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Direct Numerical Simulations of two superposed fluids in a channel with atextured surface on the lower wall have been carried out. A parametric studyvarying the viscosity ratio between the two fluids has been performed to mimicboth {\bf idealised} super hydrophobic and liquid infused surfaces and assessits effect on the frictional, form and total drag for three different texturedgeometries: longitudinal square bars, transversal square bars and staggeredcubes. The interface between the two fluids is assumed to be slippery in thestreamwise and spanwise directions and not deformable in the verticaldirection, corresponding to the ideal case of infinite surface tension. Toidentify the role of the fluid-fluid interface, an extra set of simulationswith a single fluid has been carried out and compared to the results obtainedwith two fluids of same viscosity separated by the interface. The drag and themaximum wall-normal velocity fluctuations were found to be highly correlatedfor all the surface configurations, whether they reduce or increase the drag.This implies that the structure of the near-wall turbulence is dominated by thetotal shear and not by the local boundary condition of super-hydrophobic,liquid--infused or rough surfaces.

Comparison between super-hydrophobic, liquid infused and rough surfaces: a DNS study