On the onset of instability in the wake of super-hydrophobic spheres

Abstract

We report an experimental investigation of free falling super-hydrophobic (SH) spheres in glycerine-water mixtures over a wide range of Reynolds number. SH coatings have the ability to reduce the contact area between the surrounding liquid and the solid surface by entrapping an air layer in the surface roughness. We investigate the effect of this air plastron on the hydrodynamic performance of spheres, focusing our attention on the onset of wake instabilities. Our results emphasise the key role of the surface roughness properties on the triggering of wake instabilities. It is shown that, unlike what was reported in previous numerical studies on SH bluff-bodies, local deformation of the interface may act as a by-pass mechanism promoting earlier transition, yielding a decrease of the critical Reynolds number at which the wake becomes unstable. A scenario coupling the hydrodynamic instabilities (scaling with the Reynolds number) and the interface deformation (scaling with the roughness-based Weber number) is proposed to describe the different transition mechanisms in presence of SH surfaces. It is found that the promotion of wake instabilities over SH surfaces occurs when the roughness-based Weber number is larger than a critical threshold. These findings are of primary importance for guiding the design of resilient and efficient SH surfaces.