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