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Self-propulsion of asymmetrically vibrating bubbles

Published online by Cambridge University Press:  26 April 2006

T. Brooke Benjamin  and
Albert T. Ellis
T. Brooke Benjamin
Affiliation:
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, UK
Albert T. Ellis
Affiliation:
Institute for Nonlinear Science, Department of Applied Mechanics and Engineering Sciences, B-010, University of California, La Jolla, CA 92093, USA
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Abstract

The theory developed aims to explain erratic motions that have been observed experimentally to be performed by small bubbles in liquids irradiated by sound. An exact relation between dynamic and kinematic integral properties of any bubble is used as the basis for calculating the propulsive effects of deformations from spherical shape. The analysis deals first with arbitrary axisymmetric perturbations, such that the equation of the bubble's surface is representable in terms of zonal spherical harmonics, and then more general deformations are treated. It is shown that self-propulsion is accountable wholly to interactions of surface modes n and n+1 (n = 2, 3,…). The resulting velocity W of the bubble's centroid is found to depend on the relative orientation of the interacting modes, |W| being greatest when they are coaxial but the direction of W having the more sensitive dependence. Supported by the theoretical results, an interpretation of the observed erratic motions is presented finally, and a few experimental observations are noted.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 65 - 80
Copyright
© 1990 Cambridge University Press

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