A diffuse interface model of a two-phase flow with thermal fluctuations

TL;DR

This paper develops a mathematical model for two-phase flow incorporating thermal fluctuations, combining Navier-Stokes and Cahn-Hilliard equations with stochastic noise, and proves the existence of solutions respecting energy conservation.

Contribution

It introduces a stochastic version of the classical two-phase flow model, accounting for thermal fluctuations and establishing the existence of dissipative martingale solutions.

Findings

Existence of dissipative martingale solutions proven.

Model accounts for thermal fluctuations via multiplicative white noise.

Energy balance is maintained in the solutions.

Abstract

We consider a model of a two phase flow proposed by Anderson, McFadden and Wheeler taking into account possible thermal fluctuations. The mathematical model consists of the compressible Navier-Stokes system coupled with the Cahn-Hilliard equation, where the latter is driven by a multiplicative temporal white noise accounting for thermal fluctuations. We show that existence of dissipative martingale solutions satisfying the associated total energy balance.