Investigations of a Two-Phase Fluid Model

TL;DR

This paper introduces a thermodynamically consistent two-phase fluid model that captures interface dynamics via volumetric stresses, validated through simulations of jet instability and spinodal decomposition.

Contribution

The paper presents a novel interface-capturing two-phase fluid model based on volumetric stresses from a Van der Waals-Cahn-Hilliard energy, with validated applications.

Findings

Successful simulation of high-Reynolds-number jet instability.

Effective modeling of spinodal decomposition.

Thermodynamic consistency of the interface representation.

Abstract

We study an interface-capturing two-phase fluid model in which the interfacial tension is modelled as a volumetric stress. Since these stresses are obtainable from a Van der Waals-Cahn-Hilliard free energy, the model is, to a certain degree, thermodynamically realistic. Thermal fluctuations are not considered presently for reasons of simplicity. The utility of the model lies in its momentum-conservative representation of surface tension and the simplicity of its numerical implementation resulting from the volumetric modelling of the interfacial dynamics. After validation of the model in two spatial dimensions, two prototypical applications---instability of an initially high-Reynolds-number liquid jet in the gaseous phase and spinodal decomposition in a liquid-gas system--- are presented.