SC Seminar: Stephan Schmidt, Melanie Gräßer

PD Dr. Stephan Schmidt, Department of Mathematics, HU Berlin,
Melanie Gräßer, Chair for Particle Technology, University of Paderborn

Computation of Capillary Bridges via Shape Optimization Techniques


The interaction of very limited amounts of fluids with solid bodies differs considerably from the fully immersed case. Instead of dealing with an uninterrupted continuum of fluid, one faces a problem, where the properties are determined by the behavior of droplets of fluids, in particular so called capillary brides, i.e., droplets of fluids that form between solid bodies and mutually connect them. The resulting capillary forces govern the macroscopic behavior of e.g. moist granulates. Sandcastles provide an intuitive access to these phenomena: It is neither possible to build a sandcastle under water, nor when using completely dry sand.

The presentation is split into two parts. The first half will present the challenges when using classical CFD simulation tools as most simulation approaches for free surface flows do not capture the various interfaces between liquids, air and solids to a satisfactory degree. The second half of the presentation focuses on tackling the problem from a purely geometric perspective. Mathematically, the formation of a capillary bridge can be considered a generalized plateau-problem, i.e. constructing a surface of zero mean curvature, which, in this case, also follows a variety of thickness, interface and contact angle constraints. We present a numerical scheme based on shape calculus and finite elements on surfaces to address the problem numerically for arbitrarily shaped liquid-solid contact surfaces. Thickness and contact constraints are dealt with in a hybrid level-set and resolved mesh approach.

Extension to quadratically convergent shape-Newton methods to this problem are straight forward but subject to future research.

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