Surface viscosity in multiphase flow - modeling, numerical analysis and simulations

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Our goal is to derive a general diffuse-interface model for multi-phase flow, including soluble surfactants, surface reactions, mass transfer and phase change which will be applicable for a wide class of problems in microprocess engineering, mirofluidics and material science. The derivation of the diffuse-interface model is thereby based on a developed general concept to couple PDEs in complicated and evolving bulk domains with PDEs on evolving surfaces. We will analyse the resulting models by means of matched asymptotic analysis to show the convergence to the sharp interface limit. We solve the resulting system of nonlinear equations by adaptive finite elements and energy dissipative time discretization schemes. The algorithms will be implemented in the toolbox AMDiS, which allows for efficient computations on high performance computers. We will validate the models and simulation results on experimental data for chemo-Marangoni convection and air release in hydraulic pumps. An application of interest is chaotic mixing for which we will solve the set of equations in an implicitly defined domain.