Transient bubbles

Thus the equation for the transient bubble size becomes... 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

Transient cavitation bubbles are voids, or vapour filled bubbles, believed to be produced using sound intensities in excess of 10 W cm. They exist for one, or at most a few acoustic cycles, expanding to a radius of at least twice their initial size, (Figs. 2.16 and 2.20), before collapsing violently on compression often disintegrating into smaller bubbles. (These smaller bubbles may act as nuclei for further bubbles, or if of sufficiently small radius (R) they can simply dissolve into the bulk of the solution under the action of the very large forces due to surface tension, 2a/R. During the lifetime of the transient bubble it is assumed that there is no time for any mass flow, by diffusion of gas, into or out of the bubble, whereas evaporation and condensation of liquid is assumed to take place freely. If there is no gas to cushion the implosion... 

Our concern is primarily with the transient bubble because it is such a bubble that produces the highest temperature. The maximum temperature and pressure of a transient bubble at its moment of collapse, assuming that it contains an ideal gas and no vapor and neglecting the effect of surface tension and fluid viscosity, are given by... 

An analysis of the equation of motion for a single transient bubble under a constant driving sound pressure can be performed by solving the Kirkwood-Bethe-Gilmore model. The best combination of sound pressure and initial bubble radius can be found by demanding a maximum bubble radius prior to collapse, a very small final radius and a collapse that is timed to be finished at the maximum positive pressure. 

A transient bubble with these attributes should give the best results because of its maximum energy content and the high speeds of the bubble wall on disintegration. For a 20kHz sound field, a pressure of 3.5 bar is sufficient to create this... 

Transient bubbles have a very small collapse time that was first deduced by Rayleigh. An approximation for the collapse time in acoustic sound fields is... 

The vapor pressure of liquids can cushion the bubble collapse like a high gas content. Vapor in a transient bubble can be condensed in the compression cycle and lead to higher cavitation intensities than gas-filled bubbles. Experiments with different solvents show that small vapor pressures are necessary for a sufficiently high cavitation intensity. Higher vapor pressures, especially near the boiling point of the liquid, can dampen the cavitation efficiency to nearly zero. If a substrate is subject to treatment within the collapsing bubbles, then a certain number of its molecules must be present in the bubbles and exert an at least measurable vapor pressure. The existence of molecules inside the bubble can easily be proved by means of molecules that exist as ionic or molecular species at different pH values. Ionic species do not enter the bubbles, and high-temperature pyrolysis products can therefore not be created. 

Another approach is the so-called shock-wave theory . The compression of transient bubbles leads to an increasing bubble-wall velocity that may eventually reach the speed of sound of the liquid. In true transient cavitation, the bubble vanishes after collapse, creating a shock wave in the liquid. Particles and macromolecules are accelerated in the steep pressure gradient and are shock fragmented. High-speed particles collide and undergo mechanical damage. 

The supercritical-water theory describes the elfects of high temperatures and pressures in aqueous systems when conditions are reached under which supercritical water is likely. Supercritical water is known to have a strong solvent action towards organic compounds and extreme chemical activity. Sonochemical effects are possible inside the supercritical water layer surrounding a transient bubble. At the present time, no direct evidence for the generation of supercritical water in ultrasound fields has been found experimentally. 

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]. 

The number of bubbles increases sharply beyond a threshold pressure. Beyond this threshold pressure the number of stable and transient bubbles decreases due... 

Figure 8.1.12 Bubble volume fractions for stable and transient bubbles as a function of normalized sound pressure.

The last piece for the model is the bubble-size distribution function and the limits for the rest radii of bubbles in the sound field. The cavitation thresholds as a function of applied sound pressure indicate the upper and lower size limits for bubbles in a cavitating sound field. A simplifying point of view would differentiate between a) transient bubbles, b) stable bubbles and c) dissolving bubbles. 

The simulation of the sound field reveals that only a very small area is effective concerning the existence and the action of transient bubbles. Figure 8.1.17 depicts the sound pressure in the conical reactor. The face of the stepped horn is located at the left side of the picture. The right side is the interface between liquid and gas. 

S. Baldy, A generation-dispersion model of ambient and transient bubbles in the close vicinity of breaking waves, J. Geophys. Res. CIO, 18277-18293 (1993). 

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