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Viscous growth and rebound of a bubble near a rigid surface

Published online by Cambridge University Press:  03 December 2018

Sébastien Michelin Open the ORCID record for Sébastien Michelin [Opens in a new window] ,
Giacomo Gallino ,
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]  and
Eric Lauga
Sébastien Michelin*
Affiliation:
LadHyX – Département de Mécanique, Ecole Polytechnique – CNRS, 91128 Palaiseau, France
Giacomo Gallino
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, CH-1015 Lausanne, Switzerland
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, EPFL, CH-1015 Lausanne, Switzerland
Eric Lauga
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface is characterised by a constant slip length allowing us to tune the hydrodynamic mobility of its surface and tackle in one formulation both clean and contaminated bubbles as well as rigid shells. Starting with a bubble of infinitesimal size, the fluid flow and hydrodynamic forces on the growing bubble are obtained analytically. We demonstrate that, depending on the value of the bubble slip length relative to the initial distance to the wall, the bubble will either monotonically drain the fluid separating it from the wall, which will exponentially thin, or it will bounce off the surface once before eventually draining the thin film. Clean bubbles are shown to be a singular limit which always monotonically get repelled from the surface. The bouncing events for bubbles with finite slip lengths are further analysed in detail in the lubrication limit. In particular, we identify the origin of the reversal of the hydrodynamic force direction as due to the change in the flow pattern in the film between the bubble and the surface and to the associated lubrication pressure. Last, the final drainage dynamics of the film is observed to follow a universal algebraic scaling for all finite slip lengths.

JFM classification

Drops and Bubbles: Bubble dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 172 - 199
Copyright
© 2018 Cambridge University Press 

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