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

Published online by Cambridge University Press:  06 July 2018

Marco Castagna ,
Nicolas Mazellier Open the ORCID record for Nicolas Mazellier [Opens in a new window]  and
Azeddine Kourta
Marco Castagna
Affiliation:
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France
Nicolas Mazellier*
Affiliation:
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France
Azeddine Kourta
Affiliation:
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France
*
†Email address for correspondence: nicolas.mazellier@univ-orleans.fr
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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 performance. 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 $\unicode[STIX]{x1D712}$. While noticeable distortions are locally observed, the plastron becomes more and more spherical on average (i.e. $\unicode[STIX]{x1D712}\rightarrow 1$) as far as ${\mathcal{W}}e$ increases. The study of the falling motion reveals that the plastron compliance has a sizeable influence on the wake development. Investigating the lift force experienced by the super-hydrophobic spheres, the onset of wake instabilities is found to be triggered earlier than for smooth spheres used as reference. Surprisingly, it is also observed that the early promotion of the wake instabilities is even more pronounced beyond a critical Weber number, ${\mathcal{W}}e_{c}$, which corresponds to a critical aspect ratio $\unicode[STIX]{x1D712}_{c}$. Furthermore, the magnitude of the hydrodynamic loads is found to be dependent on the average deformation of the gas/liquid interface. Indeed, in comparison to the reference spheres, the high deformation achieved for $\unicode[STIX]{x1D712}>\unicode[STIX]{x1D712}_{c}$ (oblate shape) leads to lift and drag increase, whereas the low deformation obtained for $\unicode[STIX]{x1D712}<\unicode[STIX]{x1D712}_{c}$ (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. These results suggest that the amount of vorticity produced at the body surface and then released in the wake is strongly impacted by the plastron compliance. If confirmed by additional studies and extrapolated to other flow configurations, 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 performance.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 646 - 673
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Copyright
© 2018 Cambridge University Press 

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Castagna et al. supplementay movie

Typical movie recorded (recording speed 1300 fps, reproduction speed 5 fps) in high magnification configuration for the SH-80 sphere (d = 20 mm). The gravity direction is from right to left.

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