Sonochemistry and Sonoluminescence pp 39-62 | Cite as
Old-Fashioned Bubble Dynamics
Abstract
This chapter reviews some basic aspects of the dynamics of gas bubbles in liquids: the effect of liquid compressibility, thermal processes inside the bubble, the stability of the spherical shape, and acoustic radiation forces. Some remarks on sonoluminescence are also included.
The laws of nature are widely believed to be invariant under a time translation. One of the consequences of this property is that a paper published 50 or 100 years ago is not necessarily irrelevant or wrong. The purpose of the present work is to review some basic results in the theory of bubble dynamics in the belief that they may benefit newcomers to the field.
Keywords
Cavitation Bubble Sound Field Bubble Radius Bubble Surface Bubble DynamicPreview
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References
- 1.Landau, L.D. and Lifshitz, E.M. (1959) Fluid Mechanics,Pergamon.Google Scholar
- 2.Cole, R.H. (1948) Underwater explosions, Princeton U.P., Princeton. Reprinted by Dover, 1965.Google Scholar
- 3.Batchelor, G.K. (1967) An Introduction to Fluid Dynamics, Cambridge U.P., Cambridge.MATHGoogle Scholar
- 4.Prosperetti, A. and Lezzi, A. (1986) Bubble dynamics in a compressible liquid. Part 1. First-order theory, J. Fluid Mech. 168, 457–478.ADSCrossRefMATHGoogle Scholar
- 5.Lezzi, A. and Prosperetti, A. (1987) Bubble dynamics in a compressible liquid. Part 2. Second-order theory, J. Fluid Mech. 185, 289–321.ADSCrossRefGoogle Scholar
- 6.Prosperetti, A. (1987) The equation of bubble dynamics in a compressible liquid, Phys. Fluids 30, 3626–3628.ADSCrossRefMATHGoogle Scholar
- 7.Rohrlich, F. (1965) Classical Charged Particles, Addison-Wesley, Reading.MATHGoogle Scholar
- 8.Burke, W.L. (1970) Runaway solutions: remarks on the asymptotic theory of radiation damping, Phys. Rev. A2, 1501–1505.MathSciNetADSCrossRefGoogle Scholar
- 9.Jackson, J.D. (1975) Classical Electrodynamics, 2nd Ed., Wiley, New York.MATHGoogle Scholar
- 10.Prosperetti, A. (1980) The motion of a charged particle in a uniform magnetic field, Nuovo Cimento 57B, 253–268.MathSciNetCrossRefGoogle Scholar
- 11.Keller, J.B. and Kolodner, I.I. (1956) Damping of underwater explosion bubble oscillations, J. Appl. Phys. 27, 1152–1161.ADSCrossRefGoogle Scholar
- 12.Keller, J.B. and Miksis, M.J. (1980) Bubble oscillations of large amplitude, J. Acoust. Soc. Am. 68, 628–633.ADSCrossRefMATHGoogle Scholar
- 13.Trilling, L. (1952) The collapse and rebound of a gas bubble, J. Appl. Phys. 23, 14–17.MathSciNetADSCrossRefGoogle Scholar
- 14.Poliman, U. (1989) Extension of the improved Gilmore equation of Lastman and Wentzell for a vapor bubble with respect to the mass-transfer at the bubble-wall, Acustica 68, 241–250.Google Scholar
- 15.Aymé-Bellegarda, E.J. (1990) Collapse and rebound of a gas-filled spherical bubble immersed in a diagnostic sound field, J. Acoust. Soc. Am. 88, 1054–1060.ADSCrossRefGoogle Scholar
- 16.Barbbne, P.E., Nadim, A., and Goldman, D. (1994) Compressibility in bubble dynamics and scattering, J. Acoust. Soc. Am. 96, 3253.ADSCrossRefGoogle Scholar
- 17.Moss, W.C. (1997) Understanding the periodic driving pressure in the RayleighPlesset equation, J. Acoust. Soc. Am. 101, 1187–1190.ADSCrossRefGoogle Scholar
- 18.Nigmatulin, R.I., Khabeev, N.S., and Nagiev, F.B. (1981) Dynamics, heat, and mass transfer of vapour-gas bubbles in a liquid, Int. J. Heat Mass Transfer 24, 1033–1044.CrossRefMATHGoogle Scholar
- 19.Fanelli, M., Prosperetti, A., and Reali, M. (1981) Radial oscillations of gas-vapor bubbles in liquids. Part I. Mathematical formulation, Acustica 47, 253–265.MATHGoogle Scholar
