Linear stability of pressure-driven flow over longitudinal superhydrophobic grooves

Abstract

The modal analysis of pressure-driven flows in channels patterned with superhydrophobic surfaces containing periodic grooves and ribs aligned longitudinally to the flow direction has been performed. The effects of shear–free fraction δ and groove-rib spatial period normalized by full-channel height L on the linear flow stability of such flows have been explored. By performing a BiGlobal linear stability analysis via the pseudo-spectral method, such surfaces have been found to potentially exert a stabilizing or destabilizing effect on the base flow, depending predominantly on the normalized groove-rib spacing. For small values of L (i.e., L = 0.01 and 0.02), a stabilizing effect is predicted for flows over longitudinal superhydrophobic grooves, in agreement with the results obtained using a local stability analysis which employs a homogeneous slip condition along the walls. For a moderate value of normalized groove-rib spacing where the groove-rib periodic spacing is one-tenth of the channel height, the presence of longitudinal superhydrophobic grooves leads to flow instabilities at a lower critical Reynolds number. The redistribution of the base flow resulting from the vanishing shear rates along the liquid-gas interface could give rise to an inflectional instability that promotes temporal instability. The effects of patterning the superhydrophobic surfaces on one or both channel walls are also examined.