Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function

Abstract

In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integrodifferential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddlepoint methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data. This article is part of the theme issue 'Heterogeneous materials: Metastable and nonergodic internal structures'. ©2019 The Author(s)Published by the Royal Society.