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Irrotational analysis of the toroidal bubble in a viscous fluid

By J. Wang1 and D.D. Joseph1

1Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA

(May, 2005)


We consider the problem of the rise of a toroidal gas bubble previously considered by Pedley (1968). We add the irrotational viscous drag to the force wrench in the impulse equation. In this case, the impulse equation and the energy equation governing the rise of the bubble are the same. The solution of this equation is computed; after a transient state the system evolves to a steady state in which the diameter, toroidal radius and rise velocity are constant.