Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T17:59:56.617Z Has data issue: false hasContentIssue false
  • English
  • Français

The rise of a gas bubble in a viscous liquid

Published online by Cambridge University Press:  28 March 2006

D. W. Moore
D. W. Moore
Affiliation:
Department of Mathematics, University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

The rise of a gas bubble in a viscous liquid at high Reynolds number is investigated, it being shown that in this case the irrotational solution for the flow past the bubble gives a uniform approximation to the velocity field. The drag force experienced by the bubble is calculated on this hypothesis and the drag coefficent is found to be 32/R, where R is the Reynolds number (based on diameter) of the bubbles rising motion. This result is shown to be in fair agreement with experiment.

The theory is extended to non-spherical bubbles and the relation of the resulting theory, which enables both bubble shape and velocity of rise to be predicted, to experiment is discussed.

Finally, an inviscid model of the spherical cap bubble involving separated flow is considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 1 , July 1959 , pp. 113 - 130
Copyright
© 1959 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1956 J. Fluid Mech. 1, 388.
Davies, R. & Taylor, G. I. 1950 Proc. Roy. Soc. A, 200, 375.
Haberman, W. L. & Morton, R. K. 1953 David Taylor Model Basin, Rep. no. 802.
Hartunian, R. A. & Sears, W. R. 1957 J. Fluid Mech. 3, 27.
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Levinson, N. 1946 Annals of Math. 47, 704.
Moore, D. W. 1958 Ph.D. Thesis, Cambridge University.
Rosenberg, B. 1950 David Taylor Model Basin, Rep. no. 727.
Saffman, P. G. 1956 J. Fluid Mech. 1, 249.