A unified framework for N-phase Navier-Stokes Cahn-Hilliard Allen-Cahn mixture models with non-matching densities

TL;DR

This paper introduces a unified, energy-stable framework for N-phase incompressible flow models with non-matching densities, simplifying the understanding and computation of complex multi-phase systems.

Contribution

It presents a novel, continuum mixture theory-based framework that unifies various N-phase models with a single momentum equation and energy-dissipative structure.

Findings

Framework naturally derived from continuum mixture theory

Energy-dissipative and invariant to variable choice

Facilitates connection and comparison of existing models

Abstract

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching modeling framework is absent. This paper provides a unified framework for N-phase incompressible Navier-Stokes Cahn-Hilliard Allen-Cahn mixture models with a single momentum equation. The framework naturally emerges from continuum mixture theory, exhibits an energy-dissipative structure, and is invariant to the choice of fundamental variables. This opens the door to exploring connections between existing N-phase models and facilitates the computation of N-phase flow models rooted in continuum mixture theory.