Slipping on grooves: an analytic study of flow over liquid-infused surfaces (LIS)*

We describe the construction of explicit solutions to a two-phase fluid problem relevant to modelling flow over a liquid-infused surface. In the longitudinal configuration, these surfaces typically comprise a periodic array of fluid-filled grooves in a no-slip surface over which flows a different working fluid. The fluid-filled grooves help to lubricate the flow of the working fluid leading to useful reduction in viscous drag. This drag reduction is quantified by explicit formulas for the slip length extracted from the analytical solutions. The case where the fluid filled grooves are closed, perhaps using ``baffles'', causing a back-pressure that deforms the fluid-fluid interface, is also analyzed.