Liquid flow through microchannels with grooved walls under wetting and superhydrophobic conditions

Recent developments in superhydrophobic surfaces have enabled significant reduction in the frictional drag for liquid flow through microchannels. There is an apparent risk when using such surfaces, however, that under some conditions the liquid meniscus may destabilize and, consequently, the liquid will wet the entire patterned surface. This paper presents analytical and experimental results that compare the laminar flow dynamics through microchannels with superhydrophobic walls featuring ribs and cavities oriented both parallel and transverse to the direction of flow under both wetting and non-wetting conditions. The results show the reduction in the total frictional resistance is much greater in channels when the liquid phase does not enter the cavity regions. Further, it is demonstrated that the wetting and non-wetting cavity results represent limiting cases between which the experimental data lie. Generalized expressions enabling prediction of the classical friction factor-Reynolds number product as a function of the relevant governing dimensionless parameters are also presented for both the superhydrophobic and wetting states. Experimental results are presented for a range of parameters in the laminar flow regime.