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The boundary layer on a spherical gas bubble

Published online by Cambridge University Press:  28 March 2006

D. W. Moore
D. W. Moore
Affiliation:
Department of Mathematics, Bristol University
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Abstract

The equations governing the boundary layer on a spherical gas bubble rising steadily through liquid of small viscosity are derived. These equations are linear are linear and are solved in closed form. The boundary layer separates at the rear stagnation point of the bubble to form a thin wake, whose structure is determined. Thus the drag force can be calculated from the momentum defect. The value obtained is 12πaaUμ, where a is the bubble radius and U the terminal velocity, and this agrees with the result of Levich (1949) who argued from the viscous dissipation in the potential flow round the bubble. The next term in an expansion of the drag in descending fractional powers of R is found and the results compared with experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 16 , Issue 2 , June 1963 , pp. 161 - 176
Copyright
© 1963 Cambridge University Press

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References

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Levich, V. 1949 Zh. Eksptl. i Teoret. Fiz. 19, 18.
Moore, D. W. 1959 J. Fluid Mech. 6, 113.