# M.Sc. Mathis Fricke

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Work
Alarich-Weiss-Str. 10

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Darmstadt

Office: L2|06 404

## Mathematical modeling and numerical analysis of transfer processes at dynamical contact lines in fluid mechanics

### Research Motivation

Many applications in the engineering sciences require a profound understanding of the physical processes in multiphase flows, i.e. flows with multiple components. A contact line arises when three thermodynamic phases come together to form a complex system. A typical example is a liquid droplet sitting (or moving) on wall, surrounded by the ambient air. The usual approach to describe such a system is continuum physics, where the microscopic structure of matter is not explicitly resolved. But the physical processes at the contact line take place at a very small scale. We therefore need to extend the standard continuum physics model to get to an accurate description of the system. In particular we want to understand the impact of the local transport of momentum, heat and substances. A guiding principle in the mathematical modeling is the second law of thermodynamics, which states that the entropy of an isolated system never decreases. This deep physical principle help us to come to a closed and reliable model.

Besides the mathematical modeling we also develop numerical tools and algorithms to solve the resulting partial differential equations, which typically are a variant of the famous Navier-Stokes-Equations. These nonlinear PDE models require a careful choice of the numerical methods and a lot of computational resources.

Together with experimentalists in the Collaborative Research Center 1194 and at the Profile Area Thermo-Fluids & Interfaces, we are able to validate our methods in realistic test cases. As a long-term objective we want to provide tools for engineers and scientists, which they can use for the engineering process.