Eur. Phys. J. Special Topics 229, 2937–2949 (2020)
https://doi.org/10.1140/epjst/e2020-000037-9

Regular Article

Kinetics of the intermediate stage of phase transition with elliptical crystals

Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russia

^a e-mail: dmitri.alexandrov@urfu.ru

Received: 12 March 2020
Accepted: 9 September 2020
Published online: 19 November 2020

Abstract

This paper is concerned with the evolution of a particulate assemblage of ellipsoidal particles in a metastable liquid with allowance for arbitrary nucleation kinetics. First, the growth of a single ellipsoidal particle is considered and its growth rate is found in the prolate ellipsoid of revolution coordinate system. Taking this into account we formulate the growth model for a polydisperse ensemble of particles in a supercooled or supersaturated liquid. This model is solved analytically using the saddle-point technique. The fundamental contributions to the particle-volume distribution function and the liquid metastability are obtained. The Meirs and Weber–Volmer–Frenkel–Zel’dovich nucleation kinetics are considered as special cases. The theory under consideration transforms into the growth of spherical aggregates in a particular limiting case, which is also described analytically.