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Phase Field Models for Two-Phase Flow with Surfactants and Biomembranes

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Transport Processes at Fluidic Interfaces

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

Abstract

We give an overview on recent developments of phase field models for two-phase flows with surfactants and lipid bilayer membranes. Starting from the two-phase flow model of a clean fluid-fluid interface we discuss the time discretization and boundary conditions for dynamic and static contact angles. Using the adsorption models of Henry and Langmuir, soluble surfactants are included in the diffuse interface formulation. To consider lipid bilayer membranes the model is extended by membrane bending stiffness and membrane inextensibility. We present phase field models to include these elastic effects, with a particular focus on the inextensibility constraint for which we discuss different phase field variants from the literature and present numerical tests.

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Acknowledgements

The author acknowledges support from the German Science Foundation through grant SPP-1506 (AL 1705/1).

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  1. Institute of Scientific Computing, TU Dresden, 01062, Dresden, Germany

    Sebastian Aland

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  1. Sebastian Aland
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Correspondence to Sebastian Aland .

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  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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Aland, S. (2017). Phase Field Models for Two-Phase Flow with Surfactants and Biomembranes. 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_11

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