Ultrasonic acoustic pressure variations

The bubble-dynamics equations are very similar to acoustic cavitation the only difference being the fact that the surrounding fluctuating pressure field is driven by hydrodynamic conditions existing downstream of the constriction, whereas in the case of acoustic cavitation, it is dependent on the frequency and intensity of the ultrasonic irradiation (sinusoidal variation). There are two approaches used for the estimation of the local pressure at any location downstream of the constriction (the typical pressure recovery profiles are shown in Fig. 8.2.6). 

The parameters that best characterize an ultrasonic field are the wave frequency and the ultrasonic energy applied, with the latter being expressed as power, intensity, or acoustic pressure. The frequency does not represent a critical point because the variation of the applied frequency is usually less than 5-10% of the nominal frequency provided by the manufacturer. In contrast, the actual applied acoustic energy could be very different from the electrical consumption, and its direct measurement is difficult. In the literature, it is possible to identify a wide variety of methods for that purpose, but the results provided may be difficult to compare one with another. The majority of these methods are based on the measurement of physical or chemical changes produced by ultrasound, and a classification was proposed by Berlan and Mason (1996) ... 

Fig. 8.7 Variation of acoustic pressure inside an ultrasonic bath (Fungsonics mod. 28 L, 20 kHz Fungilab S.A., Barcelona, Spain) containing distilled water (281). Measurements were carried out with and without water agitation at different distances from the bottom of the bath.

These values show that the dynamic acmistic pressure varies SOOOOO times per second between +5.4 bar and —5.4 bar. The primary acoustic pressure, the particle amplibide and the velocity have relatively low values, so that exceptional effects are not to be expected from them. The acceleratkm of the particles of the liquid, however, can be very lai in tte case coisidered the acceleratkm is 100000 times greater than the action of gravity. The rapid variation of die acoustk pressure causes the formation of small cavities in the liquid, which, as will be shown later, are responsible for mo effects of hi -intensity ultrasonics in liquids. 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

Cook RK (1957) Variation of elastic constants and static strains with hydrostatic pressure a method for calculation from ultrasonic measurements. J Acoust Soc Am 29 445-449 David WIF (1992) Transformations in neutron powder diffraction. Physica B 180 181 567-574 Decker DL (1971) High-pressure equations of state forNaCl, KCl, and CsCl. J ApplPhys 42 3239-3244 Decker DL, Petersen S, Debray D, Lambert M (1979) Pressure-induced ferroelastic phase transition in Pb3(P04)2 A neutron diffraction study. Phys Rev B 19 3552-3555 Eggert JH, Xu L-W, Che R-Z, Chen L-C, Wang J-F (1992) High-pressure refractive index measurements of 4 1 methanol ethanol. J Appl Phys 72 2453-2461... 

Fig. 5. Calculated variation of radius R/R of a void cavitation bubble with time (r) under rectangular ultrasonic waves. Rqi initial radius of the bubble T period of ultrasonic vibration Pg. static pressure exerted on liquid Pqi acoustic pressiue amplitude. Parameter of curves i PqIP, for/U 0 bubble starts to oscillate IR (7/)]...

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