Grün G, Metzger S (2017)
Publication Language: English
Publication Type: Book chapter / Article in edited volumes
Publication year: 2017
Publisher: Springer
Edited Volumes: Advances in Mathematical Fluid Mechanics
Series: Transport processes at fluidic interfaces
Pages Range: 291-303
We derive a diffuse-interface model for two-phase flow of incompressible fluids with dissolved noninteracting polymers. Describing the polymers as bead chains governed by general elastic spring potentials, including in particular Hookean and finitely extensible, nonlinear elastic (FENE) potentials, it couples a Fokker-Planck type equation describing distribution and orientation of the polymer chains with Cahn–Hilliard and Navier–Stokes type equations describing the balance of mass and momentum. Allowing for different solubility properties which are modelled by Henry type energy functionals, the presented model covers the case of one Newtonian fluid and one non-Newtonian fluid as well as the case of two non-Newtonian fluids. In the case of Hookean spring potentials, we derive a macroscopic diffuse-interface model for two-phase flow of Oldroyd-B-type liquids.
In the case of dumbbell models, we show existence of solutions and present numerical simulations in two space dimensions on oscillating polymeric droplets.
APA:
Grün, G., & Metzger, S. (2017). Micro-macro-models for two-phase flow of dilute polymeric solutions: macroscopic limit, analysis, numerics. In Advances in Mathematical Fluid Mechanics. (pp. 291-303). Springer.
MLA:
Grün, Günther, and Stefan Metzger. "Micro-macro-models for two-phase flow of dilute polymeric solutions: macroscopic limit, analysis, numerics." Advances in Mathematical Fluid Mechanics. Springer, 2017. 291-303.
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