Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. H. Besant, Hydrostatics and Hydrodynamics (Cambridge Univ. Press, London, 1859).

    Google Scholar 

  2. M. S. Plesset and A. Prosperetti, “Bubble Dynamics and Cavitation,” J. Fluid Mech. 9, 145–185 (1977).

    Article  ADS  MATH  Google Scholar 

  3. V. F. K. Bjerknes, Fields of Force (Columbia Univ. Press, New York, 1906).

    MATH  Google Scholar 

  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).

    Article  ADS  MATH  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  6. W. Lauterborn and T. Kurz, “Physics of Bubble Oscillations,” Rep. Progress Phys. 73, 106501 (2010); https://doi.org/10.1088/0034-4885/73/10/106501.

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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. 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).

    MathSciNet  MATH  Google Scholar 

  10. J. R. Blake and D. C. Gibson, “Cavitation Bubbles near Boundaries,” Ann. Rev. Fluid Mech. 19, 99–123 (1987).

    Article  ADS  Google Scholar 

  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. G. L. Chahine and R. Duraiswami, “Dynamical Interactions in a Multibubble Cloud,” Trans. ASME, J. Fluids Eng. 114, 680–686 (1992).

    Article  Google Scholar 

  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).

    Article  ADS  MATH  Google Scholar 

  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; https://doi.org/10.1115/IMECE2014-36972.

  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).

Download references

Author information

Authors and Affiliations

  1. Center for Micro- and Nanoscale Dynamics of Dispersed Systems, Bashkir State University, Ufa, 450076, Russia

    Yu. A. Pityuk, N. A. Gumerov, O. A. Abramova & I. A. Zarafutdinov

  2. Institute for Advanced Computer Studies, University of Maryland, College Park, 21075, USA

    N. A. Gumerov

  3. Skolkovo Institute of Science and Technology (Skoltech), Moscow, 143026, Russia

    I. Sh. Akhatov

Authors
  1. Yu. A. Pityuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. A. Gumerov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. A. Abramova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. I. A. Zarafutdinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. Sh. Akhatov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. A. Pityuk.

Additional information

Original Russian Text © Yu.A. Pityuk, N.A. Gumerov, O.A. Abramova, I.A. Zarafutdinov, I.Sh. Akhatov.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 4, pp. 81–90, July–August, 2019.

The program code was developed under the partnership program of the Skoltech Center; the study of the dynamics of two separate bubbles was supported by the Russian Foundation for Basic Research (Grant No. 18-31-00074), and the study of the dynamics of a bubble cluster by the Russian Science Foundation (Grant No. 18-71-00068).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pityuk, Y.A., Gumerov, N.A., Abramova, O.A. et al. Numerical Study of Interaction of Two Deformable Bubbles in an Acoustic Field. J Appl Mech Tech Phy 60, 661–668 (2019). https://doi.org/10.1134/S0021894419040096

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894419040096

Keywords

Search

Navigation