The Scaling of Drag Reduction and Sustainability Bounds of Superhydrophobic and Liquid-Infused Surfaces in High Reynolds Number Turbulent Flows*

Using results from DNS and scaling arguments we show that the magnitude of drag reduction (DR) with superhydrophobic (SH) and liquid infused (LI) surfaces is not only a function of the geometry and size of the surface micro-texture in wall units, but also the Reynolds number (Re) of the flow. A Re independent measure of DR can be constructed by parameterizing the magnitude of DR in terms of the friction coefficient of the base flow and the shift, (B-B0), in the intercept of a logarithmic law representation of the mean velocity profile in the flow with micro-textured walls compared to the base flow, where (B-B0) is Re independent. The scaling laws for (B-B0), in terms of the geometrical parameters of the surface micro-texture in wall units, are presented for longitudinal microgrooves and aligned microposts. These scaling laws, along with the parametrization of DR in terms of (B-B0), allow for a priori prediction of the DR with any SH or LI longitudinal micrgoove or aligned micropost geometry in turbulent flow at any Re. It is further shown that the stability bounds of SH surfaces are also strongly Re dependent. Implications for design of SH and LI surfaces for application in high Re turbulent flows will be discussed.