Stable cavitation bubbles

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...

From Fig. 1.1, it is seen that stable cavitation bubbles are tiny bubbles of a few pm in ambient radius or relatively large bubbles of about 10 pm or more in radius at 515 kHz. The range of ambient radius for transient cavitation bubbles becomes... 

On the other hand stable cavitation (bubbles that oscillate in a regular fashion for many acoustic cycles) induce microstreaming in the surrounding liquid which can also induce stress in any microbiological species present [5]. This type of cavitation may well be important in a range of applications of ultrasound to biotechnology [6]. An important consequence of the fluid micro-convection induced by bubble collapse is a sharp increase in the mass transfer at liquid-solid interfaces. In microbiology there are two zones where this ultrasonic enhancement of mass transfer will be important. The first is at the membrane and/or cellular wall and the second is in the cytosol i. e. the liquid present inside the cell. 

It is widely thought that the high pressure emitted from a "transient" cavitation bubble is responsible for the nucleation process (Hickling, 1994) however, experiments utilizing a single oscillating bubble have shown that ice can be initiated by a "stable" cavitation bubble. The mechanism of nucleation may be related to the asymmetric bubble shape, the flow field associated with the cavitation bubble, or the production of microbubbles. 

There are two types in acoustic cavitation. One is transient cavitation and the other is stable cavitation [14, 15]. There are two definitions in transient cavitation. One is that the lifetime of a bubble is relatively short such as one or a few acoustic cycles as a bubble is fragmented into daughter bubbles due to its shape instability. The other is that bubbles are active in light emission (sonoluminescence (SL)) or chemical reactions (sonochemical reactions). Accordingly, there are two definitions in stable cavitation. One is that bubbles are shape stable and have a long lifetime. The other is that bubbles are inactive in SL and chemical reactions. There exist... 

Ashokkumar M, Lee J, Iida Y, Yasui K, Kozuka T, Tuziuti T, Towata A (2009) The detection and control of stable and transient acoustic cavitation bubbles. Phys Chem Chem Phys 11 10118-10121... 

The bubble formed in stable cavitation contains gas (and very small amount of vapor) at ultrasonic intensity in the range of 1-3 W/cm2. Stable cavitation involves formation of smaller bubbles with non linear oscillations over many acoustic cycles. The typical bubble dynamics profile for the case of stable cavitation has been shown in Fig. 2.3. The phenomenon of growth of bubbles in stable cavitation is due to rectified diffusion [4] where, influx of gas during the rarefaction is higher than the flux of gas going out during compression. The temperature and pressure generated in this type of cavitation is lower as compared to transient cavitation and can be estimated as ... 

It is cavitation in a heterogeneous medium which is the most studied by sonoche-mists. When produced next to a phase interface, cavitation bubbles are strongly deformed. A liquid jet propagates across the bubble towards the interface at a velocity estimated to hundreds of metres per second. At a liquid-liquid interface, the intense movement produces a mutual injection of droplets of one liquid into the other one, i. e. an emulsion (Fig. 3.3). Such emulsions, generated through sonication, are smaller in size and more stable than those obtained conventionally and often require little or no surfactant to maintain stability. It can be anticipated therefore that Phase Transfer Catalysed (PTC) reactions will be improved by sonication. Examples are provided later in this chapter. 

Cavitation is the formation of gaseous cavities in a medium upon ultrasound exposure. The primary cause of cavitation is ultrasound-induced pressure variation in the medium. Cavitation involves either the rapid growth and collapse of a bubble (inertial cavitation) or the slow oscillatory motion of a bubble in an ultrasound field (stable cavitation). Collapse of cavitation bubbles releases a shock wave that can cause structural alteration in the surrounding tissue [13]. Tissues contain air pockets trapped in the fibrous structures that act as nuclei for cavitation upon ultrasound exposure. The cavitational effects vary inversely with ultrasound frequency and directly with ultrasound intensity. Cavitation might be important when low-frequency ultrasound is used, when gassy fluids are exposed, or when small gas-filled spaces are exposed. 

The first and second derivatives of R with respect to time are represented by R and R, respectively. Solving this equation for different values of R0 can be quite illustrative on the complex nonlinear dynamics of cavitation bubbles. Fig. 2 shows two different cases when a frequency of 20 kHz and an intensity equivalent to Py — 2.7 bar are used. In the first case (Fig. 2a), a relatively large (R0 = 2 mm) bubble couples with the sonic field through small-amplitude growth and compression cycles (stable cavitation). In contrast, a smaller bubble (P0 = 20 pm) experiences resonant coupling, which results... 

Depending on the particular type of bubbles, ultrasound cavitation can be transient or stable. In the transient type, also known as inertial cavitation, bubbles are either voids or vapour bubbles, which are believed to be produoed by intensities above 10 W/cm. They exist for one, or at most a few aooustic cycles, and expand to a radius of at least twice their initial size before collapsing abruptly on oompression and often disintegrating into small bubbles. The smaller bubbles formed can act as nuclei for further bubbles or, if their radius is sufficiently small, they can simply dissolve into the bulk solution under the aotion of the very large surface tension forces present. The lifetime of transient bubbles is believed to be too short to allow any mass flow by diffusion of gas into or out of the bubbles by contrast, evaporation and condensation of liquid are believed to ocour freely. In the absence of gas to cushion the implosion, the bubbles will collapse highly abruptly. 

Figure 8.1.4 Stable cavitation. Time-dependent radius of a bubble with 1 pm rest radius Rq.

A more illustrative description of the bubble motion in an acoustic field can be introduced by the concept of cavitation thresholds for different types of bubble behavior. Depending on the nature of the motion four basic types of cavitating voids are distinguished stable cavitation, rectified diffusion, dissolving bubbles, and transient cavitation. 

Only bubbles with the attributes stable or transient are Ukely to exist in a steady-state cavitating sound field. The lower size of a bubble at a given sound pressure is defined by the lower limit for stable cavitation. Any bubble smaller than this size would dissolve rather quickly under the action of its own surface tension. 

The upper size limit is made up by the transient cavitation threshold. Smaller bubbles may exist as stable oscillating bubbles that eventually grow in size by rectified diffusion or their path into regions with higher sound pressures. Bigger bubbles than this will collapse and create smaller daughter bubbles. The bubble size Rq is rather small and is of the order of several micrometers. 

Figure 8.1.13 Regions of stable cavitation, transient cavitation and dissolving bubbles for a frequency of 20 kHz in water at ambient temperature and a static pressure of 1 bar. Bubble radius R is normalized by the resonant bubble radius R,.

---