Diffuse planar phase boundaries in a two-phase fluid with one very dense phase

TL;DR

This paper investigates diffuse planar phase boundaries in a two-phase fluid model with a very dense phase, demonstrating existence results for small density ratios and connecting to the Navier-Stokes-Korteweg model.

Contribution

It establishes the existence of diffuse phase boundaries in Navier-Stokes-Allen-Cahn models for small density ratios, extending known results to new parameter regimes.

Findings

Existence of diffuse planar phase boundaries for small density ratios

Connection to Navier-Stokes-Korteweg model at zero density ratio

Validity of the model under natural mixing energy assumptions

Abstract

This note studies Navier-Stokes-Allen-Cahn models for compressible fluids that are mixtures of two incompressible phases whose density ratio eps=rho_1/rho_2 is very small. Under a natural assumption on the mixing energy, it shows the existence of diffuse planar phase boundaries for all 0=eps<eps_0. For eps=0, one recovers the Navier-Stokes-Korteweg model and its well-known diffuse phase boundaries.