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The toroidal bubble

Published online by Cambridge University Press:  28 March 2006

T. J. Pedley
T. J. Pedley
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore
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Abstract

It has been observed by Walters & Davidson (1963) that release of a mass of gas in water sometimes produces a rising toroidal bubble. This paper is concerned with the history of such a bubble, given that at the initial instant the motion is irrotational everywhere in the water. The variation of its overall radius a with time may be predicted from the vertical impulse equation, and it should be possible to make the same prediction by equating the rate of loss of combined kinetic and potential energy to the rate of viscous dissipation. This is indeed seen to be the case, but not before it is recognized that in a viscous fluid vorticity will continually diffuse out from the bubble surface, destroying the irrotationality of the motion, and necessitating an examination of the distribution of vorticity. The impulse equation takes the same form as in an inviscid fluid, but the energy equation is severely modified. Other results include an evaluation of the effect of a hydrostatic variation in bubble volume, and a prediction of the time which will have elapsed before the bubble becomes unstable under the action of surface tension.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 1 , 9 April 1968 , pp. 97 - 112
Copyright
© 1968 Cambridge University Press

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