Abstract
Using thermodynamic and variational principles we study a basic phase field model for the mixture of two incompressible fluids in strongly perforated domains. We rigorously derive an effective macroscopic phase field equation under the assumption of periodic flow and a sufficiently large Péclet number 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). As for the classical convection-diffusion problem, we obtain systematically diffusion-dispersion relations (including Taylor-Aris-dispersion). 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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Acknowledgements
We acknowledge financial support from EPSRC Grant No. EP/H034587, EU-FP7 ITN Multiflow and ERC Advanced Grant No. 247031.
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Schmuck, M., Pavliotis, G.A., Kalliadasis, S. (2013). Effective Macroscopic Stokes-Cahn-Hilliard Equations for Periodic Immiscible Flows in Porous Media. In: Gilbert, T., Kirkilionis, M., Nicolis, G. (eds) Proceedings of the European Conference on Complex Systems 2012. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-00395-5_121
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DOI: https://doi.org/10.1007/978-3-319-00395-5_121
Publisher Name: Springer, Cham
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