Linear stability of pressure-driven flow over longitudinal superhydrophobic grooves

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 (d) 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. (C) 2016 AIP Publishing LLC.