Abels, Helmut and Garcke, Harald and Grün, Günther
Thermodynamically consistent diffuse interface models for incompressible two-phase flows with different densities.
Preprintreihe der Fakultät Mathematik 20/2010,
A new diffuse interface model for a two-phase
ow 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 also 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 two latter cases the classical Gibbs-Thomson equation has to be modified to include kinetic terms. Finally, we show that all sharp interface models fulfill natural energy inequalities.
|Item Type:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Helmut Abels|
|Keywords:||Two-phase flow, diffuse interface model, Cahn-Hilliard equation, free boundary value problems|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||13 Apr 2011 03:51|
|Last Modified:||06 Sep 2011 07:17|