Phase separation in quasi incompressible fluids: Cahn-Hilliard model in the Cattaneo-Maxwell framework

TL;DR

This paper introduces a thermodynamically consistent mathematical model for phase separation in quasi-incompressible fluids, incorporating heat flux governed by the Cattaneo-Maxwell equation, and coupling concentration, velocity, temperature, and heat flux dynamics.

Contribution

It develops a novel coupled model integrating Cahn-Hilliard, Navier-Stokes, and Cattaneo-Maxwell equations for heat flux in phase separation.

Findings

Model is compatible with thermodynamics.

Maximum principle holds for the system.

Couples heat flux dynamics with phase separation.

Abstract

In this paper we propose a mathematical model of phase separation for a quasi-incompressible binary mixture where the spinodal decomposition is induced by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase separation is considered in the framework of phase field modeling so that the transition is described by an additional field, the concentration c. The evolution of concentration is described by the Cahn-Hilliard equation and in our model is coupled with the Navier-Stokes equation. Since thermal effect are included, the whole set of evolution equations is set up for the velocity, the concentration, the temperature and the heat flux. The model is compatible with thermodynamics and a maximum theorem holds.