulate the crystal shape and size distributions and their morphologies. (C) 2008 Elsevier Ltd. All rights reserved.