Dynamics of Two-Phase Fluid Interfaces in Random Porous Media

Explicit account is given of the nonlocal dynamics (in a quasistatic approximation) involved in two-phase fluid dynamics quantifying flow through porous media. The results are used to derive the dynamical equation of motion of a Darcy-scale interfacial fluid front. We consider the cases of invasion and imbibition separately, and point out the features responsible for the different depinning exponents observed in the two cases. A Flory-type scaling analysis is also performed on this model, yielding a roughness exponent α0ex0ex=0ex0ex3/4 in a range of intermediate length scales---in good agreement with experimental observations. Possible reasons are outlined for the different universality classes of exponents observed during imbibition experiments.