Acoustic streaming

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.

[1] 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: Consider a plane standing sound wave that corresponds to the velocity field

However viscous effects will be important close to a solid wall; there then exists a boundary layer of thickness or, penetration depth

In addition, the characteristic time scale within the boundary layer is very large (because of the smallness of

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.

in the sound wave is very small, we can formally obtain the solution for the boundary layer equation by introducing the asymptotic series for

In the first approximation, one obtains The solution that satisfies the no-slip condition at the wall

terms correspond to time independent forcing for

Let us find solution that corresponds only to this time-independent part.

satisfies the equation[6] where prime denotes differentiation with respect to

This velocity forcing will drive a steady streaming motion outside the boundary layer.

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

The outer steady streaming incompressible motion will depend on the geometry of the problem.

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

The Navier–Stokes equations implies for the acoustic streaming velocity: The steady streaming originates from a steady body force

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.

, the quadratic non-linearity generates a steady force proportional to

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.

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.

[12][13] These applications may include cell manipulation and cell sorting, drug delivery, 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.