Acoustic cavitation bubbles pulsation

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. 

In Fig. 1.1, the parameter space for transient and stable cavitation bubbles is shown in R0 (ambient bubble radius) - pa (acoustic amplitude) plane [15]. The ambient bubble radius is defined as the bubble radius when an acoustic wave (ultrasound) is absent. The acoustic amplitude is defined as the pressure amplitude of an acoustic wave (ultrasound). Here, transient and stable cavitation bubbles are defined by their shape stability. This is the result of numerical simulations of bubble pulsations. Above the thickest line, bubbles are those of transient cavitation. Below the thickest line, bubbles are those of stable cavitation. Near the left upper side, there is a region for bubbles of high-energy stable cavitation designated by Stable (strong nf0) . In the brackets, the type of acoustic cavitation noise is indicated. The acoustic cavitation noise is defined as acoustic emissions from... 

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...

In a multibubble field, every pulsating bubble radiates secondary acoustic wave called acoustic cavitation noise. The pulsation of a bubble is driven by both the primary ultrasound and the acoustic cavitation noise. The influence of the latter on the bubble pulsation is called bubble-bubble interaction [89, 90]. Generally speaking, the bubble-bubble interaction suppresses the bubble expansion as shown in Fig. 1.16 [38, 89-91]. Further studies are required on this topic. 

Theoretical analysis of acoustic cavitation is focused, normally, on the study with the help of Nolting-Nepairas, Hering-Flinn equations and Kirkwood-Bete pulsations in the fluid of a single cavitation bubble 55 56). This approach features a number of... 

Eller, A. Flynn, H.G. Rectified diffusion during nonlinear pulsations of cavitation bubbles. J. Acoust. Soc. Am. 1965, 37 (3), 493-503. 

It is well known that some amounts of cavities or small bubbles are present in rubber during any type of mbber processing (Kasner and Meinecke, 1996). The formation of bubbles can be nucleated by precursor cavities of appropriate size (Gent and Tompkins, 1969). The proposed models (Isayev et al., 1996a,c,d Yashin and Isayev, 1999,2000) were based upon a mechanism of rubber network breakdown caused by cavitation, which is created by high intensity ultrasonic waves in the presence of pressure and heat. Driven by ultrasound, the cavities pulsate with amplitude depending mostly upon the ratio between ambient and ultrasonic pressures (acoustic cavitation). 

The main advantages of hydrophones are (1) the relative ease of use, (2) the fact that FFT analysis can be carried out, a feature which gives information on the type of cavitation (transient vs stable, access to chaos via a cascade of period doubling in the acoustic emissions from pulsating bubbles), (3) the topology of the reactors, (4) the shape of a pulsed signal in pulsed ultrasound, etc. ... 

Let us consider a bubble of initial radius Rq, pulsating in an acoustic field for a long period (several hundred or thousand cycles) which characterize the so-called "stable cavitation" regime. The bubble dynamics is linear (or non-linear) according to whether the bubble radius follows (or does not follow) the acoustic amplitude according to a law of proportionality. Since the evaporation and condensation phenomena are much more rapid than the bubble dynamics, it is usually assumed that the vapor pressure inside the bubble remains constant at the equilibrium value. 

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