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 p arallel Bow of immiscible fluids in a porous media geometry. We consid er flow on opposite sides of a planar interface, consisting of alterna ting solid and open (slit) segments. We use the analytical solution of Tio and Sadhal [15] to derive explicit expressions for viscous coupli ng in terms of the fractional area of contact between the fluids and t he viscosity ratio, M. For M = 1, the coefficient matrix obtained is s ymmetric 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 for M = 1 us ing the BGK model support the theoretical results and show that viscou s coupling further diminishes as the wall thickness increases. Assumin g the same configuration, analytical results are next derived for M no t equal 1. The results confirm an existing reciprocity relation betwee n the off-diagonal terms. Viscous coupling remains small.