Rayleigh-Plesset equation bubble collapse

Now the bubble collapse is discussed using the Rayleigh-Plesset equation. After the bubble expansion, a bubble collapses. During the bubble collapse, important terms in the Rayleigh-Plesset equation are the two terms in the left hand side of (1.13). Then, the bubble wall acceleration is expressed as follows. 

There is always an uncertainty associated with the exact quantification of the collapse pressure generated. Use of the Rayleigh-Plesset equation will dictate the termination condition as bubble-wall velocity exceeding the velocity of sound in the medium, whereas for the case of equations considering the compressibility of liquid, new termination criteria will have to be considered. Thus, for some other conditions with better computational facilities, a different collapse criteria (cavity size lower than 1 or even 0.1% of the initial size) may look feasible. Another collapse criteria based on Vander Wall s equation of state has also been considered [Gastagar, 2004]. The criteria considers that the cavity is assumed to be collapsed when the volume occupied by the cavity is equal to the material volume given by the product of the constant b in the Vander Wall s equation of state and the number of moles. The exact predictions of the collapse pressure pulse is always a matter of debate, nevertheless, a new proportionality constant to avoid this uncertainty can always be developed based on the relative rates of the reaction. 

By combining the Rayleigh-Plesset equation with a mass and energy balance over the bubble, the temperature and pressure in the bubble can be calculated (16,17). The model also describes the dynamic movement of the bubble wall, which results in a calculated radius of the cavitation bubble as a fimction of time (see Fig. 2). The explosive growth phase and the collapse phase of the bubble can clearly be distinguished. Moreover, in case dynamic effects are more important than the surface tension, the cavitation threshold can be calculated with the dynamic model, while the Blake threshold pressure cannot be used at these conditions. 

Indeed, the P(t) curve resulting from this extended Rayleigh-Plesset equation (7.2) leads to a delayed bubble collapse for the two-bubble case, see Fig. 7.5, in good quantitative agreement with the measurements, despite the fact that the bubbles feel an anisotropic pressure field around their surface, especially in the last stage of their collapse. When the bubbles come closer to each other (middle... 

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