Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids

TL;DR

This paper develops thermodynamically consistent diffuse-interface models for incompressible multicomponent fluids, aligning with continuum mixture theory and clarifying simplifications in existing models like Navier-Stokes Cahn-Hilliard.

Contribution

It introduces a new class of mixture models compatible with continuum theory, allowing direct comparison and highlighting modeling simplifications.

Findings

Models are compatible with continuum mixture theory

Comparison with Navier-Stokes Cahn-Hilliard reveals key simplifications

Framework facilitates analysis of multicomponent fluid dynamics

Abstract

In this paper we derive a class of thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. The class of mixture models is fully compatible with the continuum theory of mixtures. The resulting mixture models may be formulated either in constituent or in mixture quantities. This permits a direct comparison with the Navier-Stokes Cahn-Hilliard model with non-matching densities, which reveals the key modeling simplifications of the latter.