Cavity growth

Acoustic cavitation can be considered to involve at least three discrete stages nucleation, bubble growth, and, under proper conditions, implosive collapse. The dynamics of cavity growth and collapse are strikingly dependent on local environment we therefore will consider separately cavitation in a homogeneous liquid and cavitation near a liquid-solid interface. 

Penetration of both types of cavity into the silicon nitride grains, as shown in Fig. 4.14, suggests that cavity growth occurs by the diffusion of silicon nitride from the cavity surface to the grain boundary. The transition between the two types of cavity can be rationalized by the Chuang theory of cavity growth,96 which relates the mode of cavity growth to the relative diffusion rate... 

Using this analysis, Zhurkov, Kuksenko and Slutslrer followed the kinetics of cavity growth and correlated their results with ESR n asurements of radical formation, as reported later in Section 3. 

Britten. J. A., and Thorsness. C. B. 1989. A model for cavity growth and resource recovery during underground coal gasification. In Situ, 13 1-53. 

Pirlot, P., Pirard, J. P., Coeme, A., Mostade, M., 1998, A coupling of chemical processes and flow in view of the cavity growth simulation of an underground coal gasifier at great depth. In Situ, 22(2), 141-156. 

In conclusion, when such an adhesive is debonded from a high energy surface such as steel, the high-strain properties of the adhesive control the formation and extension of the fibrillar structure which provides the bulk of the work necessary to detach the adhesive from the surface, and hence the major part of the peel force. We have seen that the level of the plateau stress can be predicted quantitatively by a simple tensile test. From the studies on cavitation, we know that the nominal stress at the plateau corresponds also to the cavity growth stress for large initial defects. 

A vacancy is created in the metal phase, which can be aimihilated by operations of structural defects, disorientation, and misfit dislocations [116, 117]. Prolonged sulfidation also can cause void nucleation and cavity growth at the interface. In the case of sulfidation by liquid sulfur, the separation of sulfide and metal by cavities could be avoided by applying a pressure on the growing sulfide [13-18]. 

The development of a cavity cluster from a distribution of supercritical cavitation nuclei at their exposure to tensile stress is discussed. An approach to this problem was presented by Hansson et al. [1], and is the basis of further analysis and comparison of planar and spherical cavity cluster development. The stress penetration into the cluster depends primarily on the inter—cavity distance and on the cluster form. In interplay with the cavity dynamics it determines an acoustic impedance of the cluster boundary which approaches zero during cavity growth, and so the tensile stress at the boundary resulting from the incident and the reflected waves becomes small which indicates that not only this pressure but also the equilibrium pressures of the cavities are important for the cluster development. 

In the numerical calculations it is assumed that the cluster develops from micro-cavities of initial radius ao = 10 pm, and that the imposed pressure (tensile stress) causing cavity growth lp >> peq, so that void dilatation due to different equilibrium sizes of the cavities during their growth is negligible. It is chosen to apply a pressure disturbance at the cluster boundary... 

A piston at the cluster boundary could produce the planar cluster described, if moved with the velocity (u)x=o also shown in fig. 3. The associated acceleration is high for a mechanical system and a frequency f = 2 kHz might be more reasonable. For such a case the tensile stress penetration into the region with microcavities is weaker, but after 30 ps the cavity growth is approximately as after 16 //s at 20 kHz. 

If the stress amplitude is reduced to Pm = 2 kPa with f = 2 kHz a cavity growth as above is obtained after about 70 ps, and then Ux=o = - 0.49 m/s with k = - 0.996. The pressure at the cluster boundary penetrates slightly deeper than above, but still only the outermost cavity "layers" are appreciably affected and the cavity growth profile is essentially the same in all cases, only the time of development changes. 

Figure 3. The pressure of the incident wave Api vs. time t at the boundary of a planar cluster causing the pressure and cavity growth distributions shown in figures 1-2, the associated wave reflection coefficient k and the velocity (u)x=o of the fluid elements at x = 0.

However, changing the intercavity distance to = 1 mm causes the tensile stress and the cavity growth to penetrate to the cluster centre as shown in figs. 6 and 7, respectively. 

As a consequence, the network of grains must move apart, giving rise to dilatational stresses which are responsible for cavitation within the material. Cavitation occurs when the dilatational stress at a multigrain junction exceeds a critical stress for cavity nucleation. Subsequent cavity growth occurs via redistribution of the secondary phases from the cavity towards the uncavitated material. As the secondary phase flows away from the cavitated junction, the stress required for cavity nucleation relaxes, thus releasing the stressed contacts between silicon nitride grains. The rearrangement of dilatation stresses then results in a new round of cavity formation. 

Fig. 6.76 Comparison of the predicted (-) and experimentally observed conditions for zero cavity growth (white square) Lucalox, 1600 °C (black square) AD99, 1300 °C, and for cavity growth (white circle) Lucalox, 1600 °C (black circle) AD99,...

C. Region I represents cavity growth and region II, cavity shrinkage [29]. With kind permission of John Wiley and Sons... 

Rice, J. R. and Chuang, T.-J. (1981), Energy variations in diffusive cavity growth. Journal of the American Ceramic Society 64, 46-53. 

---