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

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

2012-04-21

arxiv.org/abs/1204.4818v1

Physics

Condensed Matter

Materials Science

Scientific paper

We derive a new effective macroscopic Cahn-Hilliard equation whose free energy can be represented by 4-th order polynomials, including the frequently used double-well potential in applications. We consider microscopically perforated/strongly heterogeneous domains. To the best knowledge of the authors, this seems to be the first attempt of upscaling the Cahn-Hilliard equation in such domains. The new homogenized equation should enjoy a broad range of application 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.

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