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

M. F.P. Ten Eikelder*, K. G. Van Der Zee, I. Akkerman, D. Schillinger

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
26 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)175-221
JournalMathematical Models and Methods in Applied Sciences
Issue number1
Publication statusPublished - 2023


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


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