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Finite-Weber-number motion of bubbles through a nearly inviscid liquid

Published online by Cambridge University Press:  25 June 2002

VOLODYMYR I. KUSHCH ,
ASHOK S. SANGANI ,
PETER D. M. SPELT  and
DONALD L. KOCH
VOLODYMYR I. KUSHCH
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA
ASHOK S. SANGANI
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA
PETER D. M. SPELT
Affiliation:
Center for Composite Materials, Imperial College, London SW7 2BY, UK
DONALD L. KOCH
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

A method is described for computing the motion of bubbles through a liquid under conditions of large Reynolds and finite Weber numbers. Ellipsoidal harmonics are used to approximate the shapes of the bubbles and the flow induced by the bubbles, and a method of summing flows induced by groups of bubbles, using a fast multipole expansion technique is employed so that the computational cost increases only linearly with the number of bubbles. Several problems involving one, two and many bubbles are examined using the method. In particular, it is shown that two bubbles moving towards each other in an impurity-free, inviscid liquid touch each other in a finite time. Conditions for the bubbles to bounce in the presence of non-hydrodynamic forces and the time for bounce when these conditions are satisfied are determined. The added mass and viscous drag coefficients and aspect ratio of bubbles are determined as a function of bubble volume fraction and Weber number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 460 , 10 June 2002 , pp. 241 - 280
Copyright
© 2002 Cambridge University Press

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