Flow past superhydrophobic surfaces containing longitudinal grooves: effects of interface curvature

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.