

BEHAVIOR OF BUBBLES IN A CLUSTER UNDER ACOUSTIC INFLUENCE
Gubaydullin A.A.^{1,2}, Gubkin A.S.^{1,2}
^{1} Khristianovich Institute Of Theoretical And Applied Mechanics SB RAS, Tyumen Branch, Tyumen, Russia ^{2} Tyumen State University, Tyumen, Russia
Citation:
Gubaydullin, A.A. and Gubkin, A.S., (2013) Behavior of bubbles in a cluster under acoustic influence, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(12), PP. 363  367.

Keywords: bubble cluster; compression wave; model of dynamic for bubble system; heat exchange of bubble with liquid 
Abstracts:
Behavior a single bubble in the compression waves into the group of bubbles may differ from the behavior of a single bubble in the inﬁnite liquid due to the collective hydrodynamic interaction. The mathematical model describing the dynamics of the system of bubbles changing radii in the inﬁnite ﬂuid with accounting compressibility and viscosity is given. Heat exchange between gas bubbles and liquid include by twotemperature scheme. The expression for the heat ﬂ ux which allows to describe a heat exchange between the gas bubbles and liquid in a sufﬁciently wide range of values of the pressure and temperature of the liquid is presented. A numeric simulation of the nonlinear dynamics is done for various conﬁ gurations of bubble clusters by effect of compression wave and harmonic perturbations various frequency. Behavior of the single bubble into the group of bubbles under effect of compression waves is investigated. It is shown that in certain conditions for some bubbles are achieved signiﬁcant degree of compression and, as a consequence, a signiﬁcant increase in pressure and temperature. Investigation of the behavior in the compression waves of a single bubble in the team bubbles is done. The example of clusters with three nested dodecahedrons and linear cluster shown that the cluster conﬁguration can have a strong impact on its dynamics. 
References:
Aganin A.A., Davledshin A.I. Modelirovanie vzaimodejstvija gazovih puzirkov v jidkosti s uchetom ih maloj nesferichnosti // Matematicheskoe modelirovanie. 2009. T. 21. # 6, S. 89102.
Voinov O.V., Golovin A.M. Uravnenija Lagranga dlja sistemi puzirej izmenjaushihsja radiusov v jidkosti maloj vjazkosti // Izv. AN SSSR. MJG.1970.  #3.  S. 117  123.
Stefan Luther, Robert Mettin and Werner Lauterborn. Modeling Acoustic Cavitation by a Lagrangian Approach.
Alexander A. Doinikov. Mathematical model for collective bubble dynamics in strong ultrasound fields // Acoustical Society of America.  2004. P. 821827.
Gubaidullin A.A., Nigmatulin N.I. Numerical simulation of Propagation of Shock Waves in Bubbly Liquids // Proceedings of The 2nd International Conference on Multiphase Flow '95Kyoto April 37, 1995.
Taleyarkhan R.P. Evidence for nuclear emissions during acoustic cavitation / Taleyarkhan R.P., West C.D., Lohey R.T., Nigmatulin R.I., Block R.C. // Science.  2002.  Vol.295, P.18681873.
Taleyarkhan R.P., West C.D., Lahey R.T. (Jr), Nigmatulin R.I., Block R.C., Xu Y. Nuclear Emissions During SelfNucleated Acoustic Cavitation // Phys. Review Let., 2006. V.96. 034301.
Amelkin S.V., Sannikov I.N. Dinamika puzirkov v klastere pri akusticheskom vozdejstvii // Dinamika sploshnoj sredi: Sb. nauch. tr. Institut gidrodinamiki SO RAN.  2002.  Vip. 121.  S. 7 11.
Rozhdestvenskij V.V. Kavitatsiya.  Leningrad: "Sudostroenie".  1977.
Nigmatulin R.I. Dinamika mnogofaznykh sred. Chast.1.  M: Nauka, Glav. izd.f.m. litry, 1987.  464 PP.


