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Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, bygenerating large effective slip, which is important for a variety ofapplications that involve a manipulation of liquids at the small scale. Here wediscuss how the dissipation in the gas phase of textures modifies theirfriction properties. We propose an operator method, which allows us the mappingof the flow in the gas subphase to a local slip boundary condition at theliquid/gas interface. The determined uniquely local slip length depends on theviscosity contrast and underlying topography, and can be immediately used toevaluate an effective slip of the texture. Besides superlubricating Cassiesurfaces our approach is valid for rough surfaces impregnated by alow-viscosity 'lubricant', and even for Wenzel textures, where a liquid followsthe surface relief. These results provide a framework for the rational designof textured surfaces for numerous applications.

'Gas cushion' model and hydrodynamic boundary conditions for superhydrophobic textures