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Viscous dissipation in the collision between a sphere and a textured wall

Published online by Cambridge University Press:  27 May 2020

Anne Mongruel Open the ORCID record for Anne Mongruel [Opens in a new window]  and
Philippe Gondret Open the ORCID record for Philippe Gondret [Opens in a new window]
Anne Mongruel
Affiliation:
PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris,75005Paris, France
Philippe Gondret*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire FAST, 91405, Orsay, France
*
†Email address for correspondence: [email protected]
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Abstract

A model is presented for the bouncing dynamics of a fluid-immersed sphere impacting normally a textured wall with micropillars. By taking into account the hydrodynamic and contact interactions between the smooth sphere and the textured wall, the complete motion of the sphere is recovered when approaching, colliding with and bouncing off the wall. We demonstrate that the critical Stokes number for the bouncing transition, $St_{c}$, is the sum of two contributions corresponding to dissipation prior to and during the collision, both contributions being critically influenced by the geometrical parameters of the model roughness. The experimental data obtained from interferometric measurements are found to be in agreement with the theoretical predictions. In the bouncing regime, the coefficient of restitution is also derived analytically and shows a linear evolution with the Stokes number, $St$, just above the bouncing transition, in agreement with the experimental data obtained very close to $St_{c}$.

JFM classification

Complex Fluids: Suspensions Low-Reynolds-number flows: Lubrication theory Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A8
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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