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Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid

Published online by Cambridge University Press:  20 April 2006

G. Ryskin
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125 Present address: Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60201.
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125

Abstract

In this paper numerical results are presented for the buoyancy-driven rise of a deformable bubble through an unbounded quiescent fluid. Complete solutions, including the bubble shape, are obtained for Reynolds numbers in the range 1 ≤ R ≤ 200 and for Weber numbers up to 20. For Reynolds numbers R ≤ 20 the shape of the bubble changes from nearly spherical to oblate-ellipsoidal to spherical-cap depending on Weber number; at higher Reynolds numbers ‘disk-like’ and ‘saucer-like’ shapes appear at W = O(10). The present results show clearly that flow separation may occur at a smooth free surface at intermediate Reynolds numbers; this fact suggests a qualitative explanation of the often-observed irregular (zigzag or helical) paths of rising bubbles.

Type
Research Article
Copyright
© 1984 Cambridge University Press

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