Evolution of Air Plastron Thickness and Slip Length over Superhydrophobic Surfaces in Taylor Couette Flows

Drag reduction (DR) using superhydrophobic surfaces (SHSs) has received intensive interest due to the emergence of SH coating technology. The air layer (plastron "delta") trapped between the SHS and the water controls the flow slip over the SHSs. We demonstrate slippage over three fabricated SHSs in laminar and low turbulent Taylor-Couette flows. We experimentally investigate how the slip length increases with a higher Reynolds number (Re) over the tested SHSs; simultaneously, the air plastron thickness investigates using a viscous model. The mean skin friction coefficient (C-f) can be fitted to a modified semi-empirical logarithmic law expressed in the Prandtl-von Karman coordinate. An effective slip length is estimated in the 35-41 mu m range with an achieved 7-11% DR for the tested surfaces. Statistical analysis is used to develop a regression model from the experimental data. The model shows an R-2 of 0.87 and good agreement with the experimental data. This shows the relation between the dimensionless slip length (b(+)), the dimensionless plastron thickness (delta(+)), and the Reynolds number, which is directly proportional. The regression model shows that b(+) and Reynolds numbers have a higher impact on the delta(+) than the surface wettability, which attribute to the small difference in the wetting degree between the three tested surfaces. The practical importance of the work lies in its ability to provide a deep understanding of the reduction in viscous drag in numerous industrial applications. Furthermore, this research serves as a groundwork for future studies on hydrophobic applications in internal flows.