Viscous coupling in a model porous medium geometry: Effect of fluid contact area

We study the effect of fluid contact area on viscous coupling in the parallel flow of immiscible fluids in a porous media geometry. We consider flow on opposite sides of a planar interface, consisting of alternating solid and open (slit) segments. We use the analytical solution of Tio and Sadhal [15] to derive explicit expressions for viscous coupling in terms of the fractional area of contact between the fluids and the viscosity ratio,M. ForM=1, the coefficient matrix obtained is symmetric showing that Onsager's relations are satisfied. In this case, the resulting viscous coupling is typically very small, in agreement with recent experimental results. Lattice gas simulations forM=1 using theBGK model support the theoretical results and show that viscous coupling further diminishes as the wall thickness increases. Assuming the same configuration, analytical results are next derived forM1. The results confirm an existing reciprocity relation between the off-diagonal terms. Viscous coupling remains small.