Abstract
An equation is proposed for the pulsation of a single cavity in an abnormally compressible bubbly liquid which is in pressure equilibrium and whose state is described by the Lyakhov equation. In the equilibrium case, this equation is significantly simplified. Numerical analysis is performed of the bubble dynamics and acoustic losses (the profile and amplitude of the radiation wave generated on the bubble wall from the side of the liquid). It is shown that as the volumetric gas concentration k0 in the equilibrium bubbly medium increases, the degree of compression of the cavity by stationary shock wave decreases and its pulsations decrease considerably and disappear already at k0 = 3%. In the compression process, the cavity asymptotically reaches an equilibrium state that does not depend on the value of k0 and is determined only by the shock-wave amplitude. The radiation wave takes the shape of a soliton whose amplitude is much smaller and whose width is considerably greater than the corresponding parameters in a single-phase liquid.
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References
S. V. Iordanskii, “On the equations of motion for liquids containing gas bubbles,” Prikl. Mekh. Tekh. Fiz., No. 3, 102–110 (1960).
B. S. Kogarko, “On one model of a cavitating liquid,” Dokl. Akad. Nauk SSSR, 137, No. 6, 1331–1333 (1961).
L. Van Wijngaarden, “On the equations of motion for mixtures of liquid and gas bubbles,” J. Fluid Mech., 33, 465–474 (1968).
V. K. Kedrinskii, “Propagation of perturbations in a liquid containing gas bubbles,” J. Appl. Mech. Tech. Phys., 4, 379–376 (1968).
V. E. Nakoryakov, B. G. Pokusaev, and I. R. Shreiber, Wave Dynamics of Gas-and Vapor-Liquid Media [in Russian], Energoatomizdat, Moscow (1990).
R. I. Nigmatulin, Foundations of the Mechanics of Heterogeneous Media [in Russian], Nauka, Moscow (1987).
V. K. Kedrinskii, Hydrodynamics of Explosion: Experiment and Models [in Russian], Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk (2000).
R. M. Garipov, “Closed equations for the motion of a liquid containing bubbles (survey),” J. Appl. Mech. Tech. Phys., No. 6, 737–756 (1973).
S. Fujikawa and H. Takahira, “A theoretical study on the interaction between two spherical bubbles and radiated pressure waves in a liquid,” J. Acust., 61, 188–199 (1986).
V. G. Gasenko, V. E. Nakoryakov, and I. R. Shreiber, “Two-wave model of the propagation of perturbations in a liquid with gas bubbles,” J. Appl. Mech. Tech. Phys., No. 6, 753–758 (1979).
G. M. Lyakhov, “Shock waves in multicomponent media,” Izv. Akad. Nauk SSSR, Ser. Mekh. Mashinostr., No. 1, 46–49 (1959).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 51–57, May–June, 2007.
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Kedrinskii, V.K. Dynamics and radiation of a single bubble under conditions of abnormal compressibility of a bubbly liquid. J Appl Mech Tech Phys 48, 340–345 (2007). https://doi.org/10.1007/s10808-007-0043-6
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DOI: https://doi.org/10.1007/s10808-007-0043-6