Resonant size

Apart from the classification based on the mode of generation of cavities, cavitation can also be classified as transient cavitation and stable cavitation [3]. The classification is based on the maximum radius reached (resonant size), life time of cavity (which decides the extent of collapse) in the bulk of liquid and the pattern of cavity collapse. Generation of transient or stable cavitation usually depends on the set of operating parameters and constitution of the liquid medium. Depending on the specific application under question, it is very important to select particular set of operating conditions such that maximum effects are obtained with minimum possible energy consumption. 

One can easily calculate from such equations, however, what size cavity would undergo maximum expansion when subjected to a given acoustic field. Minnaert, for example, derives (34) (from a simplified model which assumed a noncondensable gas and neglected viscosity) this resonant size of a transient cavity as... 

Further, if an insonation frequency of 50 kHz is employed neither of these two bubbles undergo collapse (Figs. 2.18 and 2.19). Only a bubble close to the resonance size (0.6 X 10 cm) will undergo collapse at the higher frequency (Fig. 2.20). 

Other microwave dielectrics have been identified and developed into commerical products and those currently exploited are listed in Table 5.8. The modified neodymium titanates are particularly important because of their high permittivity values and the reduction in resonator size this offers. 

Under the appropriate conditions, the acoustic force on a bubble can be used to balance against its buoyancy, holding the bubble stable in the liquid by acoustic levitation. This permits examination of the dynamic characteristics of the bubble in considerable detail, from both a theoretical and an experimental perspective. Such a bubble is typically quite small compared to an acoustic wavelength (e.g., at 20 kHz, the resonance size is approximately 150 pm). For rather specialized but easily obtainable conditions, a single, stable, oscillating gas bubble can be forced into such large-amplitude pulsations that it produces sonoluminescence emissions on each (and every) acoustic cycle. Such SBSL is outside the scope of this chapter. 

To identify nanoparticles there are several analytical techniques, including crystalline nature, surface plasmon resonance, size, shape, stability, nature, etc., which was done by various analytical instruments, such as UV-visible spectroscopy, X-ray diffractometry, Fourier transform infrared spectroscopy, scanning electron microscopy, transmission electron microscopy, energy dispersive analysis, zeta potential, etc. These are mostly used for analysis of synthesized nanoparticles, which helps us to study crystalline nature, functional groups, and morphological studies, and to identify its stability. 

The synthesized fucoidans polysaccharides isolated from marine algae C. okamuranus and K. crassifolia and used for synthesis of AgNPs were reported by Soisuwan et al. (2010). The synthesized AgNPs were characterized for surface plasmon resonance, size, and morphological studies. The results suggest that the SPR band was at 527—530 nm and was spherical in shape with average size of 8-10 nm. 

Secondary Bjerknes forces arise when two oscillating bubbles are present in a pressure field. Attractive forces between bubbles with inphase pulsation cause coalescence. Bubbles oscillating out of phase are repelled. The bubble oscillation is in phase when both bubbles are smaller or larger than the resonance size and attractive forces dominate. If one bubble is smaller and one larger than the resonance size, they oscillate in and out of phase and repel one another. 

Primary and secondary Bjerknes forces lead to structures known as cavitation streamers. A large bubble above the resonance size oscillating with surface insta-... 

The case of two spherical bubbles, smaller than resonance size, for example (i.e., pulsating in phase), is considered. Of course, the situation can be transposed to bubbles larger than resonance size both vibrating out-of-phase with respect to the acoustic pressure, i.e., in phase with one another. In Fig. 26, the left-hand L and... 

For most applications of interest, including cells in aqueous solution, the acoustic force will act towards the pressure node, however in the case of bubbles that are smaller than resonant size, and certain two-phase fluid mixtures, the bubble, or second phase fluid, will experience an acoustic force acting towards the pressure antinode. 

Thus time-resolved experiments can be performed [6.51,52]. Data for a number of facilities producing synchrotron radiation are given in Table 6.1. With synchrotrons of resonable sizes the intensity per Doppler width that is achievable is comparable to that which is obtained from efficent line light sources. However, the intensity increases towards the extreme UV (XUV) and X-ray regions, where no comparable continuum light sources exist. 

