Diffuse-interface model for rapid phase transformations in nonequilibrium systems

TL;DR

This paper develops a thermodynamic phase-field model for rapid phase transformations in nonequilibrium systems, incorporating finite interface propagation speed and fast variables, with theoretical validation and comparison to existing models.

Contribution

It introduces a hyperbolic and memory-inclusive phase-field model for rapid transformations, extending classical approaches to account for finite propagation speeds and nonequilibrium effects.

Findings

Model ensures positive entropy production.

Provides a consistent thermodynamic framework.

Shows agreement with existing sharp and diffuse interface models.

Abstract

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe the transformation within the diffuse interface, we use the phase-field model which allows us to follow the steep but smooth change of phases within the width of diffuse interface. The governing equations of the phase-field model are derived for the hyperbolic model, model with memory, and for a model of nonlinear evolution of transformation within the diffuse-interface. The consistency of the model is proved by the condition of positive entropy production and by the outcomes of the fluctuation-dissipation theorem. A comparison with the existing sharp-interface and diffuse-interface versions of the model is given.