ALE-FEM For Two-Phase Flows With Insoluble Surfactants

Authors

  • Andreas Hahn,

    Corresponding author
    1. Institute of Analysis and Computational Mathematics, Faculty of Mathematics, Otto-von-Guericke-University Magdeburg, PF 4120, 39106 Magdeburg
    • Institute of Analysis and Computational Mathematics, Faculty of Mathematics, Otto-von-Guericke-University Magdeburg, PF 4120, 39106 Magdeburg
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  • Lutz Tobiska

    1. Institute of Analysis and Computational Mathematics, Faculty of Mathematics, Otto-von-Guericke-University Magdeburg, PF 4120, 39106 Magdeburg
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Abstract

We present a finite element method for the flow of two immiscible incompressible fluids in two and three dimensions. Thereby the presence of surface active agents (surfactants) on the interface is allowed, which alter the surface tension. The model consists of the incompressible Navier-Stokes equations for velocity and pressure and a convection-diffusion equation on the interface for the distribution of the surfactant. A moving grid technique is applied to track the interface, on that account a Arbitrary-Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equation is used. The surface tension force is incorporated directly by making use of the Laplace-Beltrami operator technique [1]. Furthermore, we use a finite element method for the convection-diffusion equation on the moving hypersurface. In order to get a high accurate method the interface, velocity, pressure, and the surfactant concentration are approximated by isoparametric finite elements. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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