Numerical Study of Interaction of Two Deformable Bubbles in an Acoustic Field

  • Yu. A. PityukEmail author
  • N. A. Gumerov
  • O. A. Abramova
  • I. A. Zarafutdinov
  • I. Sh. Akhatov


Three-dimensional deformation of two bubbles and bubbles in a cluster in an ideal incompressible liquid in an acoustic field is investigated using the boundary element method for potential flows. The dependence of the dynamics of two interacting bubbles on the frequency and amplitude of the acoustic field and the distance between bubbles is studied. The parameters of the acoustic field and the cluster for which jets are formed and the bubbles are deformed or remain spherical are determined. The behavior of two central bubbles in a structured cluster in an acoustic field with different frequency and amplitude is investigated as a function of the distance between bubbles in the cluster. A comparative analysis of the deformation of the investigated bubbles in the presence and absence of adjacent bubbles is performed.


bubble deformation bubble interaction numerical simulation boundary element method potential flow 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. H. Besant, Hydrostatics and Hydrodynamics (Cambridge Univ. Press, London, 1859).Google Scholar
  2. 2.
    M. S. Plesset and A. Prosperetti, “Bubble Dynamics and Cavitation,” J. Fluid Mech. 9, 145–185 (1977).ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    V. F. K. Bjerknes, Fields of Force (Columbia Univ. Press, New York, 1906).zbMATHGoogle Scholar
  4. 4.
    A. A. Doinikov and S. T. Zavtrak, “On the Mutual Interaction of Two Gas Bubbles in a Sound Field,” Phys. Fluids 7 (8), 1923–1930 (1995).ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    H. N. Oguz and A. Prosperetti, “Bubble Oscillations in the Vicinity of a Nearly Plane Free Surface,” J. Acoust. Soc. Amer. 87, 2085–2092 (1990).ADSCrossRefGoogle Scholar
  6. 6.
    W. Lauterborn and T. Kurz, “Physics of Bubble Oscillations,” Rep. Progress Phys. 73, 106501 (2010); Scholar
  7. 7.
    N. A. Gumerov and I. Sh. Akhatov, “Modes of Self-Organization of Diluted Bubbly Liquids in Acoustic Fields: One-Dimensional Theory,” J. Acoust. Soc. Amer. 141 (2), 1190–1202 (2017).ADSCrossRefGoogle Scholar
  8. 8.
    Yu. A. Itkulova (Pityuk), O. A. Abramova, N. A. Gumerov, and I. Sh. Akhatov, “Simulation of Bubble Dynamics in Three-Dimensional Potential Flows on Heterogeneous Computing Systems Using the Fast Method of Multipoles and the Boundary Element Method,” Vychisl. Metody Program. 15, 239–257 (2014).Google Scholar
  9. 9.
    E. Canot and J.-L. Achard, “An Overview of Boundary Integral Formulations for Potential Flows in Fluid-Fluid Systems,” Arch. Mech. 43, 453–498 (1991).MathSciNetzbMATHGoogle Scholar
  10. 10.
    J. R. Blake and D. C. Gibson, “Cavitation Bubbles near Boundaries,” Ann. Rev. Fluid Mech. 19, 99–123 (1987).ADSCrossRefGoogle Scholar
  11. 11.
    A. A. Aganin, L. A. Kosolapova, and V. G. Malakhov, “Numerical Simulation of the Evolution of a Gas Bubble in a Liquid near a Wall,” Mat. Model 29 (7), 15–28 (2017).Google Scholar
  12. 12.
    G. L. Chahine and R. Duraiswami, “Dynamical Interactions in a Multibubble Cloud,” Trans. ASME, J. Fluids Eng. 114, 680–686 (1992).CrossRefGoogle Scholar
  13. 13.
    Y. L. Zhang, K. S. Yeo, B. C. Khoo, and C. Wang, “3D Jet Impact and Toroidal Bubbles,” J. Comput. Phys. 166, 336–360 (2001).ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    Yu. A. Itkulova (Pityuk), O. A. Abramova, N. A. Gumerov, and I. S. Akhatov, “Boundary Element Simulations of Free and Forced Bubble Oscillations in Potential Flow,” in Proc. of the Int. Mech. Engng Congress and Exposition, Montreal (Canada), November 14–20, 2014 (Amer. Soc. Mech. Eng, 2014), V007T09A059;
  15. 15.
    O. A. Abramova, I. S. Akhatov, N. A. Gumerov, et al., “Numerical and Experimental Study of the Dynamics of a Bubble in Contact with a Solid Surface,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 3–13 (2018).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • Yu. A. Pityuk
    • 1
    Email author
  • N. A. Gumerov
    • 1
    • 2
  • O. A. Abramova
    • 1
  • I. A. Zarafutdinov
    • 1
  • I. Sh. Akhatov
    • 3
  1. 1.Center for Micro- and Nanoscale Dynamics of Dispersed SystemsBashkir State UniversityUfaRussia
  2. 2.Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  3. 3.Skolkovo Institute of Science and Technology (Skoltech)MoscowRussia

Personalised recommendations