Abels, Helmut and Garcke, Harald and Gruen, Guenther (2012) THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 22 (3): 1150013. ISSN 0218-2025,
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A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is frame indifferent. Moreover, it is generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation, we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the latter case a new term resulting from surface diffusion appears in the momentum balance at the interface. Finally, we show that all sharp interface models fulfill natural energy inequalities.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD FLUIDS; PHASE-FIELD MODEL; HELE-SHAW CELL; RECONNECTION; PINCHOFF; Two-phase flow; diffuse interface model; Cahn-Hilliard equation; free boundary value problems |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 May 2020 05:58 |
| Last Modified: | 19 May 2020 05:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/19189 |
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