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This article considers Couette and Poiseuille flows past superhydrophobic surfaces containing alternating micro-grooves and ribs aligned longitudinally to the flow. The effects of interface curvature on the effective slip length are quantified for different shear-free fractions and groove-rib spatial periods normalized using the channel height. The numerical results obtained demonstrate the importance of considering interface curvature effects in ascertaining the effective slip length. The effective slip length and performance of longitudinal grooves are compared with those corresponding to transverse grooves, for which analytical results are available for small shear-free fractions and normalized groove-rib periodic spacing. For the same shear-free fraction and interface protrusion angle, the effective slip length corresponding to the Poiseuille flow is found to be strongly affected by the normalized groove-rib spacing, in contrast to the Couette flow. For the Poiseuille flow, when the interface deforms by large protrusion angles into the liquid phase, the effective slip length approaches zero or becomes negative for large values of shear-free fraction and normalized groove-rib spacing due to significant flow blockage effects.

Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in microand nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shearfree fraction and the periodic extent of each groove-rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove-rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove-rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.

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