Nucleation and evolution of crystals taking into account fluctuations in their growth rates: Test of theory with experiment

Abstract

This article presents a mathematical model of the crystal growth process in a metastable liquid. The model takes into account the presence of fluctuations in crystal growth rates and “diffusion” of the crystal-size distribution function along the axis of particle radii. For the sake of definiteness, the model equations are reformulated in dimensionless form. An exact analytical solution of the model under consideration is found and compared with experimental data. Namely, the distribution function, liquid supercooling (supersaturation), and nucleation rate are analytically found using the integral Laplace transform method. Two frequently met cases of the Meirs and Weber-Volmer-Frenkel-Zel’dovich nucleation kinetics are considered. In the case of Meirs kinetics, the analytical solution is obtained in an explicit form. The distribution function takes a bell-shaped form, and eventually moves towards larger crystal radii with decreasing the maximal function value. It is shown that the metastability degree (supersaturation of the liquid phase) is in good agreement with experimental data on canavalin crystallization.