Crystal growth rate dispersion modeling using morphological population balance

Crystal growth in solution is a surface-controlled process. The variation of growth rates of different crystal faces is considered to be due to the molecular arrangement in the crystal unit cell as well as the crystal surface structures of different faces. As a result, for sonic crystals, the growth rate for a specific facet is not only a function of Supersaturation, but also dependent on sonic other factors such as its size and the lattice spread angle. This phenomenon of growth rate dispersion (GRD) or fluctuation has been described in literature to have attributed to the formation of some interesting and sophisticated crystal structures observed in experimental studies. In this article, GRD is introduced to a recently proposed morphological population balance model to simulate the dynamic evolution of crystal size distribution in each face direction for the crystallization of potash alum, a chemical that has been reported to show GRD phenomenon and sophisticated crystal structures. The GRD is modeled as a function of the effective relative supersaturation, which is directly related to crystal size, lattice spread angle, relative supersaturation, and solution temperature. The predicted results clearly demonstrated the significant effect of GRD on the shape evolution of the crystals. (C) 2008 American Institute of Chemical Engineers.