Eur. Phys. J. Special Topics 229, 365-373 (2020)
https://doi.org/10.1140/epjst/e2019-900081-0

Regular Article

Towards the theory of phase transformations in metastable liquids. Analytical solutions and stability analysis

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

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

Received: 10 May 2019
Published online: 11 February 2020

Abstract

The process of ongoing nucleation and evolution of particles in a metastable liquid caused by external mass sources and crystal withdrawal mechanism is considered. The steady-state and unsteady-state analytical solutions are found analytically. The crystal-size distribution function, as well as the standard Cauchy problem for the liquid supersaturation, are derived. The linear dynamic stability theory of steady-state solutions is developed. The neutral stability surface as a function of system parameters is determined.