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The two-dimensional elliptical cap bubble

Published online by Cambridge University Press:  29 March 2006

J. H. Hills
J. H. Hills
Affiliation:
Department of Chemical Engineering, University of Cambridge
Present address: Department of Chemical Engineering, University of Nottingham.
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Abstract

A study of the closed wakes behind large gas bubbles rising between two parallel plates reveals that they are elliptical in shape, rather than circular. Fitting an are of an ellipse, rather than a circle, to the curved upper surface of such a bubble eliminates a discrepancy between theory and experiment noted by Collins (1965a). Collins’ analysis of the effect of finite channel width is extended to the elliptical case, and the stability of the closed wake is examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 3 , 15 April 1975 , pp. 503 - 512
Copyright
© 1975 Cambridge University Press

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References

Collins R. 1965a J. Fluid Mech. 22, 763.
Collins R. 1965b Chem. Engng Sci. 20, 851.
Collins R. 1967 Chern. Engng Sci. 22, 89.
Collins R. 1968 Ph.D. thesis, University of London.
Crabtree, J. R. & Bridowater J. 1967 Chem. Engineering Sci. 22, 1517.
Davies, R. M. & Taylor G. I. 1950 Proc. Roy. Soc. A 200, 375.
Garabedian P. R. 1957 Proc. Roy. Soc. A 241, 423.
Garabedian P. R. 1961 Modern Mathematics for the Engineer, p. 365. McGraw-Hill.
Grace, J. R. & Harrison D. 1967 Chem. Engineering Sci. 22, 1337.
Haberman, W. L. & Morton R. K. 1953 David Taylor Model Basin Rep. no. 802.
Hills J. H. 1971 Ph.D. thesis, University of Cambridge.
Lamb H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Maxworthy T. 1967 J. Fluid Mech. 27, 367.
Moore D. W. 1959 J. Fluid Mech. 6, 113.
Wegener, P. P. & Parlange J. Y. 1973 Ann. Rev. Fluid Mech. 5, 79.