- 20.Fanelli, M., Prosperetti, A., and Reali, M. (1981) Radial oscillations of gas-vapor bubbles in liquids. Part II. Numerical examples, Acustica 49, 98–109.MATHGoogle Scholar
- 21.Kamath, V., Prosperetti, A., and Egolfopoulos, F. (1993) A theoretical study of sonoluminescence, J. Acoust. Soc. Am. 93, 248–260.ADSCrossRefGoogle Scholar
- 22.Nigmatulin, R.I. and Khabeev, N.S. (1974) Heat exchange between a gas, bubble and a liquid, Fluid Dyn. 9, 759–764.ADSCrossRefGoogle Scholar
- 23.Prosperetti, A., Crum, L.A., and Commander, K.W. (1988) Nonlinear bubble dynamics, J. Acoust. Soc. Am. 83, 502–514.ADSCrossRefGoogle Scholar
- 24.Prosperetti, A. (1991) The thermal behaviour of oscillating gas bubbles, J. Fluid Mech. 222, 587–616.MathSciNetCrossRefMATHGoogle Scholar
- 25.Löfstedt, R., Barber, B.P., and Putterman, S.J. (1993) Toward a hydrodynamic theory of sonoluminescence, Phys. Fluids A5, 2911–2928.ADSCrossRefMATHGoogle Scholar
- 26.Barber, B.P., Hiller, R.A., Löfstedt, R., Putterman, S.J. and Weninger, K.R. (1997) Defining the unknowns of sonoluminescence, Phys. Rep. 281, 66–143.ADSCrossRefGoogle Scholar
- 27.Verrall, R.E. and Sehgal, C.M. (1988) Sonoluminescence, in Suslick, K.S. (ed.), Ultrasound: its Chemical, Physical, and Biological Effects, VCH, New York, pp. 227–286.Google Scholar
- 28.Suslick, K.S. (1990) Sonochemistry, Science 247, 1439–1445.ADSCrossRefGoogle Scholar
- 29.Flint, E.B. and Suslick, K.S. (1991) The temperature of cavitation, Science 253, 1397–1399.ADSCrossRefGoogle Scholar
- 30.Watanabe, M. and Prosperetti, A. (1994) Shock waves in dilute bubbly liquids, J. Fluid Mech. 274, 349–381.MathSciNetADSCrossRefMATHGoogle Scholar
- 31.Löfstedt, R, Weninger, K., Putterman, S., and Barber, B.P. (1995) Sonoluminescing bubbles and mass diffusion, Phys. Rev. E 51, 4400–4410.ADSCrossRefGoogle Scholar
- 32.Kameda, M. and Matsumoto, Y. (1996) Shock waves in a liquid containing small gas bubbles, Phys. Fluids 8, 322–335.MathSciNetADSCrossRefGoogle Scholar
- 33.Kameda, M., Shimaura, N., Higashino, F., and Matsumoto, Y. (1997) Shock waves in a uniform bubbly flow, Phys. Fluids, submitted.Google Scholar
- 34.Crum, L.A. and Prosperetti, A. (1983) Erratum and comments on “Nonlinear oscillations of gas bubbles in liquids: An interpretation of some experimental results”, J. Acoust. Soc. Am. 75, 1910–1912.Google Scholar
- 35.Holt, R.G. and Crum, L.A. (1992) Acoustically forced oscillations of air bubbles in water: Experimental results, J. Acoust. Soc. Am. 91, 1924–1932.ADSCrossRefGoogle Scholar
- 36.Miksis, M.J. and Ting, L. (1984) Nonlinear radial oscillations of a gas bubble including thermal effects, J. Acoust. Soc. Am. 76, 897–905; Miksis, M.J. and Ting, L. (1987) A numerical study of thermal effects on nonlinear bubble oscillations, J. Acoust. Soc. Am. 81, 1331–1340.ADSCrossRefGoogle Scholar
- 37.Kamath, V., Oguz, H.N., and Prosperetti, A. (1992) Bubble oscillations in the nearly adiabatic limit, J. Acoust. Soc. Am. 92, 2016–2023.ADSCrossRefGoogle Scholar
- 38.Yuan, H. and Prosperetti, A. (1997) Gas-liquid heat transfer in a bubble collapsing near a wall, Phys. Fluids 9, 127–142.ADSCrossRefGoogle Scholar
- 39.Crum, L.A. and Nordling, D.A. (1972) Velocity of transient cavities in an acoustic stationary wave, J. Acoust. Soc. Am. 52, 294–301.ADSCrossRefGoogle Scholar
- 40.Plesset, M.S. (1954) On the stability of fluid flows with spherical symmetry, J. Appl. Phys. 25, 96–98.MathSciNetADSCrossRefMATHGoogle Scholar
- 41.Feng, Z.C. and Leal, L.G. (1997) Nonlinear bubble dynamics, Ann. Rev. Fluid Mech. 29, 201–243.MathSciNetADSCrossRefGoogle Scholar
- 42.Strasberg, M. and Benjamin, T.B. (1958) Excitation of oscillations in the shape of pulsating bubbles — experimental work, J. Acoust. Soc. Am. 30, 697.ADSCrossRefGoogle Scholar
