Geodesic
Nonlinear radial oscillations and spatial translations of a~nonspherical gas bubble in a~liquid
Matematičeskoe modelirovanie, Tome 23 (2011) no. 5, pp. 56-70.

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A mathematical model of dynamics of a gas bubble in a liquid with non-small distortions of its spherical shape has been developed with allowing for the spatial translations of the bubble, influence of the gravitational force and the liquid velocity. The liquid viscosity and compressibility are taken into account approximately. It has been shown that in some particular cases the derived equations are coincident with those obtained by the other authors. Some results of solving the problem of oscillations of moving nonspherical bubble under periodic variation of the liquid pressure are presented.
Keywords: a nonspherical gas bubble, potential flow of fluid, nonlinear oscillations. 
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A. A. Aganin; L. A. Kosolapova; V. G. Malakhov. Nonlinear radial oscillations and spatial translations of a~nonspherical gas bubble in a~liquid. Matematičeskoe modelirovanie, Tome 23 (2011) no. 5, pp. 56-70. http://geodesic.mathdoc.fr/item/MM_2011_23_5_a3/

[1] Plesset M. S., Prosperetti A., “Bubble dynamics and cavitation”, Annu. Rev. Fluid Mech., 9 (1977), 145–185 | DOI | Zbl

[2] Feng Z. C., Leal L. G., “Nonlinear bubble dynamics”, Annu. Rev. Fluid Mech., 29 (1997), 201–242 | DOI | MR

[3] Feng Z. C., Leal L. G., “Translation instability of a bubble undergoing shape oscillations”, Phys. Fluids, 7:6 (1995), 1325–1336 | DOI | Zbl

[4] Doinikov A. A., “Translational motion of a bubble undergoing shape oscillations”, J. Fluid. Mech., 501 (2004), 1–24 | DOI | MR | Zbl

[5] Levich V. G., Fiziko-khimicheskaya gidrodinamika, Gos. izd-vo f.-m. liter., M., 1959, 700 pp.

[6] Show S. J., “Translation and oscillation of a bubble under axisymmetric deformation”, Physics of fluids, 18 (2006), 072104, 15 pp. | DOI | MR

[7] Mettin R., Doinikov A. A., Translational instability of a spherical bubble in a standing ultrasound wave, Preprint submitted in Elsevier 21 November 2008, 18 pp.

[8] Aganin A. A., Ilgamov M. A., Kosolapova L. A., Malakhov V. G., “Nelineinye nesfericheskie kolebaniya puzyrka gaza pri periodicheskom izmenenii davleniya okruzhayuschei zhidkosti”, Teplofizika i aeromekhanika, 15:3 (2008), 521–533

[9] Nigmatullin R. I., Akhatov I. Sh., Vakhitova N. K., “O szhimaemosti zhidkosti v dinamike gazovogo puzyrka”, Dokl. RAN, 348:6 (1996), 768–771 | MR

[10] Ilgamov M. A., Aganin A. A., Kosolapova L. A. i dr., “Modeli dinamiki nesfericheskogo puzyrka s uchetom vyazkosti zhidkosti”, Modeli mekhaniki sploshnoi sredy, Materialy 16-i sessii Mezhdunar. shkoly po modelyam mekhaniki sploshnoi sredy, Tr. Mat. Tsentra im. N. I. Lobachevskogo, 16, Izd-vo Kazan. mat. ob-va, Kazan, 2002, 192–201

[11] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990, 512 pp. | MR

[12] Voinov O. V., Petrov A. G., “Dvizhenie sfery peremennogo ob'ema v idealnoi zhidkosti okolo ploskoi poverkhnosti”, Mekhanika zhidkosti i gaza, 1971, no. 5, 94–103