Experiments have shown that aqueous sonochemistry is unchanged over the frequency range in which cavitation occurs i.e. 10 Hz to 10 MHz [22]. Since there is no direct coupling of the sound field with species on a molecular level, changing the frequency of the sound input simply alters the resonant size of the cavitation bubble. The effect of this over the range of interest is negligible. It should, however, be noted that although there is both an upper and a lower limit to the frequencies at which cavitation will occur, the band of frequencies used for sonochemistry lies well within these limits. 

Taking the pulse off time at which SL disappeared, the resonance size of the cavitation bubbles was calculated. Epstein Plesset equation, (Eq. 1.3) which relates bubble dissolution time to its radius, was used for this purpose. 

Fig. 1.1 Schematic representation [Adapted from Ref. 41] of pulsed sonoluminescence technique to determine the resonance size of cavitation bubbles. Bubbles grow during pulse on (T) and dissolve during pulse off (To). With increasing T , steady-state SL intensity decreases top right) eventually to zero—the corresponding To is used to calculate the bubble size using Eq. 1.3...

D—diffusion coefficient Cs—dissolved gas concentration pg—density of gas Ro—initial bubble radius t—dissolution time M—molar mass of gas y—surface tension of the liquid R— gas constant and T—solution temperature. Replacing t with To, Ro (assumed to be equal to resonance size) can be determined. The resonance size of eavitation bubbles at 515 kHz was found to be in the range 2.8-3.S pm. 

A follow up work by Brotchie et al. [42] noted that the resonance sizes of sono-luminescence and sonochemically active bubbles are different. The sonochemilu-minescence, resulting from the reaction between OH radicals generated within cavitation bubbles and luminol molecules, intensity was used to determine the sono-ehemically active (SCL) bubbles. The resonance size of SL bubbles are found to be relatively larger than that of SCL bubbles. In addition, Eq. (1.2) shows that the resonance size decreases with an increase in ultrasonic frequency. Brotchie et al. [42] have also confirmed this experimentally. The sizes were found to be 3.9, 3.2, 2.9, 2.7 and 2 pm at 213, 355, 647, 875 and 1056 kHz frequency, respectively. Another important aspect that needs to be mentioned is the difference between theoretical and experimentally determined resonance sizes of the cavitation bubbles. Equation (1.2) provides a theoretical value of 14 pm at 213 kHz whereas the experimental value is found to be 3.9 pm. This is also known from single bubble work at 20 kHz where the experimental resonance size was found to be about 5 pm compared to the theoretical value of 150 pm [43]. The difference between the resonance size determined by Eq. (1.2) and experimental value is due to the fact that Eq. (1.2) is a very simplified one that does not consider the physical properties of the liquid or bubble contents. 

When bubbles reach the resonance size range, they grow to a maximum size within one acoustic cycle and implode. Bubble implosion/collapse is a near adiabatic process. In simple thermodynamic terms, the volume of the bubble decreases instantaneously resulting in the generation of extreme heat within the bubble. Theoretical estimates predict greater than 15,000 K [44, 45]. However, experimental methods estimate about 1000-5000 K [46-50]. A number of techniques have been used to calculate the bubble temperatures. First, the bubble temperature could be theoretically calculated using Eq. (1.4). 

In brief, for a given solution volume and acoustic power, a change in acoustic frequency results in an increase in the number of active bubbles and a decrease in the resonance size of the bubble. This would have two opposing effects. A decrease in bubble size means a decrease in collapse intensity and hence lower bubble temperature. This leads to a decrease in the amount of primary and secondary radicals generated per bubble. In the meantime, an increase in the number of bubbles (due to an increase in the number of standing waves) leads to an increase in the amount of radicals generated. It has been shown in many studies [96-100] that the sonochemical reaction yield peaks around 200-800 kHz beyond which a decline in the yield is observed. 

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