Solid liquid phase changes with different densities

TL;DR

This paper introduces a thermodynamically consistent phase transition model for liquid-solid changes with varying densities, analyzing the resulting nonlinear PDE system and proving existence and uniqueness of solutions.

Contribution

It develops a new phase transition model accounting for density differences and non-homogeneous freezing, with rigorous mathematical analysis of the PDE system.

Findings

Existence of a global weak solution was established.

Uniqueness was proved for specific nonlinear functions.

The model captures non-homogeneous freezing phenomena.

Abstract

In this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container $\Omega$ when we freeze the container. Since the density $\varrho_{2}$ of ice with volume fraction $\beta_{2}$, is lower than the density $\varrho_{1}$ of water with volume fraction $\beta_{1}$, experiments - for instance the freezing of a glass bottle filled with water - show that the water pressure increases up to the rupture of the bottle. When the container is not impermeable, freezing may produce a non-homogeneous material, for instance water ice or sorbet. Here we describe a general class of phase transition processes including this example as particular case. Moreover, we study the resulting nonlinear and singular PDE system from the analytical viewpoint recovering existence of a global (in time) weak solution and also uniqueness for some particular choices of the nonlinear functions involved.