Diffuse planar phase boundaries in a two-phase fluid with one incompressible phase

TL;DR

This paper investigates a Navier-Stokes-Allen-Cahn model for a two-phase fluid system, showing how temperature variations induce the formation of diffuse planar phase boundaries, modeling water-like behavior.

Contribution

It introduces a simplified Navier-Stokes-Allen-Cahn model for water with one incompressible and one compressible phase, analyzing phase boundary formation.

Findings

Planar diffuse phase boundaries form below a critical temperature.

Transition from no phase boundaries to diffuse boundaries occurs at a specific temperature.

Model captures key features of water's phase transition behavior.

Abstract

This note studies a family of Navier-Stokes-Allen-Cahn systems parameterized by temperature. Derived from an internal energy that corresponds to one incompressible and one compressible phase, this family is considered as a simple model for water. Decreasing temperature across a critical value, a transition takes places from a situation without towards one with planar diffuse phase boundaries.