Unsteady Stokes Flow Modeling of Superhydrophobic Surfaces in Turbulent Flow

The interaction between the surface topology of superhydrophobic surfaces and the inner flow of the turbulent boundary layer is studied theoretically and numerically. An analytical solution of the flow field near transverse/longitudinal grooved multiphase textures subject to turbulent flow is presented. The flow is modeled by the unsteady Stokes equation. The solution is verified with direct numerical simulation (DNS) implemented with the volume of fluid method. A parametric study is conducted that involves the frequency of the external flow, viscosity ratio of the multiphase interface and the location of the interface with respect to the velocity transfer function between the interior and the exterior regions of the grooves. The effective slip length and the shear stress over the grooved plane are also examined. The analytical solution to single-phase flow is compared to DNS of turbulent flow over longitudinal grooves at friction Reynolds number Re_τ=400. Good agreement is seen with DNS at low frequencies. It is suggested that higher frequency disturbances are produced by smaller spanwise structures near the wall, and when this effect is accounted for, good agreement is also observed at higher frequencies.