Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids

2017 ◽  
pp. 231-253 ◽  
Author(s):  
Helmut Abels ◽  
YuNing Liu ◽  
Andreas Schöttl
Keyword(s):  
Incompressible Fluids ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Two Phase Flows ◽  
Two Phase ◽  
Interface Models

scholarly journals On sharp interface limits for diffuse interface models for two-phase flows

2014 ◽  
Vol 16 (3) ◽  
pp. 395-418 ◽  
Author(s):  
Helmut Abels ◽  
Daniel Lengeler
Keyword(s):  
Sharp Interface ◽  
Diffuse Interface ◽  
Two Phase Flows ◽  
Two Phase ◽  
Interface Models

scholarly journals THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

2012 ◽  
Vol 22 (03) ◽  
pp. 1150013 ◽  
Author(s):  
HELMUT ABELS ◽  
HARALD GARCKE ◽  
GÜNTHER GRÜN
Keyword(s):  
Surface Diffusion ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Momentum Balance ◽  
Two Phase ◽  
Interface Models ◽  
Natural Energy ◽  
Soluble Species ◽  
Sharp Interface Models ◽  
Dissipation Inequalities

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.

scholarly journals On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids

2015 ◽  
Vol 35 (6) ◽  
pp. 2497-2522 ◽  
Author(s):  
Michela Eleuteri ◽  
◽  
Elisabetta Rocca ◽  
Giulio Schimperna ◽  
◽  
...  
Keyword(s):  
Incompressible Fluids ◽  
Diffuse Interface ◽  
Interface Model ◽  
Two Phase Flows ◽  
Diffuse Interface Model ◽  
Two Phase
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