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Transport Processes at Fluidic Interfaces pp 291–303Cite as

Birkhäuser

Micro-Macro-Models for Two-Phase Flow of Dilute Polymeric Solutions: Macroscopic Limit, Analysis, and Numerics

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Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

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.

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Authors and Affiliations

  1. Department Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058, Erlangen, Germany

    Günther Grün & Stefan Metzger

Authors
  1. Günther Grün
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  2. Stefan Metzger
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Correspondence to Günther Grün .

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Editors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt , Darmstadt, Germany

    Dieter Bothe

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Arnold Reusken

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Grün, G., Metzger, S. (2017). Micro-Macro-Models for Two-Phase Flow of Dilute Polymeric Solutions: Macroscopic Limit, Analysis, and Numerics. In: Bothe, D., Reusken, A. (eds) Transport Processes at Fluidic Interfaces. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-56602-3_12

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