Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains
File(s)
Accepted version
Author(s)
Schmuck, Markus
Pradas, Marc
Pavliotis, Grigorios A
Kalliadasis, Serafim
Type
Journal Article
Abstract
<jats:p>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.</jats:p>
Date Issued
2012-11-08
Citation
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2012, 468 (2147), pp.3705-3724
ISSN
1364-5021
Publisher
ROYAL SOC
Start Page
3705
End Page
3724
Journal / Book Title
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume
468
Issue
2147
Copyright Statement
© 2012 The Royal Society
License URL
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
phase-field models
Cahn-Hilliard equation
multi-scale modelling
homogenization
porous media
wetting
MULTIPHASE FLOW
DIFFUSION
HOMOGENIZATION
APPROXIMATION
SURFACES
Publication Status
Published
Date Publish Online
2012-06-27