Bubble collapse

It is postulated that bubble collapse may well have generated sufficient pressure to commence propagation of the pre-existing crack, which then continued, either by direct conversion of the bubble energy, or by the rapid conversion of potential to kinetic energy in the water column. The presence of gas in the lute vessel implies the possibility of a head of 

Had there been no bubble impulse the environmental stress crack would probably have reached the outside within a few weeks, and this would have caused a leak, but no catastrophic failure. Conversely, had there been no pre-existing crack, the bubble impulse would not have caused failure. 

We see that the deformation is not homogeneous. It is a maximum at the gas-liquid interface, r = R, and decreases with r . The rate is most easily evaluated at the interface 

Bubble radius can be measured directly by a film or video camera. Pearson and Middleman (1977) found their bubbles were sightly nonspherical and used an average radius. For opaque liquids one can infer the bubble radius by measuring the small change in gas pressure above the liquid sample caused by the collapsing bubble (Johnson and Middleman, 1978). This method is also simpler and faster to use. 

Log-reduced radius versus time for the collapse of a bubble in a high density polyethylene melt at IWC. The initial radius need not be known exactly because the ratio R/R comes from the decrease in pressure above the melt. Adapted from Mun-stedt and Middleman (1981). 

Stress can be determined from the pressure difference across the bubble. Papanastasiou et al. (1984) have shown that even for the rapid bubble collapse in polymer solutions, the unsteady and inertial terms in the momentum balance may generally be neglected. Neglecting viscosity of the gas, but considering interfacial tension, leads to 

Log-reduced radius versus time for bubble collapse in hydroxypropylcellulose, 2% in water, (a) Low rates and (b) high rate also showing necking as the bubble shrinks to the capillary size (/f, 0.5 mm, R - 2 mm). Data from high speed camera (Pearson and Middleman, 1977). 

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Cavitation has three negative side effects in valves—noise and vibration, material removal, and reduced flow. The bubble-collapse process is a violent asymmetrical implosion that forms a high-speed microjet and induces pressure waves in the fluid. This hydrodynamic noise and the mechanical vibration that it can produce are far stronger than other noise-generation sources in liquid flows. If implosions occur adjacent to a solid component, minute pieces of material can be removed, which, over time, will leave a rough, cinderlike surface. 

Cavitation Formation of transient voids or vacuum bubbles in a liquid stream passing over a surface is called cavitation. This is often encountered arouna propellers, rudders, and struts and in pumps. When these bubbles collapse on a metal surface, there is a severe impact or explosive effec t that can cause considerable mechanical damage, and corrosion can be greatly accelerated because of the destruction of protective films. Redesign or a more resistant metal is generally required to avoid this problem. 

Damage will be confined to the bubble-collapse region, usually immediately downstream of the low-pressure zone. Components exposed to high velocity or turbulent flow, such as pump impellers and valves, are subject. The suction side of pumps (Case History 12.3) and the discharge side of regulating valves (Fig. 12.6 and Case History 12.4) are frequently affected. Tube ends, tube sheets, and shell outlets in heat exchanger equipment have been affected, as have cylinder liners in diesel engines (Case History 12.1). 

One solution that was considered by Rayleigh (Lamb, 1945) for the determination of bubble collapse time, tm, used the model of a bubble with initial size Rm, suddenly subjected to a constant excess liquid pressure pL. Neglecting the surface tension and the gas pressure in the bubble, Eq. (2-29) may be rearranged to... 

The rate of bubble collapse Rcl is primarily important in the first transition zone where the bulk liquid is subcooled. A number of studies have been published on subcooled boiling as well as the prediction of the point of net vapor generation, characteristics defining Transition Zone I, and the onset of nucleation. These studies all result in empirical correlations, and have not led to quantitative conclusions which can be generalized. The radial velocity... 

Abstract Acoustic cavitation is the formation and collapse of bubbles in liquid irradiated by intense ultrasound. The speed of the bubble collapse sometimes reaches the sound velocity in the liquid. Accordingly, the bubble collapse becomes a quasi-adiabatic process. The temperature and pressure inside a bubble increase to thousands of Kelvin and thousands of bars, respectively. As a result, water vapor and oxygen, if present, are dissociated inside a bubble and oxidants such as OH, O, and H2O2 are produced, which is called sonochemical reactions. The pulsation of active bubbles is intrinsically nonlinear. In the present review, fundamentals of acoustic cavitation, sonochemistry, and acoustic fields in sonochemical reactors have been discussed. 

