Bubble-Induced Acoustic Streaming

The FEM calculations were carried out at an amplitude where nonlinear effects can be neglected. Actual oscillation amplitudes in experiment, on the other hand, are between 0.1 and 1 nm, and there 

For acoustic waves in incompressible liquids with constant density, the source term of acoustic streaming is the Re3molds force density, /r, given as 

V is the instantaneous speed, the index 0 denotes an amplitude of an oscillatory quantity, the indices i,j denote directions in space, the star denotes the complex conjugate and angle brackets denote time averaging. The first relation on the left makes use of incompressibility (Edvy/dxy = 0). The second relation makes use of the feet that the time average of cos ( wt) is 1/2. 

Nanobubbles located on the surface of a shear-wave resonator behave peculiarly. First, they may look like rigid objects due to Laplace pressure. They may decrease the frequency and increase the bandwidth and thereby seemingly contradict the simple-minded models of slip. Also, they act as a source of acoustic streaming. Since acoustic streaming increases mass transport close to the interface, the bubbles thereby speed up their own dissolution. 

This work highlights the peculiar behavior of soft matter in acoustic shear fields. It also shows how FEM calculations help in the interpretation of experimental findings. The authors are convinced that acoustic shear waves and the related phenomena are of broad 

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Figure 8.8 Oscillation-induced stationary flow of liquid around a bubble. See the main text for the geometry. Acoustic streaming is absent in pure shear flow because the flow direction and the gradient direction are perpendicular. However, the bubble deviates the flow, which creates a time-averaged net force. The stationary flow increases the rate of dissolution of the bubble in the liquid phase, which presumably is part of the reason why nanobubbles are less often observed in EQCM experiments than expected. We believe that shear-induced acoustic streaming is a second reason— in addition to Lapiace pressure and apparently "solid nanobubbles—why nanobubbles are less commonly observed in EQCM experiments than one might think.

Mitome H, Kozuka T, Tuziuti T, Wang L (1997) Quasi acoustic streaming induced by generation of cavitation bubbles. IEEE Ultrason Sympo Proc 1 533-536... 

In the literature we can now find several papers which establish a widely accepted scenario of the benefits and effects of an ultrasound field in an electrochemical process [13-15]. Most of this work has been focused on low frequency and high power ultrasound fields. Its propagation in a fluid such as water is quite complex, where the acoustic streaming and especially the cavitation are the two most important phenomena. In addition, other effects derived from the cavitation such as microjetting and shock waves have been related with other benefits reported for this coupling. For example, shock waves induced in the liquid cause not only an enhanced convective movement of material but also a possible surface damage. Micro jets of liquid, with speeds of up to 100 ms-1, result from the asymmetric collapse of cavitation bubbles at the solid surface [16] and contribute to the enhancement of the mass transport of material to the solid surface of the electrode. Therefore, depassivation [17], reaction mechanism modification [18], surface activation [19], adsorption phenomena decrease [20] and the mass transport enhancement [21] are effects derived from the presence of an ultrasound field on electrode processes. We have only listed the main phenomena referring to the reader to the specific reviews [22, 23] and reference therein. 

Many heterogeneous reactions are accelerated by the enhanced micromixing properties of cavitating sound fields. Oscillating and transient bubbles create intense microstreaming in the vicinity of suspended solids. Macromixing is induced by acoustic streaming and the oscillation of bubbles in the sound field. In most cases, a locally different mass-transport coefficient is observed. A tenfold increase in mass-transfer coefficients compared with silent reactions was measured [18]. 

Fig. 3 Representation of (a) acoustic streaming and (b) an ultrasonically induced cavitational bubble collapsing in the vicinity of a surface.

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