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In this Letter, the falling of super-hydrophobic spheres is investigatedexperimentally at low Reynolds numbers. In particular, we show thatsuper-hydrophobic coatings become ineffective at reducing drag unlike predictedby theoretical and numerical approaches. A time scale analysis describing bothMarangoni-induced stresses and air/liquid interface deformation shows thatthese mechanisms are unlikely to account for the slippage effect disappearanceobserved in our study. Instead, we propose a simple model based on an isotropicporous medium approach, derived to account for losses induced by the motion ofthe gas encapsulated around the sphere. The key parameter of this mechanism isfound to be the surface tortuosity, whose range estimated from microscopicsurface imaging corroborate those predicted by our scaling analysis andprevious studies.

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