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. 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. 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
Acoustic streaming is a non-linear effect.  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
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:
- 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 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 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 .
- see video on http://media.efluids.com/galleries/all?medium=749
- 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. CiteSeerX 10.1.1.471.6679. doi:10.1007/s10494-005-4132-4.
- Sir James Lighthill (1978) "Acoustic streaming", 61, 391, Journal of Sound and Vibration
- Squires, T. M. & Quake, S. R. (2005) Microfluidics: Fluid physics at the nanoliter scale, Review of Modern Physics, vol. 77, page 977
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- 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.