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## Journal of Fluid Mechanics

- Journal of Fluid Mechanics / Volume 10 / Issue 02 / March 1961, pp 166- 188
- Copyright © 1961 Cambridge University Press
- DOI: http://dx.doi.org/10.1017/S0022112061000160 (About DOI), Published online: 28 March 2006

## The motion of long bubbles in tubes
## AbstractA long bubble of a fluid of negligible viscosity is moving steadily in a tube filled with liquid of viscosity μ at small Reynolds number, the interfacial tension being σ. The angle of contact at the wall is zero. Two related problems are treated here. In the first the tube radius In the second problem the tube is wider, vertical, and sealed at one end. The bubble now moves under the effect of gravity, but it is shown that it will not rise at all if $\rho gr^2| \sigma \; \textless \; 0 \cdot 842,$ where ρ is the difference in density between the fluids inside and outside the bubble. If $0 \cdot 842 \; \textless \; 1 \cdot 04,$ then $\rho gr^2| \sigma - 0 \cdot842 \simeq 1 \cdot 25 (\mu U|\sigma)^{\frac {2}{9}} + 2 \cdot 24(\mu U|\sigma)^{\frac {1}{3}},$ accurate to within 10%. Experiments are adduced in support of these results, though there is disagreement with previous work. (Published Online March 28 2006)(Received November 9 1960) |