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

Superhydrophobic surfaces are microscopically textured surfaces that reduce skin friction in turbulent flows thanks to the nearly shear-free boundary created by entrapping air pockets within surface textures. Owing to their heterogeneity, it is desirable to model these surfaces with a single effective slip length. However, the relationship between the heterogeneity of superhydrophobic surfaces and their effective slip length is not fully explored for turbulent flows. In this talk, we will present our recent efforts to systematically develop a model that captures the effective slip length of superhydrophobic surfaces in terms of surface features such as texture size and solid fraction. Firstly, we perform direct numerical simulations of turbulent channel flows with an effective slip length for friction Reynolds numbers up to 600 to derive a correlation between drag reduction and effective slip length. Secondly, from the literature, we collect the drag reduction of superhydrophobic surfaces with various texture sizes and solid fractions. Lastly, a physical model for an effective slip length of superhydrophobic surfaces as a function of texture size and solid fraction is developed by utilizing the derived correlation and the drag reduction of superhydrophobic surfaces. The physical model will be validated against experimental and computational data.