- Acoustic streaming
Acoustic streaming is a steady current forced 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 two situations where sound is absorbed in its medium of propagation:
* during propagation [ see video on http://www.lmfa.ec-lyon.fr/perso/Valery.Botton/acoustic_streaming_bis.html (French) ] . 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 know as the "Quartz wind".
* near a boundary. Either when sound reaches a boundary, or when a boundary is vibrating in a still medium. 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 microns in both air and water at 1 MHz.
Origin: a body force due to acoustic absorption in the fluid
Acoustic streaming is a non-linear effect. [ Sir
James Lighthill(1978) "Acoustic streaming", 61, 391, Journal of Sound and Vibration ] We can decompose the velocity field in a vibration part and a steady part , a vector with components The vibration part due to sound, while the steady part is acoustic streaming velocity.The average velocity in time is , and the Navier–Stokes equationsimplies 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 stressesin turbulence . The Reynolds stress is 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
Even if viscosity is responsible for acoustic streaming, the value of viscosity disappears from the resulting streaming velocities.
The order of magnitude of streaming velocities are [ Squires, T. M. & Quake, S. R. (2005) Microfluidics: Fluid physics at the nanoliter scale, Review of Modern Physics, vol. 77, page 977 ] :
* near a boundary (outside of the boundary layer)::with along the wall. The flow is directed towards decreasing sound vibrations (vibration nodes).
* near a vibrating bubble [cite journal | last=Longuet-Higgins | first=M. S. | authorlink=Michael S. Longuet-Higgins | title=Viscous streaming from an oscillating spherical bubble | journal=Proc. R. Soc. Lond. A | year=1998 | volume=454 | pages=725–742 ] 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 :
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