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On the statics and dynamics of fully confined bubbles

Published online by Cambridge University Press:  18 August 2017

Olivier Vincent Open the ORCID record for Olivier Vincent [Opens in a new window]  and
Philippe Marmottant
Olivier Vincent*
Affiliation:
CNRS/Université Grenoble-Alpes, LIPhy UMR 5588, Grenoble, F-38401, France Cornell University, Robert Frederick Smith School of Chemical and Biomolecular Engineering, 120 Olin Hall, Ithaca, NY 14850, USA
Philippe Marmottant
Affiliation:
CNRS/Université Grenoble-Alpes, LIPhy UMR 5588, Grenoble, F-38401, France
*
†Email address for correspondence: orv3@cornell.edu
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Abstract

We investigate theoretically the statics and dynamics of bubbles in fully confined liquids, i.e. in liquids surrounded by solid walls in all directions of space. This situation is found in various natural and technological contexts (geological fluid inclusions, plant cells and vessels, soil tensiometers, etc.), where such bubbles can pre-exist in the trapped liquid or appear by nucleation (cavitation). We focus on volumetric deformations and first establish the potential energy of fully confined bubbles as a function of their radius, including contributions from gas compressibility, surface tension, liquid compressibility and elastic deformation of the surrounding solid. We evaluate how the Blake threshold of unstable bubble growth is modified by confinement and we also obtain an original bubble stability phase diagram with a regime of liquid superstability (spontaneous bubble collapse) for strong confinements. We then calculate the liquid velocity field associated with radial deformations of the bubble and strain in the solid, and we predict large deviations in the kinematics compared to bubbles in extended liquids. Finally, we derive the equations governing the natural oscillation dynamics of fully confined bubbles, extending Minnaert’s formula and the Rayleigh–Plesset equation, and we show that the compressibility of the liquid as well as the elasticity of the walls can result in ultra-fast bubble radial oscillations and unusually quick damping. We find excellent agreement between the predictions of our model and recent experimental results.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation Drops and Bubbles: Drops and Bubbles

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Papers
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Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , pp. 194 - 224
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© 2017 Cambridge University Press 

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