Abels, Helmut and Garcke, Harald and Weber, Josef (2019) EXISTENCE OF WEAK SOLUTIONS FOR A DIFFUSE INTERFACE MODEL FOR TWO-PHASE FLOW WITH SURFACTANTS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 18 (1). pp. 195-225. ISSN 1534-0392, 1553-5258
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Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system coupled to non-linear diffusion equations that describe the diffusion of the surfactant in the bulk phases as well as along the diffuse interface. Moreover, the surfactant concentration influences the free energy and therefore the surface tension of the diffuse interface. For this system existence of weak solutions globally in time for general initial data is proved. To this end a two-step approximation is used that consists of a regularization of the time continuous system in the first and a time-discretization in the second step.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | COMPUTATION; Two-phase flow; diffuse interface model; variable surface tension; surfactants; global existence; implicit time discretization; Navier-Stokes equations; Cahn-Hilliard equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Apr 2020 06:47 |
| Last Modified: | 28 Apr 2020 06:47 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27960 |
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