Journal of Fluid Mechanics

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

G.  Ryskin a1p1 and L. G.  Leal a1
a1 Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125

Article author query
ryskin g   [Google Scholar] 
leal lg   [Google Scholar] 


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 [less-than-or-equal] R [less-than-or-equal] 200 and for Weber numbers up to 20. For Reynolds numbers R [less-than-or-equal] 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.

(Published Online April 20 2006)
(Received April 11 1983)
(Revised April 27 1984)

p1 Present address: Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60201.

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