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

Schmuck, Markus; Pradas, Marc; Pavliotis, Grigorios A. and Kalliadasis, Serafim (2012). Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2147) pp. 3705–3724.

URL: http://rspa.royalsocietypublishing.org/content/468...
DOI (Digital Object Identifier) Link: https://doi.org/10.1098/rspa.2012.0020
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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.

Item Type: Journal Item
Copyright Holders: 2012 The Royal Society
ISSN: 1471-2946
Keywords: phase-field models; Cahn–Hilliard equation; multi-scale modelling; homogenization; porous media; wetting
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 41214
Depositing User: Marc Pradas
Date Deposited: 03 Nov 2014 10:08
Last Modified: 07 Dec 2018 10:26
URI: http://oro.open.ac.uk/id/eprint/41214
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