Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Collapse of spherical bubbles in fluids with nonlinear viscosity


Authors: M. A. Brutyan and P. L. Krapivsky
Journal: Quart. Appl. Math. 51 (1993), 745-749
MSC: Primary 76D99
DOI: https://doi.org/10.1090/qam/1247438
MathSciNet review: MR1247438
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Abstract | References | Similar Articles | Additional Information

Abstract: An analysis is given of the collapse of a spherical bubble in a large body of a viscous incompressible fluid with strain-dependent nonlinear viscosity. Two types of asymptotic behaviors are found analytically, namely the collapse over finite time and viscous damping over infinite time.


References [Enhancements On Off] (What's this?)

  • [1] Lord Rayleigh, On the pressure developed in a liquid during the collapse of a spherical cavity, Philos. Mag. 34, 94-96 (1917)
  • [2] Garrett Birkhoff and E. H. Zarantonello, Jets, wakes, and cavities, Academic Press Inc., Publishers, New York, 1957. MR 0088230
  • [3] Milton S. Plesset, Bubble dynamics, Cavitation in Real Liquids (Proc. Sympos., General Motors Res. Lab., War ren, Mich., 1962) Elsevier, Amsterdam, 1964, pp. 1–18. MR 0183201
  • [4] D. J. Evans and G. P. Morris, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, New York, 1990
  • [5] M. P. Allen and D. Tildesley, Computer Simulation of Liquids, Clarendon, Oxford, 1987
  • [6] M. S. Plesset and A. Prosperetti, Bubble dynamics and cavitation, Ann. Rev. Fluid Mech. 9, 145-185 (1977)
  • [7] H. S. Fogler and J. D. Goddard, Collapse of spherical cavities in viscoelastic fluids, Phys. Fluids 13, 1135-1141 (1970)
  • [8] A. Prosperetti, A generalization of the Rayleigh-Plesset equation of bubble dynamics, Phys. Fluids 25, 409-410 (1982)
  • [9] R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics, 2nd ed., Wiley, New York, 1987
  • [10] C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell’s kinetic theory of a simple monatomic gas, Pure and Applied Mathematics, vol. 83, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. Treated as a branch of rational mechanics. MR 554086
  • [11] R. Zwanzig, Nonlinear shear viscosity of a gas, J. Chem. Phys. 71, 4416-4420 (1979)
  • [12] A. Santos, J. J. Brey, and J. M. Dufty, Divergence of the Chapman-Enskog expansion, Phys. Rev. Lett. 56, 1571-1574 (1986); J. Gomez Ordonez, J. J. Brey, and A. Santos, Velocity distribution function of a dilute gas under uniform shear flow. A comparison between a Monte Carlo simulation method and the BGK equation, Phys. Rev. A (3) 41, 810-815 (1990)
  • [13] J. Gomez Ordonez, J. J. Brey, and A. Santos, Shear-rate dependence of the viscosity for dilute gases, Phys. Rev. A (3) 39, 3038-3040 (1989)

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DOI: https://doi.org/10.1090/qam/1247438
Article copyright: © Copyright 1993 American Mathematical Society


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