An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

Dallaston, Michael C. & McCue, Scott W. (2012) An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell. The ANZIAM Journal, 54, C309-C326.

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Abstract

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

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ID Code: 60117
Item Type: Journal Article
Refereed: Yes
Keywords: Hele-Shaw flow, Saffman-Taylor instability, viscous fingering, bubble extinction, pinch-off, surface tension, kinetic undercooling
ISSN: 1446-8735
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Cambridge University Press
Copyright Statement: Material on these pages is copyright Cambridge University Press or reproduced with permission from other copyright owners. It may be downloaded and printed for personal reference, but not otherwise copied, altered in any way or transmitted to others (unless explicitly stated otherwise) without the written permission of Cambridge University Press. Hypertext links to other Web locations are for the convenience of users and do not constitute any endorsement or authorisation by Cambridge University Press.
Deposited On: 20 May 2013 22:41
Last Modified: 15 Jun 2013 11:32

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