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

by Ganesan, S; Tobiska, L.

Series: 2010-23, Preprints

65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
76D05 ~Navier-Stokes equations

A finite element scheme based on coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for computations of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependant Navier-Stokes equations and an evolution equation for surfactants in the bulk phase using second order isoparametric finite elements in moving meshes together with an evolution equation for surfactants on the interface using second order isoparametric surface finite elements, simultaneously. Since the interface resolved moving meshes are used in this numerical scheme, the surface force, Marangoni force and the jumps in the material parameters are accurately incorporated into the system. Further, the approximation of the surface evolution equation does not require a separate lower dimensional interface mesh, instead the discrete representation of the interface is used. The numerical scheme is validated for test examples with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. An excellent conservation of the mass of the fluid and the total mass of surfactants is obtained with the proposed numerical scheme.

Finite elements, ALE approach, Interfacial fluid flows, Soluble surfactant, Navier-Stokes equations