Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions

2025/05/08 by Helmut Abels, Harald Garcke, Abels, Helmut +2 · 2 citations
Engineering · Materials Science · Mathematics · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2505.05383

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two quasi-incompressible diffuse interface models with singular free energies are analyzed, differing primarily in their velocity averaging. Firstly, to generalize a model by Abels, Garcke, and Grün, a thermodynamically consistent system of Navier--Stokes/Cahn--Hilliard type with source terms is derived in a framework of continuum fluid dynamics, followed by a proof of existence of weak solutions to the latter. Secondly, the quasi-stationary version of a model by Aki, Dreyer, Giesselmann, and Kraus is investigated analytically, with existence of weak solutions being established for the resulting quasi-stationary Stokes system coupled to a Cahn--Hilliard equation with a source term.

Cited by

• On a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities: Energy equality and Lyapunov stability
• Weak solutions and incompressible limit of a quasi-incompressible Navier--Stokes/Cahn--Hilliard model for viscous two-phase flows

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