Microchannel flows with superhydrophobic surfaces: Effects of Reynolds number and pattern width to channel height ratio

Abstract

Superhydrophobic surfaces are widely adopted for reducing the flow resistance in microfluidic channels. The structures on the superhydrophobic surfaces may consist of longitudinal grooves, transverse grooves, posts, holes, etc. In this paper their effective slip performances are systematically studied and compared in detail through numerical simulations. The numerical results show that channel wall confinement effects have a positive influence on the effective slip length for square posts and longitudinal grooves, and a negative influence for square holes and transverse grooves. Square posts, holes, and transverse grooves all exhibit deteriorating effective slip performances at higher Reynolds numbers, while the effective slip performance of longitudinal grooves remains independent of the Reynolds number. For small pattern width to channel height ratios and at low Reynolds numbers, for low shear-free fractions, the effective slip length of square posts is equivalent of that of transverse grooves, and both geometries yield effective slip lengths which are in turn lower than those of square holes and longitudinal grooves. With increasing shear-free fractions, the effective slip length of square posts surpasses that of square holes and longitudinal grooves, but it becomes lower than that of longitudinal grooves at high Reynolds numbers or large pattern width to channel height ratios. Scaling laws for the effective slip length of superhydrophobic surfaces with square posts, square holes, and transverse grooves have previously been reported for shear-driven flows. This study extends the validity of these scaling laws to pressure-driven channel flows, even at high Reynolds numbers. The findings in this study serve as a useful guide for applications involving the reduction in flow resistance in microchannels containing superhydrophobic surfaces.