Eur. Phys. J. Special Topics 228, 25–34 (2019)
https://doi.org/10.1140/epjst/e2019-800201-3

Regular Article

Effects of external heat/mass sources and withdrawal rates of crystals from a metastable liquid on the evolution of particulate assemblages

^a e-mail: eugenya1m@gmail.com

Received: 16 November 2018
Received in final form: 4 March 2019
Published online: 30 May 2019

Abstract

A complete analytical solution of an integro-differential model describing the transient nucleation of solid particles and their subsequent growth at the intermediate stage of phase transitions in metastable systems is constructed. A functional Fokker–Plank type equation for the density distribution function is solved by the separation of variables method for the Weber–Volmer–Frenkel–Zeldovich nucleation kinetics. A non-linear integral equation with memory kernel connecting the density distribution function and the system supercooling/supersaturation is analytically solved on the basis of the saddle point method for the Laplace integral. The analytical solution obtained shows that the transient phase transition process attains its steady-state solution at large times. An exact analytical solution for the steady-state problem is found too. It is demonstrated that the crystal-size distribution function increases with increasing the intensity of external sources. In addition, the number of larger (smaller) particles decreases (increases) with increasing the withdrawal rate of crystals from a metastable liquid.