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Distorted gas bubbles at large Reynolds number

Published online by Cambridge University Press:  29 March 2006

M. El Sawi
M. El Sawi
Affiliation:
Department of Mathematics, Imperial College, London
Present address: Department of Mathematics, University of Khartoum, Sudan.
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Abstract

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber number W. The virial method leads to an expression relating W and the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order in W, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained by W differs only by about 2.8% from the critical Weber number obtained by Hartunian & Sears (1957) for the onset of instability.

An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 1 , 8 January 1974 , pp. 163 - 183
Copyright
© 1974 Cambridge University Press

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