Approximate analytical solution of the integro-differential model of bulk crystallization in a metastable liquid with mass supply (heat dissipation) and crystal withdrawal mechanism

Abstract

This paper deals with an approximate analytical solution of an integro-differential model describing nucleation and growth of particles. The model includes a thermal-mass exchange with the environment and the removal of product crystals from a metastable medium. The method developed for solving model equations (kinetic equation for the particle-size distribution function and balance equations for temperature/impurity concentration) is based on the saddle point technique for calculating the Laplace-type integral. We show that the metastability degree decreases with time at a fixed mass (heat) flux. The crystal-size distribution function is an irregular bell-shaped curve increasing with the intensification of heat and mass exchange. © 2022 John Wiley & Sons, Ltd.