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Acoustic radiation pressure on a compressible sphere in a viscous fluid

Published online by Cambridge University Press:  26 April 2006

Alexander A. Doinikov
Alexander A. Doinikov
Affiliation:
Laboratory of Gamma-Optics, Institute of Nuclear Problems, 220050 Minsk, Byelorussia
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Abstract

The acoustic radiation pressure exerted by a plane — progressive or standing — sound wave on a compressible sphere suspended freely in a viscous fluid is calculated. In deriving the general expression for the radiation pressure, it is supposed that the radius of the sphere is arbitrary. Two limiting cases of interest are then considered. In the first of these, it is assumed that the sound wavelength is much larger than the radius of the sphere which is, in turn, much larger than the viscous wavelength, it being supposed that this condition is satisfied both outside and inside the sphere. In the second case, the situation is investigated when the radius of the sphere is small compared with the viscous wavelength which is, in turn, much smaller than the sound wavelength, it being supposed that this condition is satisfied, as before, both outside and inside the sphere. It is shown that in both cases the expressions for the radiation pressure are drastically different from the well-known expressions for the radiation pressure in a perfect fluid: the calculation of the radiation pressure from the formulae obtained for a perfect fluid in the cases when the effect of viscosity is not negligible gives both quantitatively and qualitatively wrong results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 267 , 25 May 1994 , pp. 1 - 22
Copyright
© 1994 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Jones, R. V. & Leslie, B. 1978 The measurement of optical radiation pressure in dispersive media. Proc. R. Soc. Lond. A 360, 347–363.Google Scholar
King, L. V. 1934 On the acoustic radiation pressure on spheres. Proc. R. Soc. Lond. A 147, 212–240.Google Scholar
Korn, G. A. & Korn, T. M. 1968 Mathematical Handbook. McGraw-Hill.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lee, C. P., Anilkumar, A. V. & Wang, T. G. 1991 Static shape and instability of an acoustically levitated liquid drop. Phys. Fluids A 3, 2497–2515.Google Scholar
Lighthill, M. J. 1978 Acoustic streaming. J. Sound Vib. 24, 471–492.Google Scholar
Rayleigh, Lord 1894 The Theory of Sound. Macmillan, London, pp. 43–45.
Trinh, E. H. 1985 Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity. Rev. Sci. Instrum. 56, 2059–2065.Google Scholar
Walton, A. J. & Reynolds, G. T. 1984 Sonoluminescence. Adv. Phys. 33, 595–660.Google Scholar
Wu, J. & Du, G. 1990 Acoustic radiation force on a small compressible sphere in a focused beam. J. Acoust. Soc. Am. 87, 997–1003.Google Scholar
Yosioka, K. & Kawasima, Y. 1955 Acoustic radiation pressure on a compressible sphere. Acustica 5, 167–173.Google Scholar