Instantaneous slip length in superhydrophobic microchannels having grooves with curved or dissimilar walls

Abstract

Superhydrophobic (SHP) surfaces can be used to reduce the skin-friction drag in a microchannel. This is due to the peculiar ability of these surfaces to entrap air in their pores and thereby reduce the contact area between water and the solid surface. The favorable drag-reduction effect, however, can quickly deteriorate if the surface geometry is not designed properly. The deterioration can be sudden, caused by exposure to excessive pressures, or gradual, due to the dissolution of the entrapped air into the ambient water. The formulations presented here provide a means for studying the time-dependent drag-reduction in a microchannel enhanced with transverse or longitudinal SHP grooves of varying wall profiles or wettabilities. Moreover, different mathematical approaches are developed to distinguish the performance of a sharp-edged groove from that of a groove with round entrance. The work starts by deriving an equation for the balance of forces on the air–water interface (AWI) inside a groove and solving this differential equation, along with Henry’s law, for the rate of dissolution of the entrapped air into water over time. It was shown that the performance of a SHP groove depends mostly on the interplay between the effects of the apparent contact angle of the AWI and the initial volume of the groove. The instantaneous slip length is then calculated by solving the Navier–Stokes equations for flow in microchannels with SHP grooves. Our results are compared with the studies in the literature whenever available, and good agreement has been observed.