Cavitation bubbles equilibrium radius

In any cavitation field most of the visible bubbles will be oscillating in a stable manner and it is perhaps pertinent that we concentrate our discussions first on the fate of such bubbles in the acoustic field. If we assume that we have a bubble with an equilibrium radius, R, existing in a liquid at atmospheric pressure Pjj, then the oscillation of the bubble and in particular the motion of the bubble wall, under the influence of the applied sinusoidal acoustic pressure (P ) is a simple dynamical problem, akin to simple harmonic motion for a spring. 

In Fig. 9 the pressure in the liquid is plotted against the corresponding equilibrium radius of a cavitation bubble. The dashed curve represents a gas bubble and the solid curve a vapour bubble. Cavitation bubbles in a cluster are very sensitive to differences in the radius. In the case of a constant pressure, all bubbles with a radius smaller than the equilibrium radius are unstable and collapse. For gas bubbles this only holds as long as its equilibrium radius is greater than the radius (cf. Fig. 9). This mechanism, in addition to stability differences due to a different amount of gas/vapour contained in the bubbles. 

Let us consider a bubble of initial radius Rq, pulsating in an acoustic field for a long period (several hundred or thousand cycles) which characterize the so-called "stable cavitation" regime. The bubble dynamics is linear (or non-linear) according to whether the bubble radius follows (or does not follow) the acoustic amplitude according to a law of proportionality. Since the evaporation and condensation phenomena are much more rapid than the bubble dynamics, it is usually assumed that the vapor pressure inside the bubble remains constant at the equilibrium value. 

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