Low Reynolds number flows across ordered arrays of micro-cylinders embedded in a rectangular micro/minichannel

Pressure drop of ordered arrays of cylinders embedded inside microchannels is experimentally and analytically studied. Two independent modeling techniques are used to predict the flow resistance for the creeping flow regime. The pressure drop is expressed as a function of the involved geometrical parameters such as micro-cylinder diameter, spacing between adjacent cylinders, channel height, and its width. To verify the developed models, 15 silicon/glass samples are fabricated using the deep reacting ion etching (DRIE) technique. Pressure drop measurements are performed over a wide range of nitrogen flow rates spanning from 0.1 sccm to 35 sccm. Both methods predict the trend of the experimental data. The porous medium approach shows a wider range of applicability with reasonable accuracy while the variable cross-section technique is more accurate for dense arrays of micro-cylinders. Our results suggest that an optimal micro-cylinder diameter exists that minimizes the pressure drop for a specific surface-area-to-volume ratio. This diameter is a function of the channel dimensions and the desired surface-area-to-volume ratio.