Abstract
The conditions for the coalescence of two pulsating spherical bubbles in a liquid in a weak low-frequency acoustic pressure field, as well as the conditions for absence of such a fusion, have been studied. Since the frequency of the pressure field is much lower than natural frequencies, the bubbles pulsate with identical relative amplitudes and phases. At large distances, bubbles approach according to the Bjerknes law. However, viscous forces near a contact can compensate the attraction force and bubbles do not coalesce. It has been shown that bubbles coalesce when the ratio of radii is smaller than 3; otherwise, periodic oscillations are established at a small gap between the surfaces of bubbles and coalescence does not occur. These theoretical results have been confirmed by existing experiments.
Similar content being viewed by others
References
T. O. Oolman and H. W. Blanch, Chem. Eng. Comm. 43, 237 (1986).
H. Feng, G. V. Barbosa-Cánovas, and J. Weiss, Ultrasound Technologies for Food and Bioprocessing (Springer, New York, 2011).
Y. Chen, G. Xie, J. Chang, J. Grundy, and Q. Liu, Fuel 248, 38 (2019).
B. V. Deryagin, S. S. Dukhin, and N. N. Rulev, Microflotation: Water Treatment, Enrichment (Khimiya, Moscow, 1986) [in Russian].
C. C. Coussios and R. A. Roy, Ann. Rev. Fluid Mech. 40, 395 (2008).
H. Lamb, Hydrodynamics (Cambridge Univ., Cambridge, 1993).
W. M. Hicks, Philos. Trans. R. Soc. 171, 455 (1880).
V. Bjerknes, Fields of Force: Supplementary Lectures, Applications to Meteorology (The Columbia Univ. Press, New York, 1906).
R. A. Herman, Quart. J. Pure Appl. Math. 87, 204 (1887).
V. F. Kazantsev, Sov. Phys. Dokl. 4, 1250 (1960).
L. A. Crum, J. Acoust. Soc. Am. 57, 1363 (1975).
J. Jiao, Y. He, T. Leong, S. E. Kentish, M. Ashokkumar, R. Manasseh, and J. Lee, J. Phys. Chem. B 117, 12549 (2013).
J. Jiao, Y. He, S. E. Kentish, M. Ashokkumar, R. Manasseh, and J. Lee, Ultrasonics 58, 35 (2015).
J. Jiao, Y. He, K. Yasui, S. E. Kentish, M. Ashokkumar, R. Manasseh, and J. Lee, Ultrason. Sonochem. 22, 70 (2015).
S. Cleve, M. Guédra, C. Inserra, C. Mauger, and P. Blanc-Benon, Phys. Rev. E 98, 033115 (2018).
E. A. Zabolotskaya, Sov. Phys. Acoust. 30, 365 (1984).
A. Harkin, T. J. Kaper, and A. L. I. Nadim, J. Fluid Mech. 445, 377 (2001).
R. Mettin, I. Akhatov, U. Parlitz, C. D. Ohl, and W. Lauterborn, Phys. Rev. E 56, 2924 (1997).
A. A. Doinikov, Phys. Rev. E 64, 026301 (2001).
G. N. Kuznetsov and I. E. Shchukin, Sov. Phys. Acoust. 18, 466 (1972).
H. N. Oguz and A. Prosperetti, J. Fluid Mech. 218, 143 (1990).
A. A. Aganin and A. I. Davletshin, Mat. Model. 21(9), 89 (2009).
A. A. Doinikov and A. Bouakaz, Phys. Rev. E 92, 043001 (2015).
Yu. A. Kobelev, L. A. Ostrovskii, and A. M. Sutin, JETP Lett. 30, 395 (1979).
P. L. Marston, E. H. Trinh, J. Depew, and J. Asaki, in Bubble Dynamics and Interface Phenomena, Ed. by J. R. Blake, J. M. Boulton-Stone, and N. H. Thomas (Kluwer Acad., Dordrecht, 1994), p. 343.
A. G. Petrov, Fluid Dyn. 46, 579 (2011).
S. V. Sanduleanu and A. G. Petrov, J. Phys.: Conf. Ser. 656, 012035 (2015).
O. V. Voinov and A. G. Petrov, Itogi Nauki Tekh., Mekh. Zhidk. Gaza 10, 86 (1976).
S. V. Sanduleanu, Fluid Dyn. 55 (7) (2020) (in press).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1988; Pergamon, New York, 1988).
D. J. Jeffrey, Mathematika 29, 58 (1982).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).
A. G. Petrov, Analytical Hydrodynamics (Fizmatlit, Moscow, 2010) [in Russian].
S. V. Sanduleanu, J. Appl. Mech. Tech. Phys. 61(4), 532 (2020).
S. Michelin, G. Gallino, F. Gallaire, and E. Lauga, J. Fluid Mech. 860, 172 (2019).
A. Z. Zinchenko, J. Appl. Math. Mech. 42(5), 1046 (1978).
S. V. Sanduleanu, in Waves and Vortices in Complex Media, Proceedings of the 10th International Conference-School of Young Scientists, December 3–5, 2019 (Premium-print, Moscow, 2019).
S. Michelin, E. Guérin, and E. Lauga, Phys. Rev. Fluids 3, 043601 (2018).
S. V. Sanduleanu and A. G. Petrov, Dokl. Phys. 63, 517 (2018).
Author information
Authors and Affiliations
Corresponding author
Additional information
Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (state task no. AAAA-A20-120011690138-6).
Russian Text © The Author(s), 2020, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 112, No. 3, pp. 165–171.
Rights and permissions
About this article
Cite this article
Sanduleanu, S.V., Petrov, A.G. Interaction of Two Nearly Contacting Gas Bubbles Pulsating in a Liquid in an Alternating Pressure Field. Jetp Lett. 112, 150–156 (2020). https://doi.org/10.1134/S0021364020150102
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364020150102