scholarly journals Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants

2019 ◽  
Vol 18 (1) ◽  
pp. 195-225 ◽  
Author(s):  
Helmut Abels ◽  
◽  
Harald Garcke ◽  
Josef Weber
Keyword(s):  
Weak Solutions ◽  
Two Phase Flow ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Two Phase ◽  
Existence Of Weak Solutions

On micro–macro-models for two-phase flow with dilute polymeric solutions — modeling and analysis

2016 ◽  
Vol 26 (05) ◽  
pp. 823-866 ◽  
Author(s):  
G. Grün ◽  
S. Metzger
Keyword(s):  
Two Phase Flow ◽  
Type Equation ◽  
Momentum Equation ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Two Phase ◽  
Energy Functionals ◽  
Spring Force

By methods from nonequilibrium thermodynamics, we derive a diffuse-interface model for two-phase flow of incompressible fluids with dissolved noninteracting polymers. The polymers are modeled by dumbbells subjected to general elastic spring-force potentials including in particular Hookean and finitely extensible, nonlinear elastic (FENE) potentials. Their density and orientation are described by a Fokker–Planck-type equation which is coupled to a Cahn–Hilliard and a momentum equation for phase-field and gross velocity/pressure. Henry-type energy functionals are used to describe different solubility properties of the polymers in the different phases or at the liquid–liquid interface. Taking advantage of the underlying energetic/entropic structure of the system, we prove existence of a weak solution globally in time for the case of FENE-potentials. As a by-product in the case of Hookean spring potentials, we derive a macroscopic diffuse-interface model for two-phase flow of Oldroyd-B-type liquids.

scholarly journals Optimal control of time discrete two-phase flow governed by a diffuse interface model

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 785-786 ◽  
Author(s):  
Harald Garcke ◽  
Michael Hinze ◽  
Christian Kahle
Keyword(s):  
Optimal Control ◽  
Two Phase Flow ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Two Phase

Non-isothermal two-phase flow with a diffuse-interface model

2011 ◽  
Vol 37 (2) ◽  
pp. 149-165 ◽  
Author(s):  
A. Pecenko ◽  
L.G.M. van Deurzen ◽  
J.G.M. Kuerten ◽  
C.W.M. van der Geld
Keyword(s):  
Two Phase Flow ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Two Phase
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