Dynamics of gas bubbles under acoustic excitation

I. A. Aganin ; A. I. Davletshin

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 3, pp. 448-461

Résumé

The dynamics of two gas (air) bubbles in liquid (water) under the action of an ultrasonic traveling wave has been considered. The wave propagates along the straight passing through the bubble centers. The dependencies of the dynamics of the bubbles on the distance between them, their total gas mass, and wave amplitude have been studied for different bubble size ratios under a fixed total gas mass. A mathematical model taking into account the small nonsphericity of the bubbles, liquid viscosity, and compressibility has been used. Three bubble interaction scenarios have been shown to arise: collision of the bubbles, their divergence, and destruction of one of them due to its large deformations. The ranges of the wave amplitude, distance between the bubbles, ratio of their sizes, and value of the total mass of the gas contained in the bubble in which those scenarios are realized have been determined.

Détail

Keywords: dynamics of gas bubbles in liquid, hydrodynamic interaction of bubbles, ultrasonic traveling wave.

Bibliographie

[1] Putterman S. J., Weninger K. P., “Sonoluminescence: How bubbles turn sound into light”, Annu. Rev. Fluid Mech, 32 (2000), 445–476 | DOI | Zbl

[2] Taleyarkhan R. P., West C. D., Cho J. S., Lahey R. T. (Jr.), Nigmatulin R. I., Block R. C., “Evidence for nuclear emissions during acoustic cavitation”, Science, 295:5561 (2002), 1868–1873 | DOI

[3] Taleyarkhan R. P., West C. D., Lahey R. T. (Jr.), Nigmatulin R. I., Block R. C., Xu Y., “Nuclear emissions during self-nucleated acoustic cavitation”, Phys. Rev. Lett., 96:3 (2006), 034301, 1–4 pp. | DOI

[4] Parlitz U., Mettin R., Luther S., Akhatov I., Voss M., Lauterborn W., “Spatio-temporal dynamics of acoustic cavitation bubble clouds”, Philos. Trans. R. Soc., A, 357:1751 (1999), 313–334 | DOI | MR

[5] Kieser B., Phillion R., Smith S., McCartney T., “The application of industrial scale ultrasonic cleaning to heat exchangers”, Proc. Int. Conf. on Heat Exchanger Fouling and Cleaning, eds. M. R. Malayeri, H. Muller-Steinhagen, A. P. Watkinson, 2011, 336–338

[6] Vetrimurugana R., “Optimization of hard disk drive heads cleaning by using ultrasonics and prevention of its damage”, APCBEE Procedia, 3 (2012), 222–230 | DOI

[7] Mason T. J., “Ultrasonic cleaning: An historical perspective”, Ultrason. Sonochem, 29 (2016), 519–523 | DOI

[8] Suslick K. S., “Sonochemistry”, Science, 247 (1990), 1439–1445 | DOI

[9] Miller D. L., Quddus J., “Diagnostic ultrasound activation of contrast agent gas bodies induces capillary rupture in mice”, Proc. Natl. Acad. Sci. U S A, 97:18 (2000), 10179–10184 | DOI

[10] Seemann S., Hauff P., Schultze-Mosgau M., Lehmann C., Reszka R., “Pharmaceutical evaluation of gas-filled microparticles as gene delivery system”, Pharm. Res., 19:3 (2002), 250–257 | DOI

[11] Bjerknes V. F. K., Field of Force, Columbia Univ. Press, N. Y., 1906, 148 pp.

[12] Mettin R., Akhatov I., Parlitz U., Ohl C. D., Lauterborn W., “Bjerknes force between small cavitation bubbles in a strong acoustic field”, Phys. Rev. E, 56:3 (1997), 2924–2931 | DOI

[13] Konovalova S., Akhatov I., “Structure formation in acoustic cavitation”, Multiphase Sci. Technol., 17:3 (2005), 343–371 | DOI

[14] Pelekasis N. A., Gaki A., Doinikov A., Tsamopoulos J. A., “Secondary Bjerknes forces between two bubbles and the phenomenon of acoustic streamers”, J. Fluid Mech., 500 (2004), 313–347 | DOI | MR | Zbl

[15] Doinikov A. A., “Mathematical model for collective bubble dynamics in strong ultrasound fields”, J. Acoust. Soc. Am., 116:2 (2004), 821–827 | DOI

[16] Margulis I. M., Margulis M. A., “Interaction dynamics of bubbles in a cavitation cloud”, Russ. J. Phys. Chem., 78:7 (2004), 1159–1170

[17] Konovalova S. I., Translational effects and structure formation in acoustic cavitation, Cand. Phys.-Math. Sci., Ufa, 2006, 120 pp. (In Russian)

[18] Doinikov A. A., “Translational motion of two interacting bubbles in a strong acoustic field”, Phys. Rev. E, 64:2 (2001), 026301, 6 pp. | DOI

[19] Harkin A., Kaper T. J., Nadim A., “Coupled pulsation and translation of two gas bubbles in a liquid”, J. Fluid Mech., 445:1 (2001), 377–411 | DOI | MR | Zbl

[20] Kuznetsov G. N., Tschekin I. E., “Interaction of pulsating bubbles in a viscous liquid”, Akust. Zh., 18 (1972), 565–570 (In Russian)

[21] Gubaidullin A. A., Gubkin A. S., “Investigation of bubble cluster dynamics”, Vestn. Tyumen. Gos. Univ., 2013, no. 7, 91–97 (In Russian)

[22] Gubaidullin A. A., Gubkin A. S., “Behavior of bubbles in a cluster under acoustic action”, Sovr. Nauka. Issled., Idei, Rezul't., Tekhnol., 2013, no. 1, 363–367 (In Russian)

[23] Reddy A. J., Szeri A. J., “Shape stability of unsteadily translating bubbles”, Phys. Fluids, 14:7 (2002), 2216–2224 | DOI

[24] Aganin I. A., Davletshin A. I., “Dynamics of two gas bubbles in liquid in an ultrasonic traveling wave”, Tr. Inst. Mekh. im. R.R. Mavlyutova UNTs RAN, 12:1 (2017), 33–39 (In Russian)

[25] Aganin A. A., Davletshin A. I., “Simulation of interaction of gas bubbles in a liquid with allowing for their small asphericity”, Mat. Model., 21:6 (2009), 89–102 (In Russian) | Zbl

[26] Aganin A. A., Davletshin A. I., Toporkov D. Yu., “The dynamics of in-line cavitation bubbles in an intense acoustic wave”, Vychisl. Tekhnol., 19:1 (2014), 3–19 (In Russian)