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The interaction of multiple bubbles in a Hele-Shaw channel
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Keeler, J. S., Gaillard, A., Lawless, J., Thompson, A. B., Juel, A. and Hazel, A. L. (2022) The interaction of multiple bubbles in a Hele-Shaw channel. Journal of Fluid Mechanics, 946 . A40. doi:10.1017/jfm.2022.618 ISSN 0022-1120.
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Official URL: http://dx.doi.org/10.1017/jfm.2022.618
Abstract
We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a Hele-Shaw channel with a small elevation along its centreline via physical experiment and numerical simulation of a depth-averaged model. For a single-bubble system we establish that, in general, the bubble propagation speed monotonically increases with bubble volume so that two bubbles of different sizes, in the absence of any hydrodynamic interactions, will either coalesce or separate in a finite time. However, our experiments indicate that the bubbles interact and that an unstable two-bubble state is responsible for the eventual dynamical outcome: coalescence or separation. These results motivate us to develop an edge-tracking routine and to calculate these weakly unstable two-bubble steady states from the governing equations. The steady states consist of pairs of ‘aligned’ bubbles that appear on the same side of the centreline with the larger bubble leading. We also discover, through time-dependent simulations and physical experiment, another class of two-bubble states that, surprisingly, are stable. In contrast to the ‘aligned’ steady states, these bubbles appear on either side of the centreline and are ‘offset’ from each other. We calculate the bifurcation structures of both classes of steady states as the flow rate and bubble volume ratio are varied. We find that they exhibit intriguing similarities to the single-bubble bifurcation structure, which has implications for the existence of n -bubble steady states.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Bifurcation theory, Bubbles -- Dynamics | ||||||
Journal or Publication Title: | Journal of Fluid Mechanics | ||||||
Publisher: | Cambridge University Press | ||||||
ISSN: | 0022-1120 | ||||||
Official Date: | 11 August 2022 | ||||||
Dates: |
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Volume: | 946 | ||||||
Article Number: | A40 | ||||||
DOI: | 10.1017/jfm.2022.618 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Copyright Holders: | © The Author(s), 2022. Published by Cambridge University Press. | ||||||
Date of first compliant deposit: | 6 September 2022 | ||||||
Date of first compliant Open Access: | 6 September 2022 |
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