Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908354523168768 |
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| author | Abels, Helmut Garcke, Harald Wittmann, Julia |
| author_facet | Abels, Helmut Garcke, Harald Wittmann, Julia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions Abels, Helmut Garcke, Harald Wittmann, Julia Analysis of PDEs 35Q30, 76D05, 35D35, 35Q35, 76T06 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. |
| title | Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions |
| topic | Analysis of PDEs 35Q30, 76D05, 35D35, 35Q35, 76T06 |
| url | https://arxiv.org/abs/2505.05383 |