A diffuse-interface method for two-phase flows with soluble surfactants

  • Authors:

  • Knut Erik Teigen;Peng Song;John Lowengrub;Axel Voigt

  • Affiliations:

  • Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;Department of Mathematics, University of California, Irvine, Irvine CA-92697, USA;Department of Mathematics, University of California, Irvine, Irvine CA-92697, USA;Department of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier-Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A nonlinear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a nonlinear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed.