Journal of Fluid Mechanics

Self-propulsion of asymmetrically vibrating bubbles

T. Brooke  Benjamin a1 and Albert T.  Ellis a2
a1 Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, UK
a2 Institute for Nonlinear Science, Department of Applied Mechanics and Engineering Sciences, B-010, University of California, La Jolla, CA 92093, USA

Article author query
benjamin tb   [Google Scholar] 
ellis at   [Google Scholar] 


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.

(Published Online April 26 2006)
(Received June 30 1989)