Bubbles shape instability

The third mechanism for nucleation is the fragmentation of active cavitation bubbles [16]. A shape unstable bubble is fragmented into several daughter bubbles which are new nuclei for cavitation bubbles. Shape instability of a bubble is mostly induced by an asymmetric acoustic environment such as the presence of a neighboring bubble, solid object, liquid surface, or a traveling ultrasound, or an asymmetric liquid container etc. [25-27] Under some condition, a bubble jets many tiny bubbles which are new nuclei [6, 28]. This mechanism is important after acoustic cavitation is fully started. 

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... 

As there is no external control of the bubble shape, it is possible for shape instabilities to occur if excessive internal pressures are used, or if the polymer melt has an unsuitable extensional viscosity response. 

The blown film process is known to be difficult to operate, and a variety of instabilities have been observed on experimental and production film lines. We showed in the previous chapter (Figure 10.10) that even a simple viscoelastic model of film blowing can lead to multiple steady states that have very different bubble shapes for the same operating parameters. The dynamical response, both experimental and from blown film models, is even richer. The dynamics of solidification are undoubtedly an important factor in the transient response of the process, but the operating space exhibits a variety of response modes even with the conventional approach of fixing the location of solidification and requiring that the rate of change of the bubble radius vanish at that point. 

Snap off by the instability mechanism may occur in the following way. A bubble in an angular constriction such as a square channel will flatten against the walls as shown in Figure 2. The radius of the circular arcs in the corners for a static bubble is about one half of the tube half width. At low liquid flow rates, a bubble trapped behind a constriction has this nonaxisymmetric shape. As liquid flow rate increases, the bubble moves farther into the constriction and the fraction of cross sectional area open to liquid flow at the front of the bubble increases until the thread becomes axisymmetric at some point near the bubble front. 

One point that has not been emphasized is that all of the preceding analysis and discussion pertains only to the steady-state problem. From this type of analysis, we cannot deduce anything about the stability of the spherical (Hadamard Rybczynski) shape. In particular, if a drop or bubble is initially nonspherical or is perturbed to a nonspherical shape, we cannot ascertain whether the drop will evolve toward a steady, spherical shape. The answer to this question requires additional analysis that is not given here. The result of this analysis26 is that the spherical shape is stable to infinitesimal perturbations of shape for all finite capillary numbers but is unstable in the limit Ca = oo (y = 0). In the latter case, a drop that is initially elongated in the direction of motion is predicted to develop a tail. A drop that is initially flattened in the direction of motion, on the other hand, is predicted to develop an indentation at the rear. Further analysis is required to determine whether the magnitude of the shape perturbation is a factor in the stability of the spherical shape for arbitrary, finite Ca.21 Again, the details are not presented here. The result is that finite deformation can lead to instability even for finite Ca. Once unstable, the drop behavior for finite Ca is qualitatively similar to that predicted for infinitesimal perturbations of shape at Ca = oo that is, oblate drops form an indentation at the rear, and prolate drops form a tail. 

As the amplitude of the volume oscillation increases, the radial motion of the bubble becomes unstable, and small disturbances cause the bubble to undergo various shape oscillations [42]. As the bubble radius increases, the threshold for the instability decreases. Excitation of different shapes is referenced to as dancing bubble motion or erratic motion . 

Fig. 8.2 Image of a collapsing viscous bubble. The bubble loses its axisymmetric shape, small amplitude ripples grow. The inset displays a schematic side view of the essentially conical deflating bubble at the onset of the instability [5]...

Slug flow The bubble dimensions are close to tube pipe diameter and the bubbles have a characteristic shape similar to a bullet with a hemispherical nose with a blunt tail end. They are commonly referred to as Taylor bubbles after the instability of that name. Taylor bubbles are separated from one another by slugs of liquid, which may include small bubbles. 

Relatively large bubbles with low excess pressure are likely to behave as if they were closed, whereas the reverse should hold true for very small bubbles. Thus, upon increasing the bubble size, a transition takes place from instability to practically complete stability. Invoking shape deformations will not necessitate any major modifications of the above discussion as the spherical shape is always associated with minimal free energy for a given bubble volume. 

FIGURE 9.26 Typical bubble instability shapes. (Reprinted by permission of the publisher from Kanai and White, 1984.)... 

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