Probing liquid distribution in partially saturated porous materials with hydraulic admittance

The distribution of two immiscible fluids in a complex porous material during displacement is often central to understanding its function. Characterization of this distribution is traditionally determined via optically transparent flow cells. However, for opaque or thin porous materials of the order of hundreds of microns, optical visualization proves to be difficult and requires sophisticated imaging techniques that are expensive and difficult to come by. We describe here a bench-top tool that dynamically probes the hydraulic pathways leading to each free-interface within a single capillary and a bundle of seven capillaries at various saturations (i.e., hydraulic path lengths). A small volumetric displacement was applied to each interface such that the interfaces remained pinned at the capillary walls and the resultant oscillatory pressure drop was measured to determine the hydraulic admittance at each applied oscillation frequency. When the magnitude of the hydraulic admittance was plotted vs. applied oscillation frequency, a resonance peak was found for each degenerately filled capillary. The corresponding peaks were represented by a half-loop (100% filled) and full loops (partially filled) in a Nyquist plot. We compared the theoretical and measured admittance curves and found good agreement for both capillary systems at high filled states. The theoretical predictions became worse when the hydraulic path length was comparable to the capillary radius. The analysis for the hydraulic admittance of a bundle of capillaries is developed here and experimentally validated for the first time.