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

Markus Schmuck, Marc Pradas, Grigorios A Pavliotis, Serafim Kalliadasis

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)3705-3724
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume468
Issue number2147
Early online date27 Jun 2012
DOIs
Publication statusPublished - 8 Nov 2012

Keywords

  • Phase-field models
  • Homogenization
  • Multi-scale model
  • Porous media
  • Wetting
  • Cahn-Hilliard equation

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