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

作者：Schmuck Markus^*; Pradas Marc; Pavliotis Grigorios A; Kalliadasis Serafim

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2012, 468(2147): 3705-3724.

DOI：10.1098/rspa.2012.0020

• phase-field models
• Cahn-Hilliard equation
• multi-scale modelling
• homogenization
• porous media
• wetting

We derive a new, effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by fourth-order polynomials, which form the frequently applied double-well potential. This upscaling is done for 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 have a broad range of applicability owing 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 modelling 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.

• 出版日期2012-11-8