Creeping flow through ordered arrays of micro-cylinders embedded in a rectangular minichannel

The pressure drop in microfluidic minichannels filled with porous media formed by square arrays of microcylinders is investigated. We investigate the problem by combining the Brinkman equation and existing models for permeability of regular arrays of cylinders to calculate the pressure drop of the studied geometries theoretically. In order to verify our theoretical analysis, a soft lithography method is employed to fabricate several Polydimethylsiloxane (PDMS) samples with porosities in the range of 0.35 to 0.95, fiber diameters varying from 50 to 400 μm, and channel depth of approximately 100 μm. Distilled water is pushed through the samples using a syringe pump with several steady flow rates and the resulting pressure drops are measured. Moreover, flow through the fabricated samples is solved numerically and the pressure drops are determined. The theoretical model shows a reasonable agreement with experimental and numerical data for all of the tested samples. Our analysis indicates that the geometrical parameters that control the pressure drop are the porous medium permeability and the channel dimensions. Furthermore, the Darcy number can be used to determine the dominating parameter.