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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference8 articles.
1. Lamb, H. 1932 Hydrodynamics , 6th ed. Cambridge University Press.
2. Moore, D. W. 1963 The boundary layer on a spherical gas bubble J. Fluid Mech. 16, 161.
3. Walters, J. K. & Davidson, J. F. 1963 The initial motion of a gas bubble formed in an inviscid liquid. II J. Fluid Mech. 17, 321.
4. Pedley, T. J. 1966 Plumes, bubbles, and vortices. Ph.D. Dissertation, Cambridge University.
5. Taylor, G. I. & Davies, R. M. 1950 Large bubbles in extended liquids and in liquids in tubes.Proc. Roy. Soc. A, 200, 375.
Cited by
40 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献