On the nonlocality of the slip length operator for scalar and momentum transport on patterned superhydrophobic surfaces in turbulent flow

Superhydrophobic surfaces (SHS) reduce skin friction drag via formation of air films on textured surfaces, resulting in an effective slip velocity. In this study, we seek to understand the effects of SHS and the usage of the Navier slip boundary condition in the context of mean mass and momentum mixing. We use the Macroscopic Forcing Method to compute the generalized eddy viscosity and slip length operators of a turbulent channel over SHS, implemented as both pattern-resolved and homogenized slip boundary conditions, for multiple pattern sizes and geometries. We present key differences in the mixing behavior of these boundary conditions through quantification of their implications on the near-wall eddy viscosity. More importantly, analysis of transport in turbulent flows over patterned surfaces reveals substantial nonlocality in the measured homogenized slip length for both scalar and momentum mixing when the Reynolds and Peclet numbers based on pattern size are finite. We present several metrics to quantify this nonlocality and observe possible trends relating to Reynolds number, texture size, and pattern geometry. We demonstrate the importance of including the nonlocality of the slip length operator by examining the impact on solutions for the mean scalar and velocity fields.