Dependence of the drag over superhydrophobic and liquid infused surfaces on the asperities of the substrate

Direct numerical simulations (DNSs) of two superposed fluids in a turbulent channel flow with a textured surface made of pinnacles of random height have been performed at Re_τ≈180 and Re_τ≈395 . The texture reproduces an etched sandblasted aluminum. The viscosity ratio between the two fluids is either m =0.02 , mimicking the viscosity ratio of a superhydrophobic surface (water over air), or m =0.40 (water over heptane) resembling a liquid infused surface. A parametric study has been carried out varying the position of the interface between the two fluids to assess the contribution to the drag of the portion of the texture emerging above the interface and to provide guidelines for design. Simulations with a deformable interface, at Weber numbers We+≈^{10-2 and 10-3 have been performed. Results have been compared to those obtained assuming the ideal case of a flat interface which is slippery in the streamwise and spanwise direction (corresponding to a Weber number We=0 ). The time-averaged position of the interface has been correlated to the pressure field induced by the random-height pinnacles while the instantaneous deformation is due to the passage of the near-wall coherent structures. We attempted to reconcile the effect of superhydrophobic and liquid infused surfaces on the coherent structures by calculating how the shear rate parameter depends on the amount of drag reduction.}