Eur. Phys. J. Special Topics 229, 2951–2959 (2020)
https://doi.org/10.1140/epjst/e2020-000048-8

Regular Article

On the theory of directional crystallization with a two-phase region with vigorous convection

¹ Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin Avenue 51, Ekaterinburg 620000, Russia
² Sirius University of Science and Technology, 1 Olympic Avenue, Sochi 354340, Russia

^a e-mail: irina.alexanderova@urfu.ru

Received: 28 March 2020
Accepted: 14 September 2020
Published online: 19 November 2020

Abstract

A time-dependent process of directional crystallization with a two-phase (mushy) region with allowance for vigorous convection in the liquid phase is analytically described. An exact solution of non-linear mushy layer equations is found in a parametric form. The temperature and solute concentration distributions, as well as the solid phase fraction profile, are determined in the two-phase and liquid regions. The moving boundary of phase transition, which is placed between the two-phase zone and liquid is defined as a function of time. The present analytical solutions are in good agreement with laboratory experiments on ice grown from aqueous solutions of isopropanol.