Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains Seminar

(joint work with Marc Pradas, Grigorios A. Pavliotis, and Serafim Kalliadasis)
We derive an effective macroscopic Cahn-Hilliard equation in [1] whose homogeneous free energy is represented by 4-th order polynomials, which include the frequently applied double-well potential. This upscaling is done for perforated/strongly heterogeneous domains. To our best knowledge, this seems to be the first attempt of upscaling the Cahn-Hilliard equation in such domains.
The new homogenized equation should have a broad range of applicability due to the well-known versatility of phase-field models. The additionally introduced feature of systematically and reliably accounting for confined geometries by homogenization allows for new modeling and numerical perspectives in both, science and engineering. Our results are applied to wetting dynamics in porous media and to a single channel with strongly heterogeneous walls.