Abels, Helmut and Garcke, Harald and Wittmann, Julia (2025) Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 28 (1): 7. ISSN 1422-6928, 1422-6952
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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 Gr & uuml;n, 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DENSITY; FLUIDS; Two-phase flow; Navier-Stokes equations; Cahn-Hilliard equation; Diffuse interface model; Weak solutions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 02 Jun 2026 08:34 |
| Last Modified: | 02 Jun 2026 08:34 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65906 |
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