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: 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.
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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)
Lord Rayleigh, On the pressure developed in a liquid during the collapse of a spherical cavity, Philos. Mag. 34, 94–96 (1917)
G. Birkhoff and E. H. Zarantonello, Jets, Wakes and Cavities, Academic Press, New York, 1957
M. S. Plesset, Cavitation in Real Liquids, R. Davies, ed., Elsevier, Amsterdam, 1964, p. 1
D. J. Evans and G. P. Morris, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, New York, 1990
M. P. Allen and D. Tildesley, Computer Simulation of Liquids, Clarendon, Oxford, 1987
M. S. Plesset and A. Prosperetti, Bubble dynamics and cavitation, Ann. Rev. Fluid Mech. 9, 145–185 (1977)
H. S. Fogler and J. D. Goddard, Collapse of spherical cavities in viscoelastic fluids, Phys. Fluids 13, 1135–1141 (1970)
A. Prosperetti, A generalization of the Rayleigh-Plesset equation of bubble dynamics, Phys. Fluids 25, 409–410 (1982)
R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics, 2nd ed., Wiley, New York, 1987
C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell’s Kinetic Theory of a Simple Monoatomic Gas, Academic Press, New York, 1980
R. Zwanzig, Nonlinear shear viscosity of a gas, J. Chem. Phys. 71, 4416–4420 (1979)
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)
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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© Copyright 1993
American Mathematical Society
