Wake of super-hydrophobic falling spheres: influence of the air layer deformation

TL;DR

This study experimentally examines how the air layer around super-hydrophobic spheres deforms under flow stresses, affecting their wake and hydrodynamic performance, with implications for designing better super-hydrophobic surfaces.

Contribution

It introduces the Weber number and aspect ratio to quantify plastron deformation and links deformation to changes in lift and drag, highlighting the importance of plastron compliance.

Findings

Increased Weber number leads to more spherical plastron shapes.

High deformation causes lift and drag increase.

Low deformation results in lift and drag reduction.

Abstract

We report an experimental investigation of the wake of free falling super-hydrophobic spheres. The mutual interaction between the air layer (plastron) encapsulating the super-hydrophobic spheres and the flow is emphasised by studying the hydrodynamic performances. It is found that the air plastron adapts its shape to the flow-induced stresses which compete with the surface tension. This competition is characterised by introducing the Weber number $\mathcal{W}e$, whilst the plastron deformation is estimated via the aspect ratio $\chi$. While noticeable distortions are locally observed, the plastron becomes more and more spherical in average (i.e. $\chi \rightarrow 1$) as far as $\mathcal{W}e$ increases. In comparison to the reference spheres, high deformation of the air plastron plastron (oblate shape) leads to lift and drag increase, whereas low deformation (spherical shape) yields lift and drag mitigation. Accordingly, taking into account the plastron deformation provides an attractive way to explain the somehow discordant results reported in other studies at comparable Reynolds numbers. If confirmed by additional studies, our findings would imply that plastron compliance and its feedback on the flow, which are currently neglected in most theoretical works and numerical simulations, must be accounted for to design super-hydrophobic surfaces and/or predict their performances.