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arXiv · 1210.6391

Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media

Markus Schmuck·Marc Pradas·Gregorios A. Pavliotis·Serafim Kalliadasis
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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., Proc. R. Soc. A 468:3705-3724, 2012.], 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 analytical and 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.

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BibTeXRIS

Markus Schmuck, Marc Pradas, Gregorios A. Pavliotis, Serafim Kalliadasis. 2013-10-19. Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media. https://doi.org/10.1088/0951-7715%2F26%2F12%2F3259

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