Acoustic amplitude

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...

Fig. 1.6 The correlation between the bubble temperature at the collapse and the amount of the oxidants created inside a bubble per collapse in number of molecules. The calculated results for various ambient pressures and acoustic amplitudes are plotted. The temperature of liquid water is 20 °C. (a) For an air bubble of 5 pm in ambient radius at 140 kHz in ultrasonic frequency, (b) For an oxygen bubble of 0.5 pm in ambient radius at 1 MHz. Reprinted with permission from Yasui K, Tuziuti T, Iida Y, Mitome H (2003) Theoretical study of the ambient-pressure dependence of sonochemical reactions. J Chem Phys 119 346-356. Copyright 2003, American Institute of Physics...

In some literature, there is a description that a bubble with linear resonance radius is active in sonoluminescence and sonochemical reactions. However, as already noted, bubble pulsation is intrinsically nonlinear for active bubbles. Thus, the concept of the linear resonance is not applicable to active bubbles (That is only applicable to a linearly pulsating bubble under very weak ultrasound such as 0.1 bar in pressure amplitude). Furthermore, a bubble with the linear resonance radius can be inactive in sonoluminescence and sonochemical reactions [39]. In Fig. 1.8, the calculated expansion ratio (/ max / Rq, where f max is the maximum radius and R0 is the ambient radius of a bubble) is shown as a function of the ambient radius (Ro) for various acoustic amplitudes at 300 kHz [39]. It is seen that the ambient radius for the peak in the expansion ratio decreases as the acoustic pressure amplitude increases. While the linear resonance radius is 11 pm at 300 kHz, the ambient radius for the peak at 3 bar in pressure amplitude is about 0.4 pm. Even at the pressure amplitude of 0.5 bar, it is about 5 pm, which is much smaller than the linear resonance radius. 

Fig. 1.15 Calculated acoustic amplitude under an ultrasonic horn as a function of the distance from the horn tip on the symmetry axis. The dotted curve is the calculated result by (1.21) when v0 = 0.77 m/s, X = 51.7 mm (29 kHz), and a = 5 mm. The solid curve is the estimated one in a bubbly liquid. Reprinted figure with permission from Yasui K, Iida Y, Tuziuti T, Kozuka T, Towata A (2008) Strongly interacting bubbles under an ultrasonic hom. Phys Rev E 77 016609 [http //link.aps.org/abstract/PRE/v77/e016609]. Copyright (2008) by the American Physical Society...

Increasing the reaction temperature allows cavitation to be achieved at lower acoustic intensity. This is a direct consequence of the rise in vapour pressure associated with heating the liquid. The higher the vapour pressure the lower the applied acoustic amplitude (P ) necessary to ensure that the apparent hydrostatic pressure, Pjj — P, is exceeded - see Section 2.4.4. Unfortunately the effects resulting from cavitational collapse are also reduced. A consideration of Eqs. 2.35 and 2.36 show that Tjjjg and Pj g fall due to the increase in P and decrease in Pjn(= Ph + Pa)- other words to get maximum sonochemical benefit any experiment should be conducted at as low a temperature as is feasible or with a solvent of low vapour pressure. 

This section of the programme allows an estimation of the acoustic amplitude (P ) of the wave from knowledge of the intensity (Int) of the wave and the velocity (vel) of sound in the medium. The value for velocity must be either entered in full (i.e. 1500) or by using the mathematical notation 1.5E3. 

In Chapter 2 we explained why there existed a cavitation threshold i. e. a limit of sound intensity below which cavitation could not be produced in a liquid. We suggested that only when the applied acoustic amplitude (P ) of the ultrasonic wave was sufficiently large to overcome the cohesive forces within the liquid could the liquid be tom apart and produce cavitation bubbles. If degradation is due to cavitation then it is expected that degradation will only occur when the cavitation threshold is exceeded. This is confirmed by Weissler who investigated the degradation of hydroxycellulose and observed that the start of degradation coincided with the onset of cavitation (Fig. 5.21). 

Damping by wall friction may be addressed on the basis of the theory of oscillatory boundary layers [35], [36]. Under conditions in real motors, the oscillatory boundary layer at the wall is much thinner than the mean-flow boundary layer [37], and the tangential acoustic velocities just outside the oscillatory boundary layer are (TJT ) times those outside the mean-flow boundary layer, where is the wall temperature and the gas temperature in the chamber. Dissipation in the oscillatory boundary layer may be analyzed by considering a flat element of the surface exposed to the complex amplitude V(T JT,) of velocity oscillation parallel to the surface, where equation (24) has been employed for the acoustic field in the chamber, with the coordinate system locally aligned in the direction of velocity oscillation. Neglecting locally the effects of density changes and the spatial variations of acoustic amplitudes, we write the combination of equations (1-2) and (1-5) for the velocity v parallel to the wall as... 

Acoustical Amplitude, phase or frequency (acoustic wave) SAW devices... 

The model predicts that methane-air flames with an equivalence ratio of 0.8 propagating downward are always unstable as a result of either the Darrieus-Landau instability or the secondary pyroacoustic instability, also known as the parametric instability, yet flames with an equivalence ratio of 1.3 will be stabilized by a small band of normalized acoustic-velocity amplitudes between 3.7 and 4. Although it was found experimentally that a methane-air flame with an equivalence ratio of 0.8 can be stabilized, the results of the model agree qualitatively with the experimental findings, specifically that a methane-air flame with an equivalence ratio of 1.3 is stable over a larger range of acoustic amplitudes than one with an equivalence ratio of 0.8. 

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 ... 

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. 

The simplest way to increase penetration of short pulses is to increase the acoustic power of the ultrasound beam, because signal from deeper tissue regions can be recorded over the noise threshold. However, concerns about potential and undesirable side effects, in particular related to acoustic cavitation, set limits on the possibility of overcoming the frequency-dependent attenuation by increasing peak acoustic amplitudes of the waves probing the tissue. Moreover, low amplitudes are mandatory... 

A substantial effort has been made by the different manufacturers of ultrasound machines to overcome limitations of peak acoustic amplitude by using long wideband transmitting sequences and compression techniques on the receiver side. Basically all use coded transmitted signals and employ correlation and averaging of the echoes on reception (Fig. 1.2). 

The acoustic pressure amplitude determines the growth of a cavitation bubble and consequently the chemical effects upon collapse. The amplitude of the pressure wave can be measured with a hydrophone or can he calculated using a calorimetric method (9,10), in which it is possible to determine the ultrasoimd power (Qus) that is transferred to the liquid. With the ultrasound power and the surface area of the ultrasound source (Aus), the acoustic amplitude can he calculated according to equation (2), for which the ultrasoimd intensity is the power input divided by the surface area of the source (11). 

Ultrasound passes through an elastic medium as a longitudinal wave, which is a series of alternating compressions and rarefactions. This means that hquid is displaced parallel to the direction of motion of the wave. Ultrasound comprises sound waves typically in the range of 20 kHz to approximately 500 MHz. The frequency (/) and the acoustic amplitude (PA,max) are the most important properties to characterize the pressure wave. The variation of the acoustic pressure (Pa) of an ultrasound wave as a function of time (t) at a fixed frequency is described by Eq. (2)... 

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