Abstract
The evolution of a small distortion of the spherical shape of a gas bubble which undergoes strong radial expansion-compression upon a single oscillation of the ambient liquid pressure under a harmonic law are analyzed by numerical experiments. It is assumed that the distortions of the spherical bubble shape are axisymmetric and have the form of individual spherical surface harmonics with numbers of 2–5. Bubble-shape oscillations prior to the beginning of expansion are taken into account. Generally, the distortion value during bubble expansion-compression depends on the phase of bubble-shape oscillation at the beginning of the expansion (initial phase). Emphasis is placed on the dependence of the maximum distortions in the initial phase at certain characteristic times of bubble expansion-compression on the amplitude of the external excitation, liquid viscosity, and distortion mode (harmonic number). The parameters of the problem are typical of the stable periodic sonolumiescence of an individual air bubble in water at room temperature. An exception is the liquid pressure oscillation amplitude, which is varied up to values that are five times the static pressure. That large excitation amplitudes are beyond the stability threshold of periodic oscillations of spherical bubbles. Their consideration is of interest from the point of view of increasing the compression ratio of the bubble gas, i. e., increasing the maximum temperature and density achievable in the final compression stage.
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REFERENCES
B. P. Barber, R. A. Hiller, R. Lofstedt, et al., “Defining the unknowns of sonoluminescence,” Phys. Rep., 281, 65–143 (1997).
S. Hilgenfeldt, S. Grossman, and D. Lohse, “Sonoluminescence light emission,” Phys. Liquids, 11(6), 1318–1330 (1999).
A. A. Aganin and M. A. Ilgamov, “Dependence of bubble compression parameters on the external pressure, ” in: Dynamics of Multiphase Systems, Proc. Int. Conf. on Multiphase Systems, Ufa (2000), pp. 269–274.
V. A. Simonenko, V. N. Nogin, Y. A. Kucherenko, et al., “Single bubble collapse: Physics and prospects, ” ibid, pp. 306–315.
R. P. Taleyarkhan, C. D. West, J. S. Cho, et al., “Evidence for nuclear emissions during acoustic cavitation,” Science, 295, 1868–1873 (2002).
C. Seife, “‘Bubble fusion’ paper generates a tempest in a beaker,” ibid, pp. 1808–1809.
A. A. Aganin and M. A. Il’gamov, “Gas bubble dynamics in a viscous liquid with considerable distortions of the spherical shape,” in: Dynamics of Gas Bubbles and Aerosols [in Russian], Izd. Kazan. Gos. Univ., Kazan’, (2003), pp. 7–22.
S. J. Putterman and K. R. Weninger, Sonoluminescence: How bubbles turn sound into light,” Annu. Rev. Liquid Mech., 32, 445–476 (2000).
V. K. Andreev, Stability of Unsteady Free-Boundary Fluid Flows [in Russian], Nauka, Novosibirsk (1992).
M. S. Plesset and T. P. Mitchell, “On the stability of the spherical shape of a vapor cavity in a liquid,” Quart. J. Appl. Math., 13(4), 419–430 (1956).
O. V. Voinov and V. V. Perepelkin, “Stability of the surface of a gas bubble pulsating in a liquid, ” J. Appl. Mech. Tech. Phys., No.3, 410–416 (1989).
O. V. Voinov, “Breakdown of bubbles: Non-linear mechanisms and effects,” in: Proc. of the Third Int. Conf. on Multiphase Flow, ICMF’98, Lyon, France, June 8–12 (1998).
C. C. Wu and P. H. Roberts, “Bubble shape instability and sonoluminescence,” Phys. Lett. A, 250, 131–136 (1998).
A. Prosperetti, “Viscous effects on perturbed spherical ows,” Quart. Appl. Math., 34, 339–352 (1977).
J. B. Keller and M. Miksis, “Bubble oscillations of large amplitude,” J. Acous. Soc. Am., 68(2), 628–633 (1980).
E. Hairier, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations: Nonstiff Problems, Springer-Verlag (1987).
G. Taylor, “The instability of liquid surfaces when accelerated is perpendicular to their planes,” Proc. Roy. Soc., A201, 192 (1950).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 17–28, July–August, 2005.
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Aganin, A.A., Guseva, T.S. Evolution of a Small Distortion of the Spherical Shape of a Gas Bubble under Strong Expansion-Compression. J Appl Mech Tech Phys 46, 471–480 (2005). https://doi.org/10.1007/s10808-005-0098-1
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DOI: https://doi.org/10.1007/s10808-005-0098-1