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. Acoustic streaming was explained first by Lord Rayleigh in 1884. 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 in bulk flow (Eckart streaming). The attenuation coefficient, following Stokes' law (sound attenuation)~10cm at 1MHz~100 m at 1MHz). In air it is known as the Quartz wind.

• near a boundary (Rayleigh streaming). 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 whose order of magnitude is a few micrometres in both air and water at 1MHz. The streaming flow generated due to the interaction of sound waves and microbubbles, elastic polymers, and even biological cells are examples of boundary-driven acoustic streaming.

Rayleigh streaming

. The flow field just described corresponds to inviscid flow. These observations imply that the flow in the boundary layer may be regarded as incompressible.

The unsteady, incompressible boundary-layer equation is

where the right-hand side terms correspond to the pressure gradient imposed on the boundary layer. The problem can be solved using the stream function etc.

In the first approximation, one obtains

The solution that satisfies the no-slip condition is given by

The equation at the next order is

satisfies the equation

must be finite. Integrating the above equation twice gives

, the steady streaming motion happening outside the boundary layer is also independent of viscosity, although its origin is due to the viscous boundary layer.

, then the solution is

which corresponds a periodic array of counter-rotating vortices, as shown in the figure.

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

Acoustic streaming is a non-linear effect. 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:

that appears on the right hand side. This force is a function of what is known as the Reynolds stresses. 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.

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):

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

• near a vibrating bubble), and whose center of mass

  far from walls.

  it has been shown that even biological species, e.g., adherent cells, can also exhibit acoustic streaming flow when exposed to acoustic waves. Cells adhered to a surface can generate acoustic streaming flow in the order of mm/s without being detached from the surface.

Applications

Research around acoustic streaming shows many effective applications, especially around particle manipulation, although translation to commercial use is in early stages for most uses. In microfluidics, it can be used for cell manipulation and sorting. These applications may include cell manipulation and cell sorting, drug delivery, and homogenizing reactants. Acoustic streaming is also relevant to sonoporation for increasing cell-membrane permeability. Acoustic streaming is also used in membrane processes, where it can control fouling and increase particle collection. It can control biofilms in other applications as well.

See also

• Acoustic tweezers

References