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Two-dimensional bubbles in slow viscous flows. Part 2

Published online by Cambridge University Press:  29 March 2006

S. Richardson
S. Richardson
Affiliation:
Applied Mathematics, University of Edinburgh
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Abstract

The present paper considers the behaviour of a two-dimensional inviscid bubble when placed in viscous fluid whose velocity at large distances varies parabolically, and whose motion is governed by the equations of Stokes flow. For arbitrary values of the surface tension a t the bubble interface, this free boundary problem can be reduced to a coupled pair of transcendental equations.

When surface tension effects are large, the cross-section of the bubble is nearly circular. In the symmetric situation, with the bubble at the centre of a parabolic velocity profile, a reduction of the surface tension first produces a fattening at the rear of the bubble which then distorts further to form a re-entrant cavity. The solution also shows that the bubble moves faster than the undisturbed fluid velocity at its centre. When in an asymmetric position, the bubble has a drift velocity taking it towards the symmetric position.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 1 , 20 March 1973 , pp. 115 - 127
Copyright
© 1973 Cambridge University Press

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References

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