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The motion of a large gas bubble rising through liquid flowing in a tube

Published online by Cambridge University Press:  19 April 2006

R. Collins ,
F. F. De Moraes ,
J. F. Davidson  and
D. Harrison
R. Collins
Affiliation:
Department of Mechanical Engineering, University College London
F. F. De Moraes
Affiliation:
Department of Chemical Engineering, University of Cambridge Present address: Department of Chemical Engineering, University of Maringá, Caixa postal 331, 87.100 Maringá, Brazil.
J. F. Davidson
Affiliation:
Department of Chemical Engineering, University of Cambridge
D. Harrison
Affiliation:
Department of Chemical Engineering, University of Cambridge
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Abstract

The theory presented here describes the motion of a large gas bubble rising through upward-flowing liquid in a tube. The basis of the theory is that the liquid motion round the bubble is inviscid, with an initial distribution of vorticity which depends on the velocity profile in the liquid above the bubble. Approximate solutions are given for both laminar and turbulent velocity profiles and have the form \begin{equation} U_s = U_c+(gD)^{\frac{1}{2}}\phi(U_c/(gD)^{\frac{1}{2}}), \end{equation}Us being the bubble velocity, Uc the liquid velocity at the tube axis, g the acceleration due to gravity, and D the tube diameter; ϕ indicates a functional relationship the form of which depends upon the shape of the velocity profile. With a turbulent velocity profile, a good approximation to (1) which is suitable for many practical purposes is \begin{equation} U_s = U_s + U_{s0}, \end{equation}Us0 being the bubble velocity in stagnant liquid. Published data for turbulent flow are known to agree with (2), so that in this case the theory supports a well-known empirical result. Our laminar flow experiments confirm the validity of (1) for low liquid velocities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 3 , 13 December 1978 , pp. 497 - 514
Copyright
© 1978 Cambridge University Press

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