Summary
This paper describes the non-spherical free and forced oscillations of a gas bubble in a compressible liquid. Generally two different cases of oscillations are possible: spherically radial motion and surface oscillations. The deviation from spherical shape is assumed to be small and is given by a spherical harmonic. Included in the theoretical model are the effect of surface tension, the compressibility of the liquid and the gas. Stability and threshold conditions for the shape oscillations are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. J. Rath, The influence of an inhomogeneous sound field on the translational motion and nonlinear radial oscillation of a cavitation gas bubble in a compressible liquid, Mechanics Research Communications 6, 4 (1979) 209–215.
R. T. Knapp, H. W. Daily, F. G. Hammit, Cavitation, Mc Graw-Hill, New York (1970).
K. J. Ebeling, Hochfrequenzholografie laser erzeugter und akustisch erzeugter Kavitationsblasen, Dissertation, Göttingen (1976).
H. J. Rath, Zum Einfluß der Kompressibilität des Fluides bei sphärisch schwingenden Glasblasen in Flüssigkeiten, Ingenieur Archiv 47 (1978) 383–390.
H. J. Rath, Free and forced oscillations of spherical gas bubbles and their translational motion in a compressible liquid, In: Cavitation and inhomogeneities in underwater acoustics, Ed. by W. Lauterborn, Springer Verlag, Berlin-New York (1980).
H. J. Rath, Über nichtlineare Schwingungen sphärisch schwingender Gasblasen in Flüssigkeiten unter Berücksichtigung der Kompressibilität des Fluides, Zeitschrift f. angew. Mathematik und Physik 30 (1979) 627–635.
J. B. Keller, I. I. Kolodner, Damping of underwater explosion bubble oscillations. Journal of Applied Physics 27, 10 (1956) 1152–1161.
H. J. Rath, Zur Kinematik sphärisch kavitierender Gasblasen und Problematik der Kavitationsschwellen in einem kompressiblen Fluid, Acustica 43, 4 (1979) 241–246.
G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, Proc. Roy. Soc. London A 201 (1950) 192–196.
A. M. Binnie, The stability of the surface of a cavitation bubble, Proc. Cambridge Phil. Soc. 49 (1953) 151–155.
M. S. Plesset, On the stability of fluid flows with spherical symmetry, Journal of Applied Physics 25, 1 (1954) 96–98.
M. Strasberg, The pulsation frequency of nonspherical gas bubbles in liquids, Journal of the Acoustical Soc. of Am. 25 (1953) 536.
M. Strasberg, Gas bubbles as sources of sound in liquids, Journal of the Acoustical Soc. of Amer. 28 (1956) 20–26.
G. I. Taylor, Proc. Roy. Soc. London A 186 (1946) 273–292.
G. Birkhoff, Note on Taylor instability, Quart. Appl. Math. 12 (1954) 306–309.
A. I. Eller, L. A. Crum, Instability of the motion of a pulsating bubble in a sound field, Journal of the Acoustical Soc. of Amer. 47, 3, 2 (1970) 762–767.
D. Y. Hsieh, M. S. Plesset, Journal of the Acoustical Soc. of Amer. 33 (1961) 206–215.
H. W. Strube, Numerische Untersuchungen zur Stabilität nichtsphärisch schwingender Blasen, Acustica 25 (1971) 289–302.
A. Prosperetti, G. Seminara, Linear stability of a growing or collapsing bubble in a slightly viscous liquid, Phys. of Fluids 21, 9 (1978) 1465–1470.
A. Prosperetti, Viscous effects on pertubed spherical flows, Quart. Appl. Math. 34 (1977) 339–352.
A. Francescutto, R. Nabergoj, Pulsation amplitude threshold for surface waves on oscillating bubbles, Acustica 41 (1978) 215–220.
M. Ceschia, R. Nabergoj, On the motion of a nearly spherical bubble in a viscous liquid, Phys. of Fluids 21, 1 (1978) 140–142.
M. Kornfeld, L. Suvorov, On the destructive action of cavitation, J. of Appl. Phys. 15 (1944) 495–506.
C. Hullin, Stabilitätsgrenze pulsierender Luftblasen in Wasser, Acustica 37 (1977) 64–73.
H. Lamb, Hydrodynamics, Dover Publications, New York (1945).
M. Minnaert, On musical air-bubbles and sounds of running water, Phil. Mag. 16 (1933) 235–248.
H. J. Rath, Eine analytische Lösung zur freien nichtlinear schwingenden Gasblase in einer kompressiblen Flüssigkeit, Acta Mechanica 34 (1979) 233–242.
G. J. Lastman, R. A. Wentzel, Cavitation of a bubble in an inviscid compressible liquid, with comparisons to a viscous incompressible liquid, Phys. of Fluids 22, 12 (1979) 2259–2266.
H. G. Flynn, Cavitation dynamics, I. A mathematical formulation, J. Acoust. Soc. Am. 57, 6 (1975) 1379–1396.
H. G. Flynn, Cavitation dynamics, II. Free pulsations and models for cavitation bubbles, J. Acoust. Soc. Am. 58, 6 (1975) 1160–1170.
D. Y. Hsieh, On the dynamics of nonspherical bubbles, J. Basic Engineering, Sept. (1972) 655–665.
D. Y. Hsieh, On thresholds for surface waves and subharmonics of an oscillating bubble, J. Acoust. Soc. Am. 56, 2 (1974) 392–393.
H. J. Rath, The stability of surface waves on non-spherical gas bubbles in compressible liquids, Mechanics Research Communications (1981) (in press).
H. J. Rath, Zur Stabilitätsgrenze nichtsphärisch pulsierender Gasblasen in kompressiblen Fluiden, Acustica (1981) (in press).
C. Herring, Theory of the pulsations of gas bubble produced by an underwater explosion, OSRD-Report 236 (1941).
Ch. Hayashi, Nonlinear oscillations in physical systems, Mc Graw-Hill Book Company, New York (1964).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rath, H.J. On the stability of gas bubbles oscillating non-spherically in a compressible liquid. J Eng Math 15, 161–170 (1981). https://doi.org/10.1007/BF00042777
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00042777