Relating Capillary Pressure to Interfacial Areas

Experiments were performed on transparent two-dimensional micro-fluidic porous systems to investigate the relationships among capillary pressure and the interfacial areas per volume among two fluid phases and one solid phase. Capillary pressures were calculated from the observed interfacial curvature of the wetting – non-wetting interface, and these correlated closely to externally measured values of applied pressure. For each applied capillary pressure, the system established mechanical equilibrium characterized by stationary interfaces, uniform curvatures across the model, and random surface normals. To study the relationships among capillary pressure and the interfacial areas, we compare the curvature-based capillary pressure to the differential change in interfacial areas per volume as a function of wetting-phase saturation. The differential pressure contributions calculated from the experimental measurements are found to be nearly independent of the measured capillary pressure. These results suggest that other contributions to the capillary pressure must be significant when imbibition and drainage processes result in saturation gradients.