Diffuse interface models for complex flow scenarios: Modeling, analysis, and simulation

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The rheological behaviour of fluids is affected by various parameters. Along with mass density and viscosity, dissolved species impact the flow field. This thesis addresses the case of two-phase flows of dilute polymeric or electrolyte solutions. The derivation of thermodynamically consistent models is discussed as well as the numerical treatment of the resulting set of equations. In particular, fully discrete, convergent finite element schemes for two-phase flow of dilute polymeric solutions and stable splitting schemes for two-phase flow of electrolyte solutions are presented.