Skip to main content
Log in

Interaction of an Acoustic Wave with a Medium Containing a Layer of Bubble Liquid

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

The mathematical model that determines reflection and transmission of an acoustic wave at different angles of incidence through a medium containing a moving and stationary layer of multifractional bubble liquid is presented. The reflection and transmission coefficients of the wave are calculated for a water–bubble liquid–water–bubble liquid–water mixture.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

REFERENCES

  1. R. I. Nigmatulin, Dynamics of Multiphase Media (Hemisphere, New York, 1991).

    Google Scholar 

  2. S. Temkin, Suspension Acoustics: An Introduction to the Physics of Suspensions (Cambridge Univ. Press, Cambridge, 2005).

    Book  Google Scholar 

  3. T. G. Leighton, The Acoustic Bubble (Academic, London, 1994).

    Google Scholar 

  4. V. E. Nakoryakov, B. G. Pokusaev, and I. R. Shreiber, Wave Propagation in Gas-Liquid Media (CRC, New York, 1993).

    Google Scholar 

  5. D. A. Gubaidullin, Dynamics of Two-Phase Gas-Vapor-Droplet Media (Kazan. Mat. Ob-vo, Kazan, 1998) [in Russian].

    Google Scholar 

  6. Y. Hao and A. Prosperetti, ‘‘The dynamics of vapor bubbles in acoustic pressure fields,’’ Phys. Fluids 11, 2008–2019 (1999).

    Article  MathSciNet  Google Scholar 

  7. K. W. Commander and A. Prosperetti, ‘‘Linear pressure waves in bubbly liquids: Comparison between theory and experiments,’’ J. Acoust. Soc. Am. 85, 732–746 (1989).

    Article  Google Scholar 

  8. R. I. Nigmatulin, V. Sh. Shagapov, and N. K. Vakhitova, ‘‘Manifestation of compressibility of continuous phase at wave propagation in bubble-containing medium,’’ Sov. Phys. Dokl. 34, 98 (1989).

    MATH  Google Scholar 

  9. R. I. Nigmatulin, N. S. Khabeev, and F. B. Nagiev, ‘‘Dynamics, heat and mass transfer of vapour-gas bubbles in a liquid,’’ Int. J. Heat Mass Transfer 24, 1033–1044 (1981).

    Article  Google Scholar 

  10. D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Acoustics of a viscoelastic medium with encapsulated bubbles,’’ J. Hydrodynamics 33, 55–62 (2021).

    Article  Google Scholar 

  11. V. A. Gusev and O. V. Rudenko, ‘‘Nonlinear sound in a gas-saturated sediment layer,’’ Acoust. Phys. 61, 152–164 (2015).

    Article  Google Scholar 

  12. V. A. Grigorev, A. A. Lunkov, and V. G. Petnikov, ‘‘Attenuation of sound in shallow-water areas with gas-saturated bottoms,’’ Acoust. Phys. 61, 85–95 (2015).

    Article  Google Scholar 

  13. V. Sh. Shagapov and V. V. Sarapulova, ‘‘Refraction and reflection of sound at the boundary of a bubbly liquid,’’ Acoust. Phys. 61, 37–44 (2015).

    Article  Google Scholar 

  14. V. Leroy, A. Strybulevych, M. Lanoy, F. Lemoult, A. Tourin, and J. H. Page, ‘‘Superabsorption of acoustic waves with bubble metascreens,’’ Phys. Rev. B 91, 020301 (2015).

    Article  Google Scholar 

  15. D. A. Gubaidullin, A. A. Nikiforov, and R. N. Gafiyatov, ‘‘Acoustic waves in multifractional bubbly liquids,’’ High Temp. 53, 240–245 (2015).

    Article  Google Scholar 

  16. D. A. Gubaidullin and R. N. Gafiyatov, ‘‘Dynamics of waves in multifractional bubble liquids,’’ J. Eng. Phys. Thermophys. 90, 1433–1438 (2017).

    Article  Google Scholar 

  17. R. N. Gafiyatov, D. A. Gubaidullin, and D. D. Gubaidullina, ‘‘Acoustic waves of various geometry in multi-fraction bubbly liquids,’’ Fluid Dyn. 53, 119–126 (2018).

    Article  MathSciNet  Google Scholar 

  18. D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Acoustic wave incidence on a multilayer medium containing a bubbly fluid layer,’’ Fluid Dyn. 52, 107–114 (2017).

    Article  MathSciNet  Google Scholar 

  19. D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Peculiarities of acoustic wave reflection from a boundary or layer of a two-phase medium,’’ Acoust. Phys. 64, 164–174 (2018).

    Article  Google Scholar 

  20. R. N. Gafiyatov, ‘‘Acoustic wave incidence on a medium containing multifractional bubbly liquid,’’ Lobachevskii J. Math. 40, 730–733 (2019).

    Article  MathSciNet  Google Scholar 

  21. R. N. Gafiyatov, ‘‘Features of acoustic wave transmission through a medium, containing a layer of multifractional bubbly liquid,’’ Lobachevskii J. Math. 41, 1180–1183 (2020).

    Article  MathSciNet  Google Scholar 

  22. D. A. Gubaidullin and R. N. Gafiyatov, ‘‘Reflection and transmission of acoustic wave through a multifractional bubble layer,’’ High Temp. 58, 97–100 (2020).

    Article  Google Scholar 

  23. R. N. Gafiyatov, ‘‘Transmission of an acoustic wave through a medium, containing a moving layer of multifractional bubbly liquid,’’ Lobachevskii J. Math. 42, 2114–2117 (2021).

    Article  Google Scholar 

  24. L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. N. Gafiyatov.

Additional information

(Submitted by D. A. Gubaidullin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gafiyatov, R.N. Interaction of an Acoustic Wave with a Medium Containing a Layer of Bubble Liquid. Lobachevskii J Math 43, 1094–1097 (2022). https://doi.org/10.1134/S1995080222080078

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080222080078

Keywords:

Navigation