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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
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
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125


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.

Research Article
© 1984 Cambridge University Press

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