An Isotropic Porous Medium Approach to Drag Mitigation Disappearance in Super-Hydrophobic Falling Spheres

TL;DR

This study experimentally investigates why super-hydrophobic coatings fail to reduce drag in falling spheres at low Reynolds numbers, proposing an isotropic porous medium model centered on surface tortuosity to explain the loss of slip effect.

Contribution

It introduces a novel porous medium approach based on surface tortuosity to explain drag mitigation failure in super-hydrophobic spheres, contrasting with previous theoretical predictions.

Findings

Super-hydrophobic coatings become ineffective at low Reynolds numbers.

Marangoni stresses and interface deformation are unlikely causes.

Surface tortuosity explains the loss of slip effect.

Abstract

In this Letter, the falling of super-hydrophobic spheres is investigated experimentally at low Reynolds numbers. In particular, we show that super-hydrophobic coatings become ineffective at reducing drag unlike predicted by theoretical and numerical approaches. A time scale analysis describing both Marangoni-induced stresses and air/liquid interface deformation shows that these mechanisms are unlikely to account for the slippage effect disappearance observed in our study. Instead, we propose a simple model based on an isotropic porous medium approach, derived to account for losses induced by the motion of the gas encapsulated around the sphere. The key parameter of this mechanism is found to be the surface tortuosity, whose range estimated from microscopic surface imaging corroborate those predicted by our scaling analysis and previous studies.