Now the bubble collapse is discussed using the Rayleigh-Plesset equation. After the bubble expansion, a bubble collapses. During the bubble collapse, important terms in the Rayleigh-Plesset equation are the two terms in the left hand side of (1.13). Then, the bubble wall acceleration is expressed as follows. 

It has been shown theoretically that the speed of the bubble collapse is limited by the sound speed in the liquid at the bubble wall [42], The sound speed is a function of pressure and density of the liquid as follows. 

Finally, the bubble collapse stops when the pressure inside a bubble (pg) in the right hand side of (1.13) dramatically increases as the density inside a bubble nearly reaches that of a condensed phase (A bubble is almost completely occupied by the van der Waals hard-cores of gas and vapor molecules at that moment). At the same time, the temperature and pressure inside a bubble dramatically increase. 

In Fig. 1.9, the results of numerical simulations at 300 kHz and 3 bar in ultrasonic frequency and pressure amplitude, respectively are shown as a function of ambient radius [39]. In Fig. 1.9a, the temperature inside a bubble at the end of the bubble collapse is shown with the molar fraction of water vapor inside a bubble. 

Fig. 1.9 The calculated results as a function of ambient radius at 300 kHz and 3 bar in ultrasonic frequency and pressure amplitude, respectively. The horizontal axis is in logarithmic scale, (a) The peak temperature (solid) and the molar fraction of water vapor (dash dotted) inside a bubble at the end of the bubble collapse, (b) The rate of production of oxidants with the logarithmic vertical axis. Reprinted with permission from Yasui K, Tuziuti T, Lee J, Kozuka T, Towata A, Iida Y (2008) The range of ambient radius for an active bubble in sonoluminescence and sonochemical reactions. J Chem Phys 128 184705. Copyright 2008, American Institute of Physics...

In acoustic cavitation, some bubbles dramatically expand and violently collapse, which is called the inertial collapse or Rayleigh collapse. It is caused by both the spherically shrinking geometry and the inertia of the surrounding liquid which inwardly flows into the bubble. The bubble collapse is similar to that in hydrodynamic cavitation which is induced by a sudden drop of pressure below the saturated vapor pressure due to a fluid flow through an orifice [92, 93]. At the end of the... 

Characterization of the cavitational phenomena and its effects in sonochemical reactors are generally described through mapping. Mapping of sonochemical reactor is a stepwise procedure where cavitational activity can be quantified by means of primary effect (temperature or pressure measurement at the time of bubble collapse) and/or secondary effect (quantification of chemical or physical effects in terms of measurable quantities after the bubble collapse) to identify the active and passive zones. 

Bhattacharya and Gedanken [11] have reported a template-free sonochemical route to synthesize hexagonal-shaped ZnO nanocrystals (6.3 1.2 nm) with a combined micro and mesoporous structure (Fig. 8.1) under Ar gas atmosphere. The higher porosity with Ar gas has been attributed to the higher average specific heat ratio of the Ar which leads to higher bubble collapse temperatures. With an intense bubble collapse temperature, more disorder is created in the product due to the incompleteness of the surface structure that led to greater porosity. Importance of gas atmosphere has been noted when the same process was carried out in the presence of air which results in the formation of ZnO without any porosity. 

Abstract Sonoluminescence from alkali-metal salt solutions reveals excited state alkali - metal atom emission which exhibits asymmetrically-broadened lines. The location of the emission site is of interest as well as how nonvolatile ions are reduced and electronically excited. This chapter reviews sonoluminescence studies on alkali-metal atom emission in various environments. We focus on the emission mechanism does the emission occur in the gas phase within bubbles or in heated fluid at the bubble/liquid interface Many studies support the gas phase origin. The transfer of nonvolatile ions into bubbles is suggested to occur by means of liquid droplets, which are injected into bubbles during nonspherical bubble oscillation, bubble coalescence and/or bubble fragmentation. The line width of the alkali-metal atom emission may provide the relative density of gas at bubble collapse under the assumption of the gas phase origin. 

Several other methods have been employed to access the conditions of bubble collapse. Misik et al. studied H20—D20 mixtures and through measurements with the use of spin traps, were able to determine the temperature from the relative rates of O—H and O—D cleavage [21]. They reported temperatures ranging from 2,000 to 4,000 K. Hart et al. developed a method based on the gas phase recombination of methyl radicals (MRR method), formed from the decomposition of methane [22]. They calculated temperatures of 2,000-2,800 K depending on the methane concentration. 

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