- 43.Eller, A.I. Crum, L.A. (1970) Instability of the motion of a pulsating bubble in a sound field, J. Acoust. Soc. Am. 47, 762–767.ADSCrossRefGoogle Scholar
- 44.Benjamin, T.B. and Ellis, A.T. (1990) Self-propulsion of asymmetrically vibrating bubbles, J. Fluid Mech. 212, 65–80.ADSCrossRefMATHGoogle Scholar
- 45.Longuet-Higgins, M.S. (1989) Monopole emission of sound by asymmetric bubble oscillations. part i. normal modes, J. Fluid Mech. 201, 543–565.MathSciNetADSCrossRefMATHGoogle Scholar
- 46.Brenner, M.P., Lohse, D., and Dupont, T.F. (1995) Bubble shape oscillations and the onset of sonoluminescence, Phys. Rev. Lett. 75, 954–957.ADSCrossRefGoogle Scholar
- 47.Weninger, K.R., Barber, B.P., and Putterman, S.J. (1997), Pulsed Mie scattering measurements of the collapse of a sonoluminescing bubble, Phys. Rev. Lett. 78, 1799–1802.ADSCrossRefGoogle Scholar
- 48.Benjamin, T.B. and Ellis, A.T. (1966) The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries, Philos. Trans. R. Soc. London A260, 221–240.ADSCrossRefGoogle Scholar
- 49.Blake, J.R. and Gibson, D.C. (1987) Cavitation bubbles near boundaries, Ann. Rev. Fluid Mech. 19, 99–123.ADSCrossRefGoogle Scholar
- 50.Best, J.P. and Blake, J.R. (1994) An estimate of the Kelvin impulse of a transient cavity, J. Fluid Mech. 261, 75–93.MathSciNetADSCrossRefMATHGoogle Scholar
- 51.Prosperetti, A. (1997) A new mechanism for sonoluminescence, J. Acoust. Soc. Am. 101, 2003–2007.ADSCrossRefGoogle Scholar
- 52.Weninger, K.R., Barber, B.P., and Putterman, S.J. (1997), UCLA preprint.Google Scholar
- 53.Ohl, C.D. and Lindau, O. and Lauterborn, W. (1997) Luminescence from spherically and aspherically collapsing laser-induced bubbles, University of Göttingen preprint.Google Scholar
- 54.Gaitan, D.F. and Crum, L.A. (1990) Observation of sonoluminescence from a single, stable cavitation bubble in a water/glycerine mixture, in Hamilton, M. & Black-stock, D.T. (eds.), Frontiers in Nonlinear Acoustics, New York, Elsevier, pp. 459463.Google Scholar
- 55.Gaitan, D.F., Crum, L.A., Church, C.C., and Roy, R.A. (1992) Sonoluminescence and bubble dynamics from a single, stable, cavitation bubble, J. Acoust. Soc. Am. 91, 3166–3183.ADSCrossRefGoogle Scholar
- 56.Chambers, L.A. (1937) The emission of visible light from cavitated liquids, J. Chem. Phys. 5, 290–292.ADSCrossRefGoogle Scholar
- 57.Hiller, R.A. and Putterman, S.J. (1995) Observation of isotope effects in sonoluminescence, Phys. Rev. Lett. 75, 3549–3551. Erratum ibid., vol. 77, p. 2345, 1996.CrossRefGoogle Scholar
- 58.Flint, E.B. and Suslick, K.S. (1991) Sonoluminescence from alkali-metal salt solutions, J. Phys. Chem. 95, 1484–1488.CrossRefGoogle Scholar
- 59.Walton, A.J. (1977) Triboluminescence, Adv. Phys. 26, 887–948.ADSCrossRefGoogle Scholar
- 60.Chapman, G.N. and Walton, A.J. (1983) Triboluminescence of glasses and quartz, J. Appl. Phys. 54, 5961–5965.ADSCrossRefGoogle Scholar
- 61.Sweeting, L.M., Rheingold, A.L., Gingerich, J.M., Rutter, A.W., Spence, R.A., Cox, C.D., and Kim, T.J. (1997) Crystal structure and triboluminescence 2. 9Anthracenecarboxylic acid and its ethers, Chem. Mater. 9, 1103–1115.CrossRefGoogle Scholar
- 62.Jarman, P. (1960) Sonoluminescence: A discussion, J. Acoust. Soc. Am. 32, 1459 1462.Google Scholar
- 63.Finch, R.D. (1963) Sonoluminescence, Ultrasonics April-June, 87–98.Google Scholar
- 64.Peterson, F.B. and Anderson, T.P. (1967) Light emission from hydrodynamic cavitation, Phys. Fluids 10, 874–879.Google Scholar
- 65.van der Meulen, J.H.J. (1985) The relation between noise and luminescence from cavitation on a hydrofoil, in Proceedings of the ASME Symposium on Cavitation in Hydraulic Structures and Turbomachinery A.S.M.E., New York, 149–159.Google Scholar