Grün G, Metzger S (2016)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2016
Publisher: World Scientific Publishing
Book Volume: 26
Pages Range: 823-866
Journal Issue: 5
DOI: 10.1142/S0218202516500196
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 springforce
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.
APA:
Grün, G., & Metzger, S. (2016). On micro-macro-models for two-phase flow with dilute polymeric solutions -- modeling and analysis. Mathematical Models & Methods in Applied Sciences, 26(5), 823-866. https://dx.doi.org/10.1142/S0218202516500196
MLA:
Grün, Günther, and Stefan Metzger. "On micro-macro-models for two-phase flow with dilute polymeric solutions -- modeling and analysis." Mathematical Models & Methods in Applied Sciences 26.5 (2016): 823-866.
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