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Bubble expansion rates in viscous compressible liquid
Earth, Planets and Space volume 58, pages 865–872 (2006)
A new equation has been derived for radial expansion of a bubble in viscous liquid, taking into account the compressibility of liquid. This model is important in understanding the time-evolution of the bubble growth in a cavitating flow. We solved the equation of motion of viscous liquid and obtained the velocity field and the pressure distribution in liquid. It is found that the expansion rate of a bubble in viscous compressible liquid is governed by the friction force due to viscosity as well as the surface tension, the inertial force, and the gas pressure. Further, the bubble expansion rate is brought by the same expression to that in an incompressible liquid only in the case that the liquid is in a hydrostatic state before the bubble grows.
Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, New York, 1967.
John, F., Partial Differential Equations, 4th edition, Springer-Verlag, New York, 1982.
Keller, B. J. and I. I. Kolodner, Damping of underwater explosion bubble oscillations, J. Appl. Phys., 27, 1152–1161, 1956.
Keller, B. J. and M. Miksis, Bubble oscillations of large amplitude, J. Acoust. Soc. Am., 68(2), 628–633, 1980.
Landau, L. D. and E. M. Lifshitz, Fluid Mechanics, 2nd edition, Butterworth-Heinemann, Oxford, 1987.
Lauterborn, W., Numerical investigation of nonlinear oscillations of gas bubbles in liquids, J. Acoust. Soc. Am., 59(2), 283–293, 1976.
Papale, P., Volcanic conduit dynamics, FROM MAGMA TO TEPHRA, Modelling Physical Processes of Explosive Volcanic Eruptions, Elsevier, Amsterdam, chapter 3, 2001.
Plesset, M. S., The dynamics of cavitation bubbles, J. Appl. Mech., 16, 277–282, 1949.
Plesset, M. S. and A. Prosperetti, Bubble dynamics and cavitation, Ann. Rev. Fluid Mech., 9, 145–185, 1977.
Prosperetti, A. and A. Lezzi, Bubble dynamics in a compressible liquid. Part 1. First-order theory, J. Fluid Mech., 168, 457–478, 1986.
Prosperetti, A., L. A. Crum, and K. W. Commander, Nonlinear bubble dynamics, J. Acoust. Soc. Am., 83(2), 502–514, 1988.
Proussevitch, A. A. and D. L. Sahagian, Dynamics and energetics of bubble growth in magmas: analytical formulation and numerical modeling, J. Geophys. Res., 103(B8), 18,223–18,251, 1998.
Rayleigh, L., On the pressure developed in a liquid during the collapse of a spherical cavity, Philos. Mag., 34, 94–98, 1917.
Scriven, L. E., On the dynamics of phase growth, Chem. Eng. Sci., 10, 1–13, 1959.
Sparks, R. S. J., The dynamics of bubble formation and growth in magmas: a review and analysis, J. Volcanol. Geotherm. Res., 3, 1–37, 1978.
Toramaru, A., Numerical study of nucleation and growth of bubbles in viscous magmas, J. Geophys. Res., 100(B2), 1913–1931, 1995.
Trilling, L., The collapse and rebound of a gas bubble, J. Appl. Phys., 23(1), 14–17, 1952.
Yamada, K., H. Tanaka, K. Nakazawa, and H. Emori, A new theory of bubble formation in magma, J. Geophys. Res., 110, B02203, doi:10.1029/2004JB003113, 2005.
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Yamada, K., Emori, H. & Nakazawa, K. Bubble expansion rates in viscous compressible liquid. Earth Planet Sp 58, 865–872 (2006). https://doi.org/10.1186/BF03351991