Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities

By Helmut Abels, Harald Garcke, Günther Grün. 2011

505 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/9fa74340d8020a436b78c14e7a3280d3a0ff4ceb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Xiaofeng Yang
2. Jie Shen
3. Dong Sun
4. Daozhi Han
5. Xiaoming Wang
6. Harald Garcke
7. A. Ratz
8. M. Roger

In Computational Theory and Mathematics

1. Xiaofeng Yang
2. Jie Shen
3. Hao Wu
4. Dong Sun
5. Daozhi Han
6. Xiaoming Wang
7. Harald Garcke
8. M. Roger

In Materials Chemistry

1. Xiaofeng Yang
2. Jie Shen
3. Xiaoming Wang
4. Dong Sun
5. Daozhi Han
6. Hao Wu
7. M. Roger
8. J. Kampmann

Citations in the corpus

• The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Phase field modeling of multiphase flows has been developed by a number of groups along with the development and numerical analysis, see, for instance [2, 315, 25, 29, 140, 225, 189, 236, 313] and the references cited therein.”
• A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes (2015, methodology): “Other examples for this method and more details on formal asymptotic analysis can be found in [2, 4, 9, 19, 21] which is by far not a comprehensive list of references.”
• Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows (2015, methodology): “Various approaches have been proposed to deal with variable density in the case of Navier-Stokes equations [13, 28, 24, 14] and in the case of phase-field models [33, 31, 2, 27].”
• Two‐phase flows in karstic geometry (2014, background): “Alternative derivations of two phase flows (in conduit) via other variational principles or rational mechanics considerations are also possible [34, 35, 36, 37, 40, 49].”
• A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “…fields and turned out to be e ffi cient tools for the study of a wide variety of segregation-like phenomena [8], for instance, diblock copolymer [9], image inpainting [10, 11], tumor growth [12, 13], biology [14], two-phase flows [7, 15–18], moving contact line dynamics [19, 20], and so on.”