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Pointed bubbles in slow viscous flow

Published online by Cambridge University Press:  29 March 2006

J. D. Buckmaster
J. D. Buckmaster
Affiliation:
Mathematics Department, New York University
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Abstract

Inviscid bubbles confined by the slow axisymmetric straining motion of a very viscous fluid are considered for the case when the surface tension is weak. The shape of the bubbles is determined using slender-body theory, and it is found that these bubbles have pointed ends, in agreement with well-established experimental results. The description obtained is invalid within exponentially small neighbourhoods of the ends and a local analysis suggests that the tips are cusp-like. In both the description of the major portion of the bubble and of the ends, there is an apparent non-uniqueness because a certain parameter can take on a countably infinite number of values. This non-uniqueness is not resolved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 3 , 10 October 1972 , pp. 385 - 400
Copyright
© 1972 Cambridge University Press

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References

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