Acoustic radiation force effect on a spherical drop placed in the vicinity of an ideal liquid free surface

Authors

  • O. P. Zhuk Timoshenko Institute of Mechanics, NAS of Ukraine, 3, Petr Nesterov str., Kyiv 03057
  • Y. A. Zhuk Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2019/1.10

Abstract

Acoustic radiation force effect on a liquid spherical drop placed in the vicinity of an ideal liquid free surface is studied. The problem of determination of the radiation forces acting on an obstacle in ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on a spherical drop of ideal liquid placed in turn in a liquid by its free plane surface is studied here for the case of the incident plane sound wave propagating perpendicularly to the liquid boundary. As a result, the liquid sphere is appeared to be located in the standing sound wave of pressure which has its displacement node at the free surface. Problem solution is obtained as a three step procedure. Initially, solution of the problem of an incident wave scattering at the drop is derived. With making use of the results obtained, the second step encompasses determining of hydrodynamic forces acting on the liquid spherical drop with their subsequent averaging over the suitable time interval at the third step. It is found there frequencies of the incident wave exist that provide zero radiation force acting on the drop which is immobile in this case. These equilibrium positions of the spherical drop could be stable or unstable with respect to the incident wave frequency variation.

Key words: ideal liquid, plane acoustic wave, liquid spherical particle, hydrodynamic force, radiation force.

Pages of the article in the issue: 50-53

Language of the article: Ukrainian

References

KING L.V. (1934) On the acoustic radiation pressure on spheres. Proc. Roy. Soc., Ser. A. 147(861). p. 246–265.

GUZ А.N. & ZHUK A.P. (2014) Effect of Acoustic Radiation in a Viscous Liquid on a Spherical Drop of Ideal Liquid. International Applied Mechanics. 50(6). p. 605−614.

ZHUK A.P. & ZHUK Y.A. (2017) Acoustic radiation force effect on a rigid spherical particle placed in the vicinity of a liquid free surface. Bulletin of Taras Shevchenko National University of Kyiv. Ser. Physics & Mathematics. No. 3. p. 55–58.

ZHUK A.P., KUBENKO V.D., ZHUK Y.A. (2012) Acoustic radiation force on a spherical particle in a fluid-filled cavity. Journal of the Acoustical Society of America. 132(4). p. 2189–2197.

ISAKOVICH M. A. (1973) Obshchaya akustika. Мoskva: Nauka.

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How to Cite

Zhuk, O. P., & Zhuk, Y. A. (2019). Acoustic radiation force effect on a spherical drop placed in the vicinity of an ideal liquid free surface. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 50–53. https://doi.org/10.17721/1812-5409.2019/1.10

Issue

Section

Differential equations, mathematical physics and mechanics