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Spherical cap bubbles

Published online by Cambridge University Press:  26 April 2006

Yumin Yang  and
Herbert Levine
Yumin Yang
Affiliation:
Department of Physics and Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0075, USA Present address: Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600, USA.
Herbert Levine
Affiliation:
Department of Physics and Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0075, USA
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Abstract

We study the rise of a spherical cap bubble in both two- and three-dimensional unbounded regions. In particular we focus on the problem of finding steady state-solutions. We assume that the fluid is incompressible, inviscid and irrotational, and use two different models to approximate the turbulent wake behind the bubble. We demonstrate numerically that in the case of zero surface tension we have a continuous spectrum of rise velocities. When we add small surface tension to the problem, the degeneracy is broken via a solvability mechanism, and we obtain velocity selection. Our results are in good agreement with the existing experimental studies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 235 , February 1992 , pp. 73 - 87
Copyright
© 1992 Cambridge University Press

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