Modeling the flow over superhydrophobic and liquid-impregnated surfaces

Superhydrophobic (SH) and liquid-impregnated surfaces (LIS) represent an interesting technique for the possible reduction of drag in applications involving the flow of liquids over solid surfaces, for a wide range of Reynolds number, from laminar to turbulent conditions. Such coatings work by the interposition of a gas/oil layer between the liquid and the solid wall, trapped by distributed microscopic roughness elements present at the wall; over the gas layer the liquid can flow with negligible friction. The present activity is focused on the numerical modeling of the slippage over such coatings and on their drag reduction performance in the turbulent regime. The problem is subdivided into two parts: a microscopic problem, accounting for the flow in the proximity of the roughness elements and a macroscopic problem, accounting for the turbulent flow over SHS/LIS, where the effect of the slippage at the wall is modeled through a proper boundary condition. The near-wall, microscopic problem, governed by the Stokes equation, is recast into an integral form and then solved using a boundary element method. The aim of the microscopic calculations, performed by varying the viscosity ratio between the fluids, is to obtain the values of the slip lengths, used to quantify slippage. The slip length are then used in the definition of Navier boundary condition, applied at the walls of a turbulent channel flow at moderate Reynolds number, solved by direct numerical simulations. The results are in excellent agreement with a theoretical model available in the literature.