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@article{Schmuck:2013:12/3259,
author = {Schmuck, M and Pradas, M and Pavliotis, GA and Kalliadasis, S},
doi = {12/3259},
journal = {Nonlinearity},
pages = {3259--3277},
title = {Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media},
url = {http://dx.doi.org/10.1088/0951-7715/26/12/3259},
volume = {26},
year = {2013}
}

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TY  - JOUR
AB  - 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. © 2013 IOP Publishing Ltd & London Mathematical Society.
AU  - Schmuck,M
AU  - Pradas,M
AU  - Pavliotis,GA
AU  - Kalliadasis,S
DO  - 12/3259
EP  - 3277
PY  - 2013///
SN  - 0951-7715
SP  - 3259
TI  - Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media
T2  - Nonlinearity
UR  - http://dx.doi.org/10.1088/0951-7715/26/12/3259
VL  - 26
ER  -

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Professor Grigorios A. Pavliotis

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