Skip to main content
×
Home
    • Aa
    • Aa

The thermal behaviour of oscillating gas bubbles

  • Andrea Prosperetti (a1)
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.

Copyright
References
Hide All
Apfel, R. E.: 1981 Acoustic cavitation. In Methods of Experimental Physics, vol. 19, Ultrasonics (ed. P. D. Edmonds), pp. 355411. Academic.
Bkoer, L. J. F.: 1964 On the interaction of non-linearity and dispersion in wave propagation. Appl. Sci. Res. B 11, 273285.
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L., 1985 Effective equation for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259273.
Chapman, R. B. & Plesset, M. S., 1971 Thermal effects in the free oscillations of gas bubbles. Trans. ASME D: J. Basic Eng. 94, 142145.
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, 19101912.
Devin, C.: 1959 Survey of thermal, radiation and viscous damping of pulsating air bubbles in water. J. Acoust. Soc. Am. 31, 16541667.
Fanelli, M., Prosperetti, A. & Reali, M., 1981a Radial oscillations of gas-vapour bubbles in liquids. Part I: Mathematical formulation. Acustica 47, 253265.
Fanelli, M., Prosperetti, A. & Reali, M., 1981b Radial oscillations of gas-vapor bubbles in liquids. Part II: Numerical examples. Acustica 49, 98109.
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, 318332.
Foldy, L. J.: 1945 The multiple scattering of waves. Phys. Rev. 67. 107119.
Gorschkov, K. A., Ostrovsky, L. A. & Pelinovsky, E. N., 1974 Some problems of asymptotic theory of nonlinear waves. Proc. IEEE 62, 15111517.
Kamath, V., Oguz, H. N. & Prosperetti, A., 1990 Bubble oscillations in the nearly adiabatic limit. J. Acoust. Soc. Am. (To be submitted).
Kamath, V. & Prosperetti, A., 1989 Numerical integration methods in gas-bubble dynamics. J. Acoust. Soc. Am. 85, 15381548.
Keller, J. B. & Kolodner, I. I., 1956 Damping of underwater explosion bubble oscillations. J. Appl. Phys. 27, 11521161.
Keller, J. B. & Miksis, M. J., 1980 Bubble oscillations of large amplitude. J. Acoust. Soc. Am. 68, 628633.
Lauterborn, W. & Parlitz, U., 1988 Methods of chaos physics and their application to acoustics. J. Acoust. Soc. Am. 84, 19751993.
Lauterborn, W. & Suchla, E., 1984 Bifurcation superstructure in a model of acoustic turbulence. Phys. Rev. Lett. 53, 23042307.
Lezzi, A. M. & Prosperetti, A., 1987 Bubble dynamics in a compressible liquid. Part 2. Second-order theory. J. Fluid Mech. 185, 289321.
Miksis, M. J. & Ting, L., 1984 Nonlinear radial oscillations of a gas bubble including thermal effects. J. Acoust. Soc. Am. 76, 897905.
Miksis, M. J. & Ting, L., 1987 A numerical study of thermal effects on nonlinear bubble oscillations. J. Acoust. Soc. Am. 81, 13311340.
Minnaert, M.: 1933 On musical air bubbles and the sounds of running water. Phil. Mag. 16, 235248.
Nagiev, F. B. & Khabeev, N. S., 1979 Heat-transfer and phase-transition effects associated with oscillations of vapor-gas bubbles. Sov. Phys. Acoust. 25, 148152.
Nigmatulin, R. I. & Khabeev, N. S., 1974 Heat Exchange between a gas bubble and a liquid. Fluid Dyn. 9, 759764.
Nigmatulin, R. I. & Khabeev, N. S., 1977 Dynamics of vapor—gas bubbles. Fluid Dyn. 12, 867871.
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, 10331044.
Plesset, M. S. & Prosperetti, A., 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 146185.
Plesset, M. S. & Zwick, S. A., 1952 A nonsteady heat diffusion problem with spherical symmetry. J. Appl. Phys. 23, 9598.
Prosperetti, A.: 1977 Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids. J. Acoust. Soc. Am. 61, 1727.
Prosperetti, A.: 1980 Free oscillations of drops and bubbles; the initial-value problem. J. Fluid Mech. 100, 333347.
Prosperetti, A.: 1981 Motion of two superposed viscous fluids. Phys. Fluids 24, 12171223.
Prosperetti, A.: 1984a Bubble phenomena in sound fields: part one. Ultrasonics 22, 6977.
Prosperetti, A.: 1984b Bubble phenomena in sound fields: part two. Ultrasonics 22, 115124.
Prosperetti, A.: 1986 Physics of acoustics cavitation. In Frontiers in Physical Acoustics (ed. D. Sette), pp. 145188. North-Holland.
Prosperetti, A.: 1987 The equation of bubble dynamics in a compressible liquid. Phys. Fluids 30, 36263628.
Prosperetti, A., Crum, L. A. & Ceommander, K. W., 1988 Nonlinear bubble dynamics, J. Acoust. Soc. Am. 83, 502514.
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. 1927. ASME.
Prosperetti, A. & Lezzi, A. M., 1986 Bubble dynamics in a compressible liquid. Part 1. First-order theory. J. Fluid Mech. 168, 457478.
Smereka, P., Birnir, B. & Banerjee, S., 1987 Regular and chaotic bubble oscillations in periodically driven pressure fields. Phys. Fluids 30, 33423350.
Whitham, G. B.: 1974 Linear and Nonlinear Waves, pp. 460471. Wiley.
Van Wijngaarden, L.: 1968 On equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33, 465474.
Van Wijngaarden, L.: 1972 One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369396.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 66 *
Loading metrics...

Abstract views

Total abstract views: 257 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd October 2017. This data will be updated every 24 hours.