Acoustic streaming

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Acoustic streaming is a steady flow in a fluid driven by the absorption of high amplitude acoustic oscillations. This phenomenon can be observed near sound emitters, or in the standing waves within a Kundt's tube. It is the less-known opposite of sound generation by a flow.

There are two situations where sound is absorbed in its medium of propagation:

  • during propagation.[1] The attenuation coefficient is , following Stokes' law (sound attenuation). This effect is more intense at elevated frequencies and is much greater in air (where attenuation occurs on a characteristic distance ~10 cm at 1 MHz) than in water (~100 m at 1 MHz). In air it is known as the Quartz wind.
  • near a boundary. Either when sound reaches a boundary, or when a boundary is vibrating in a still medium.[2] A wall vibrating parallel to itself generates a shear wave, of attenuated amplitude within the Stokes oscillating boundary layer. This effect is localised on an attenuation length of characteristic size whose order of magnitude is a few micrometres in both air and water at 1 MHz.

Origin: a body force due to acoustic absorption in the fluid[edit]

Acoustic streaming is a non-linear effect. [3] We can decompose the velocity field in a vibration part and a steady part . The vibration part is due to sound, while the steady part is the acoustic streaming velocity (average velocity). The Navier–Stokes equations implies for the acoustic streaming velocity:

The steady streaming originates from a steady body force that appears on the right hand side. This force is a function of what is known as the Reynolds stresses in turbulence . The Reynolds stress depends on the amplitude of sound vibrations, and the body force reflects diminutions in this sound amplitude.

We see that this stress is non-linear (quadratic) in the velocity amplitude. It is non vanishing only where the velocity amplitude varies. If the velocity of the fluid oscillates because of sound as , the quadratic non-linearity generates a steady force proportional to .

Order of magnitude of acoustic streaming velocities[edit]

Even if viscosity is responsible for acoustic streaming, the value of viscosity disappears from the resulting streaming velocities in the case of near-boundary acoustic steaming.

The order of magnitude of streaming velocities are:[4]

  • near a boundary (outside of the boundary layer):

with the sound vibration velocity and along the wall boundary. The flow is directed towards decreasing sound vibrations (vibration nodes).

  • near a vibrating bubble[5] of rest radius a, whose radius pulsates with relative amplitude (or ), and whose center of mass also periodically translates with relative amplitude (or ). with a phase shift
  • far from walls[6] far from the origin of the flow ( with the acoustic power, the dynamic viscosity and the celerity of sound). Nearer from the origin of the flow, the velocity scales as the root of .

References[edit]

  1. ^ see video on http://www.lmfa.ec-lyon.fr/perso/Valery.Botton/english/videos_streaming.html
  2. ^ Wan, Qun; Wu, Tao; Chastain, John; Roberts, William L.; Kuznetsov, Andrey V.; Ro, Paul I. (2005). "Forced Convective Cooling via Acoustic Streaming in a Narrow Channel Established by a Vibrating Piezoelectric Bimorph". Flow, Turbulence and Combustion 74 (2): 195–206. doi:10.1007/s10494-005-4132-4. 
  3. ^ Sir James Lighthill (1978) "Acoustic streaming", 61, 391, Journal of Sound and Vibration
  4. ^ Squires, T. M. & Quake, S. R. (2005) Microfluidics: Fluid physics at the nanoliter scale, Review of Modern Physics, vol. 77, page 977
  5. ^ Longuet-Higgins, M. S. (1998). "Viscous streaming from an oscillating spherical bubble". Proc. R. Soc. Lond. A 454 (1970): 725–742. Bibcode:1998RSPSA.454..725L. doi:10.1098/rspa.1998.0183. 
  6. ^ Moudjed, B.; V. Botton; D. Henry; Hamda Ben Hadid; J.-P. Garandet (2014-09-01). "Scaling and dimensional analysis of acoustic streaming jets". Physics of Fluids 26 (9): 093602. Bibcode:2014PhFl...26i3602M. doi:10.1063/1.4895518. ISSN 1070-6631. Retrieved 2014-09-18.