In-Plane Hydraulic Resistance Through Paper-Thin Porous Media

This work investigates the special case of in-plane fluid flow of a Newtonian incompressible fluid at low Reynolds numbers across a paper-thin porous medium in a confined conduit. Fluid transport in sheets with these characteristics are used in emerging devices such as microscale paper-based analytical devices (μPADs) and “e-paper” displays. Darcy’s law is applied and tested to determine if experimentally measured pressures at two flow rates of 5 μL/min and 10 μL/min agree with predicted values. A test device was designed using kinematic design principles to ensure a deterministic 318 μm gap that directs prescribed flow, unidirectionally across porous filter paper. The paper used was Grade 50 Whatman filter paper with an average pore size of 2.7 μm. Pressure was measured along the direction of flow over a 125 mm distance by six pressure ports placed at uniform increments of 25 mm to determine a profile of pressure along the flow path. Measurements were recorded at discrete time intervals over a period up to 48 hours with at least four replicates. Experimental measurements of the pressure profile show a linear relationship as predicted by Darcy’s law, allowing material permeability to be calculated. Among replicates measured under the same set of controllable conditions, experimental data also show a nonlinear relationship. The nonlinearity suggests evidence of transition into an inertia region, providing insight into the factors and behavior of the Darcy-Forchheimer transition for this special case of porous media flow.