A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities

A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities

ten Eikelder, M.F.P. (Technische Universität Darmstadt; Leibniz Universität)
Van Der Zee, K. G. (University of Nottingham)
Akkerman, I. (TU Delft Ship Hydromechanics and Structures)
Schillinger, D. (Technische Universität Darmstadt)

2023

Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard (NSCH) models with non-matching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. The overarching objective of this work is to bring all of these models together by laying down a unified framework of NSCH models with non-zero mass fluxes. Our development is based on three unifying principles: (1) there is only one system of balance laws based on continuum mixture theory that describes the physical model, (2) there is only one natural energy-dissipation law that leads to quasi-incompressible NSCH models, (3) variations between the models only appear in the constitutive choices. The framework presented in this work now completes the fundamental exploration of alternate non-matching density NSCH models that utilize a single momentum equation for the mixture velocity, but leaves open room for further sophistication in the energy functional and constitutive dependence.

incompressible two-phase flow
mixture theory
Navier-Stokes Cahn-Hilliard equations
phase-field models
thermodynamic consistency

http://resolver.tudelft.nl/uuid:add002ef-0e24-4a60-a07a-d0063efc2711

https://doi.org/10.1142/S0218202523500069

0218-2025

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 33 (1), 175-221

Institutional Repository

journal article

© 2023 M.F.P. ten Eikelder, K. G. Van Der Zee, I. Akkerman, D. Schillinger