Sonochemistry amplitudes

Fig. 1.1 The regions for transient cavitation bubbles and stable cavitation bubbles when they are defined by the shape stability of bubbles in the parameter space of ambient bubble radius (R0) and the acoustic amplitude (p ). The ultrasonic frequency is 515 kHz. The thickest line is the border between the region for stable cavitation bubbles and that for transient ones. The type of bubble pulsation has been indicated by the frequency spectrum of acoustic cavitation noise such as nf0 (periodic pulsation with the acoustic period), nfo/2 (doubled acoustic period), nf0/4 (quadrupled acoustic period), and chaotic (non-periodic pulsation). Any transient cavitation bubbles result in the broad-band noise due to the temporal fluctuation in the number of bubbles. Reprinted from Ultrasonics Sonochemistry, vol. 17, K.Yasui, T.Tuziuti, J. Lee, T.Kozuka, A.Towata, and Y. Iida, Numerical simulations of acoustic cavitation noise with the temporal fluctuation in the number of bubbles, pp. 460-472, Copyright (2010), with permission from Elsevier...

Fig. 1.4 The calculated results for one acoustic cycle when a bubble in water at 3 °C is irradiated by an ultrasonic wave of 52 kHz and 1.52 bar in frequency and pressure amplitude, respectively. The ambient bubble radius is 3.6 pm. (a) The bubble radius, (b) The dissolution rate of OH radicals into the liquid from the interior of the bubble (solid line) and its time integral (dotted line). Reprinted with permission from Yasui K, Tuziuti T, Sivaknmar M, Iida Y (2005) Theoretical study of single-bubble sonochemistry. J Chem Phys 122 224706. Copyright 2005, American Institute of Physics...

Hatanaka et al. [50], Didenko and Suslick [51], and Koda et al. [52] reported the experiment of chemical reactions in a single-bubble system called single-bubble sonochemistry. Didenko and Suslick [51] reported that the amount of OH radicals produced by a single bubble per acoustic cycle was about 10s 106 molecules at 52 kHz and 1.3 1.55 bar in ultrasonic frequency and pressure amplitude, respectively. The result of a numerical simulation shown in Fig. 1.4 [43] is under the condition of the experiment of Didenko and Suslick [51]. The amount of OH... 

One of the most important characteristics necessary to completely identify a wave is its intensity, where the intensity is a measure of the sound energy the wave produces. For a sound wave in air, the mass (m) of air moving with an average velocity (v) will have associated with it a kinetic energy of (mv )/2 (joules). In the strictest sense the intensity is the amount of energy carried per second per unit area by the wave. Since the units of energy are joules (J) and a joule per second is a watt (W), then the usual unit of sound intensity (especially in sonochemistry) will be W cm. As we will see later (Eq. 2.13), the maximum intensity (I) of the sound wave is proportional to the square of the amplitude of vibration of the wave (P ). This will have important repercussions in our study of chemical systems. 

Many of the phenomena in acoustics can be described by means of a theory either linear in acoustic amplitude or including the first term of non-linear equations. In sonochemistry, the displacement amplitude of the wave is so large that nonlinear terms of the propagation equation cannot be neglected. 546 This leads to considerable complexity in the description. In this section, we follow a route of increasing complexity up to the major question what can be done to quantify the medium in which sonochemistry (or sonoluminescence) occurs ... 

The human ear can be excited by an energy as low as 10 J, corresponding to the work spent in lifting a mass of 10 g by 1 mm against gravity. Our perception of sound-wave strength is linked to acoustic intensity, i.e., the acoustic pressure amplitude of the wave (Pa, in Pa or bars). Normal speech corresponds to a pressure of lO bar. In sonochemistry, pressures of a few bars are commonly used, which means that sonochemists deal with extremely non-linear systems. In the case of a progressive planar or spherical wave,i the acoustic pressure and intensity (in W m"2) of the ultrasoimd are linked as in Eq. 2 ... 

Since sonochemistry takes its origin in cavitation, the reactivity depends on the characteristics of the bubbles. Their size and lifetime, and the content of the gaseous phase, depend on the physical properties of the medium and the parameters (amplitude and frequency) of the wave. Conducting a sonochemical reaction implies that a multiparameter problem is examined. 

Schuchmann, H.P.,andTavman, S. (2008) Influence of hydrostatic pressure and sound amplitude on the ultrasoimd induced dispersion and de-agglomeration of nanoparticles. Ultrasonics Sonochemistry,... 

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