Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

  • Authors:

  • Sashikumaar Ganesan;Lutz Tobiska

  • Affiliations:

  • Numerical Mathematics and Scientific Computing, Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore 560012, India;Institute of Analysis and Numerical Mathematics, Otto-von-Guericke University, PF 4120, D-39016 Magdeburg, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant.