On the effective slip length of superhydrophobic surfaces in turbulent flows*

Superhydrophobic surfaces have been widely used for drag reduction in laminar and turbulent flows. These surfaces are capable of entrapping air pockets within surface textures to sustain a slip boundary condition in a certain range of Reynolds numbers. These heterogeneous surfaces can be effectively modeled as homogenous surfaces with a single effective slip length. Although several studies have investigated the relation between the heterogeneous surface features and effective slip length, it has yet to be fully explored. In this talk, we will present our two recent efforts in this regard. Firstly, using the phenomenological model developed by Seo and Mani, PoF (2016), the realistically-achievable effective slip length is calculated in terms of surface features such as texture size and solid fraction up to a friction Reynolds number of 600. Given the texture size and effective slip length, the physically-possible solid fraction is also calculated. Secondly, direct numerical simulations are performed to develop a new phenomenological model for the relation between superhydrophobic surface features and effective slip length. Drag reduction of superhydrophobic surfaces with various surface textures and homogenous surfaces with various slip lengths will be considered for the model.