Non-isothermal crystallization from liquid solutions: effect of heat of crystallization on growth rate

Abstract

The kinetic behaviour of crystal growth from liquid solutions is analysed. In particular, the effects of the heat of crystallization and the moving boundary of a crystal on the growth kinetics are considered. On the basis of a perturbation parameter ε, defined by [(C_b–C_e0)/ρ_s], C_b, C_e0 and ρ_s being, respectively, the concentration of solute in the bulk liquid phase, the equilibrium solute concentration and the density of solid, the set of non-linear governing equations are solved. We find that the dimensionless linear growth rate of a crystal, G, is a weak function of crystal size for an isothermal crystallization. As the size of a crystal increases, G approaches an asymptotic value for both endothermic and exothermic crystallization. The asymptotic values for these three cases follow the order exothermic > isothermal > endothermic. For crystals commonly encountered in practice, the heat of crystallization can be neglected. However, depending on the magnitudes of ε and the relative thickness of the diffusion layer δ*, a pseudo-steady-state assumption (neglect of the effect of the moving boundary) may lead to a significant deviation in the prediction of G. The greater the value of ε(or δ*), the greater the deviation. The present approach provides a way of estimating the functional dependence of G on the degree of supersaturation, which is essential in practice.