  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 P\'eclet 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.
