Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media
File(s)
Accepted version
Author(s)
Schmuck, Markus
Pradas, Marc
Pavliotis, Greg A
Kalliadasis, Serafim
Type
Journal Article
Abstract
Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg–Landau/Cahn–Hilliard-type equations (Schmuck et al 2012 Proc. R. Soc. A 468 3705–24), we rigorously derive an effective macroscopic phase field formulation under the assumption of periodic flow and a sufficiently large Péclet number. As for classical convection–diffusion problems, we obtain systematically diffusion–dispersion relations (including Taylor–Aris-dispersion). Our results also provide a convenient computational framework to macroscopically track interfaces in porous media. In view of the well-known versatility of phase field models, our study proposes a promising model for many engineering and scientific applications such as multiphase flows in porous media, microfluidics, and fuel cells.
Date Issued
2013-12-01
Date Acceptance
2013-10-11
Citation
Nonlinearity, 2013, 26 (12), pp.3259-3277
ISSN
0951-7715
Publisher
IOP Publishing
Start Page
3259
End Page
3277
Journal / Book Title
Nonlinearity
Volume
26
Issue
12
Copyright Statement
Copyright © 2013 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0951-7715/26/12/3259
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
PHASE-FIELD MODEL
INTERFACIAL DYNAMICS
MULTIPHASE FLOW
DISPERSION
FLUIDS
HOMOGENIZATION
APPROXIMATION
CONVECTION
DIFFUSION
TRANSPORT
Publication Status
Published
Date Publish Online
2013-11-20