Toward a correlation for the effective slip length of superhydrophobic surfaces in turbulent flows

Superhydrophobic surfaces (SHSs) are microscopically textured surfaces that reduce skin friction in turbulent flows thanks to air pockets within surface textures. These entrapped air pockets generate a nearly shear-free boundary that enables a slip boundary condition in a certain range of Reynolds numbers. It is desirable that a single effective slip length captures the effect of the heterogeneous SHSs, but a correlation between the heterogeneity of SHSs and their effective slip length has yet to be fully explored for turbulent flows. In this talk, we will present our recent efforts to develop a correlation for the effective slip length of superhydrophobic surfaces in terms of texture size and solid fraction. In addition, different geometries of SHSs are considered, namely streamwise-aligned ridges and isotropic square posts. Direct numerical simulations with homogeneous slip surfaces are performed for friction Reynolds numbers up to 600 to investigate the drag reduction in terms of various slip lengths. We also perform direct numerical simulations of heterogeneous SHSs with various texture sizes and solid fractions. A correlation for an effective slip length of superhydrophobic surfaces as a function of texture size and solid fraction is then developed by utilizing the drag reduction of homogeneous slip surfaces and heterogeneous SHSs. Interestingly, different correlations are identified for small and large texture sizes.