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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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References

Batchelor, G. K.: 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B.: 1964 Surface effects in non-spherical motions of small cavities. In Cavitation in Real liquids (ed. R. Davies), pp. 164–180. Elsevier.
Benjamin, T. B.: 1987 Hamiltonian theory for motions of bubbles in an infinite liquid. J. Fluid Mech. 181, 349–379.Google Scholar
Benjamin, T. B.: 1989 Note on shape oscillations of bubbles. J. Fluid Mech. 203, 419–424.Google Scholar
Benjamin, T. B. & Strasberg, M., 1958 Excitation of oscillations in the shape of pulsating gas bubbles; theoretical work. (Abstract) J. Acoust. Soc. Am. 30, 697.Google Scholar
Ciliberto, S. & Gollub, J. P., 1985 Chaotic mode competition in parametrically forced surface waves. J. Fluid Mech. 158, 381–398.Google Scholar
Ellis, A. T.: 1955 Production of accelerated cavitation damage by an acoustic field in a cylindrical cavity. J. Acoust. Soc. Am. 27, 913–921.Google Scholar
Ellis, A. T. & Benjamin, T. B., 1990 Behaviour of bubbles in liquids subject to intense sound fields. (In preparation.)
Gaines, N.: 1932 Magnetostriction oscillator producing intense audible sound and some effects obtained. Physics 3, 209–229.Google Scholar
Gollub, J. P. & Meyer, C. W., 1983 Symmetry-breaking instabilities on a fluid surface. Physica D 7, 153–180.Google Scholar
Hsieh, D.-Y. & Plesset, M. S. 1961 Theory of rectified diffusion of mass into gas bubbles. J. Acoust. Soc. Am. 33, 206–215.Google Scholar
Jeffreys, H. & Jeffreys, B. S., 1956 Methods of Mathematical Physics, 3rd edn. Cambridge University Press.
Kochin, N. E., Kibel, I. A. & Roze, N. V., 1964 Theoretical Hydromechanics. Interscience.
Kornfeld, M. & Suvorov, L., 1944 On the destructive action of cavitation. J. Appl. Phys. 15, 495–506.Google Scholar
Lamb, H.: 1932 Hydrodynamics, 6th edn. Cambridge University Press (Dover edition 1945).
Lighthill, M. J.: 1978 Waves in Fluids. Cambridge University Press.
Milne-Thomson, L. M.: 1968 Theoretical Hydrodynamics, 5th edn. Macmillan.
Plesset, M. S. & Mitchell, T. P., 1956 On the stability of the spherical shape of a vapor cavity in a liquid. Q. Appl. Maths 13, 419–430.Google Scholar
Saffman, P. G.: 1967 The self-propulsion of a deformable body in a perfect fluid. J. Fluid Mech. 28, 385–389.Google Scholar
Strasberg, M. & Benjamin, T. B., 1958 Excitation of oscillations in the shape of pulsating gas bubbles; experimental work. (Abstract) J. Acoust. Soc. Am. 30, 697.Google Scholar
Whittaker, E. T. & Watson, G. N., 1927 Modern Analysis, 4th edn. Cambridge University Press.