Hydraulic Sheet Resistance In Paper­-Based Porous Media

HYDRAULIC SHEET RESISTANCE IN PAPER­BASED POROUS MEDIA by Stefan M. Doser This work investigates the special case of in­plane fluid flow of a Newtonian incompressible fluid across a thin paper­based porous medium at very low Reynolds numbers (Re ≪ 1). Fluid transport with these characteristics is used in emerging devices such as microscale paper­based analytical devices ( μ PADs). The mathematical similarity between Darcy’s law and Ohm’s law is considered, and hydraulic equivalents of current, voltage and resistance are determined to propose hydraulic sheet resistance. Darcy flow is predicted under these conditions and tested by experiment at two flow rates of 5 μL/min and 10 μL/min. A device was designed and fabricated to ensure a deterministic 310 μm gap that directs prescribed flow, unidirectionally across Grade 50 Whatman filter paper. Pressure was measured along the direction of flow over a 125 mm distance at six pressure ports placed at uniform increments of 25 mm. Measurements were recorded over a time period up to 48 hours at discrete intervals with at least four replicates. Measurements of the pressure profile showed a linear relationship as predicted by Darcy’s law, which allow hydraulic permeability, hydraulic bulk resistivity and hydraulic sheet resistivity to be calculated as 324 mm 2 , 2995 s ­1 and 9433 (mm⋅s) ­1 respectively. Among replicates measured under the same set of controllable experimental conditions, the data also show a nonlinear relationship, suggesting transition into a nonlinear flow regime dependent upon inlet pressure and media tortuosity.