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Solution selection of axisymmetric Taylor bubbles

Published online by Cambridge University Press:  22 March 2018

A. Doak Open the ORCID record for A. Doak [Opens in a new window]  and
J.-M. Vanden-Broeck
A. Doak*
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
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Abstract

A finite difference scheme is proposed to solve the problem of axisymmetric Taylor bubbles rising at a constant velocity in a tube. A method to remove singularities from the numerical scheme is presented, allowing accurate computation of the bubbles with the inclusion of both gravity and surface tension. This paper confirms the long-held belief that the solution space of the axisymmetric Taylor bubble for small surface tension is qualitatively similar to that of the plane Taylor bubble. Furthermore, evidence suggesting that the solution selection mechanism associated with plane bubbles also occurs in the axisymmetric case is presented.

JFM classification

Drops and Bubbles: Bubble dynamics Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 843 , 25 May 2018 , pp. 518 - 535
Copyright
© 2018 Cambridge University Press 

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