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

ten Eikelder, M. F. P.; van der Zee, K. G.; Akkerman, I.; Schillinger, D.

Abstract

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.

Citation

ten Eikelder, M. F. P., van der Zee, K. G., Akkerman, I., & Schillinger, D. (2023). A unified framework for Navier–Stokes Cahn–Hilliard models with non-matching densities. Mathematical Models and Methods in Applied Sciences, 33(01), 175-221. https://doi.org/10.1142/s0218202523500069

• Journal Article Type: Article
• Acceptance Date: Dec 13, 2022
• Online Publication Date: Feb 16, 2023
• Publication Date: 2023-01
• Deposit Date: Feb 2, 2023
• Publicly Available Date: Feb 2, 2023
• Journal: Mathematical Models and Methods in Applied Sciences
• Print ISSN: 0218-2025
• Electronic ISSN: 1793-6314
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 01
• Pages: 175-221
• DOI: https://doi.org/10.1142/s0218202523500069
• Keywords: Applied Mathematics, Modeling and Simulation, Navier–Stokes Cahn–Hilliard equations, Phase-field models, Incompressible two-phase flow, Mixture theory, Thermodynamic consistency
• Public URL: https://nottingham-repository.worktribe.com/output/16797700
• Publisher URL: https://www.worldscientific.com/doi/10.1142/S0218202523500069