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The thermal behaviour of oscillating gas bubbles

Published online by Cambridge University Press:  26 April 2006

Andrea Prosperetti
Andrea Prosperetti
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

Several aspects of the oscillations of a gas bubble in a slightly compressible liquid are discussed by means of a simplified model based on the assumption of a spatially uniform internal pressure. The first topic considered is the linear initial-value problem for which memory effects and the approach to steady state are analysed. Large-amplitude oscillations are studied next in the limit of large and small thermal diffusion lengths obtaining, in the first case, an explicit expression for the internal pressure, and, in the second one, an integral equation of the Volterra type. The validity of the assumption of uniform pressure is then studied analytically and numerically. Finally, the single-bubble model is combined with a simple averaged-equation model of a bubbly liquid and the propagation of linear and weakly nonlinear pressure waves in such a medium is considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 587 - 616
Copyright
© 1991 Cambridge University Press

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References

Apfel, R. E.: 1981 Acoustic cavitation. In Methods of Experimental Physics, vol. 19, Ultrasonics (ed. P. D. Edmonds), pp. 355–411. Academic.
Bkoer, L. J. F.: 1964 On the interaction of non-linearity and dispersion in wave propagation. Appl. Sci. Res. B 11, 273–285.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L., 1985 Effective equation for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273.Google Scholar
Chapman, R. B. & Plesset, M. S., 1971 Thermal effects in the free oscillations of gas bubbles. Trans. ASME D: J. Basic Eng. 94, 142–145.Google Scholar
Crum, L. A. & Prosperetti, A., 1984 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
Devin, C.: 1959 Survey of thermal, radiation and viscous damping of pulsating air bubbles in water. J. Acoust. Soc. Am. 31, 1654–1667.Google Scholar
Fanelli, M., Prosperetti, A. & Reali, M., 1981a Radial oscillations of gas-vapour bubbles in liquids. Part I: Mathematical formulation. Acustica 47, 253–265.Google Scholar
Fanelli, M., Prosperetti, A. & Reali, M., 1981b Radial oscillations of gas-vapor bubbles in liquids. Part II: Numerical examples. Acustica 49, 98–109.Google Scholar
Fokas, A. S. & Yortos, Y. C., 1982 On the exactly solvable equation St = [(βS+γ)−2Sx], + α(βS+)−2Sx occurring in two-phase flow in porous media. SIAM J. Appl. Maths 42, 318–332.Google Scholar
Foldy, L. J.: 1945 The multiple scattering of waves. Phys. Rev. 67. 107–119.Google Scholar
Gorschkov, K. A., Ostrovsky, L. A. & Pelinovsky, E. N., 1974 Some problems of asymptotic theory of nonlinear waves. Proc. IEEE 62, 1511–1517.Google Scholar
Kamath, V., Oguz, H. N. & Prosperetti, A., 1990 Bubble oscillations in the nearly adiabatic limit. J. Acoust. Soc. Am. (To be submitted).Google Scholar
Kamath, V. & Prosperetti, A., 1989 Numerical integration methods in gas-bubble dynamics. J. Acoust. Soc. Am. 85, 1538–1548.Google Scholar
Keller, J. B. & Kolodner, I. I., 1956 Damping of underwater explosion bubble oscillations. J. Appl. Phys. 27, 1152–1161.Google Scholar
Keller, J. B. & Miksis, M. J., 1980 Bubble oscillations of large amplitude. J. Acoust. Soc. Am. 68, 628–633.Google Scholar
Lauterborn, W. & Parlitz, U., 1988 Methods of chaos physics and their application to acoustics. J. Acoust. Soc. Am. 84, 1975–1993.Google Scholar
Lauterborn, W. & Suchla, E., 1984 Bifurcation superstructure in a model of acoustic turbulence. Phys. Rev. Lett. 53, 2304–2307.Google Scholar
Lezzi, A. M. & Prosperetti, A., 1987 Bubble dynamics in a compressible liquid. Part 2. Second-order theory. J. Fluid Mech. 185, 289–321.Google Scholar
Miksis, M. J. & Ting, L., 1984 Nonlinear radial oscillations of a gas bubble including thermal effects. J. Acoust. Soc. Am. 76, 897–905.Google Scholar
Miksis, M. J. & Ting, L., 1987 A numerical study of thermal effects on nonlinear bubble oscillations. J. Acoust. Soc. Am. 81, 1331–1340.Google Scholar
Minnaert, M.: 1933 On musical air bubbles and the sounds of running water. Phil. Mag. 16, 235–248.Google Scholar
Nagiev, F. B. & Khabeev, N. S., 1979 Heat-transfer and phase-transition effects associated with oscillations of vapor-gas bubbles. Sov. Phys. Acoust. 25, 148–152.Google Scholar
Nigmatulin, R. I. & Khabeev, N. S., 1974 Heat Exchange between a gas bubble and a liquid. Fluid Dyn. 9, 759–764.Google Scholar
Nigmatulin, R. I. & Khabeev, N. S., 1977 Dynamics of vapor—gas bubbles. Fluid Dyn. 12, 867–871.Google Scholar
Nigmatulin, R. I., Khabeev, N. S. & Nagiev, F. B., 1981 Dynamics, heat and mass transfer of vapor-gas bubbles in a liquid. Int. J. Heat Mass Transfer 24, 1033–1044.Google Scholar
Plesset, M. S. & Prosperetti, A., 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 146–185.Google Scholar
Plesset, M. S. & Zwick, S. A., 1952 A nonsteady heat diffusion problem with spherical symmetry. J. Appl. Phys. 23, 95–98.Google Scholar
Prosperetti, A.: 1977 Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids. J. Acoust. Soc. Am. 61, 17–27.Google Scholar
Prosperetti, A.: 1980 Free oscillations of drops and bubbles; the initial-value problem. J. Fluid Mech. 100, 333–347.Google Scholar
Prosperetti, A.: 1981 Motion of two superposed viscous fluids. Phys. Fluids 24, 1217–1223.Google Scholar
Prosperetti, A.: 1984a Bubble phenomena in sound fields: part one. Ultrasonics 22, 69–77.Google Scholar
Prosperetti, A.: 1984b Bubble phenomena in sound fields: part two. Ultrasonics 22, 115–124.Google Scholar
Prosperetti, A.: 1986 Physics of acoustics cavitation. In Frontiers in Physical Acoustics (ed. D. Sette), pp. 145–188. North-Holland.
Prosperetti, A.: 1987 The equation of bubble dynamics in a compressible liquid. Phys. Fluids 30, 3626–3628.Google Scholar
Prosperetti, A., Crum, L. A. & Ceommander, K. W., 1988 Nonlinear bubble dynamics, J. Acoust. Soc. Am. 83, 502–514.Google Scholar
Prosperetti, A. & Kim, D. H., 1988 Pressure waves in bubbly liquids at small gas volume fractions. In Fundamentals of Gas-Liquid Flows (ed. E. E. Michaelides & M. P. Sharma), pp. 19–27. ASME.
Prosperetti, A. & Lezzi, A. M., 1986 Bubble dynamics in a compressible liquid. Part 1. First-order theory. J. Fluid Mech. 168, 457–478.Google Scholar
Smereka, P., Birnir, B. & Banerjee, S., 1987 Regular and chaotic bubble oscillations in periodically driven pressure fields. Phys. Fluids 30, 3342–3350.Google Scholar
Whitham, G. B.: 1974 Linear and Nonlinear Waves, pp. 460–471. Wiley.
Van Wijngaarden, L.: 1968 On equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33, 465–474.Google Scholar
Van Wijngaarden, L.: 1972 One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–396.Google Scholar