Cavitation dynamics: II. Free pulsations and models for cavitation bubbles

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A mathematical formalism developed for investigating the dynamics of cavitation bubbles has been used to obtain numerical solutions describing the behavior of bubbles of different initial radii that are damped by heat conduction, viscosity, and compressibility. Calculations have been made to determine two measures of damping, the maximum temperatures, the maximum pressures, and the resonance frequencies of bubbles set into pulsations by a pressure pulse. In general, these quantities are controlled by heat conduction and viscosity at small amplitudes and mainly by compressibility at large amplitudes of motion. One measure of damping—the energy dissipation modulus—has a peak at a well-defined maximum radius. This peak serves to define a transition radius; for pulsations with amplitudes greater than this transition radius, the fraction of available energy dissipated in a cycle decreases and hence very large internal energy densities may occur. A second transition occurs at a radius called the critical radius; for pulsations with amplitudes greater than this critical radius, inertial forces control the collapse of a bubble and very large kinetic energy densities may occur in the liquid at the interface. The transition radius and the critical radius, which are functions of the initial size of a cavity, have been used to define a dynamical threshold for cavitation. In a motion where the maximum radius exceeds this proposed threshold, the characteristic phenomena of cavitation may be expected to appear. The dynamical threshold has in turn been used as the basis for models of cavitation bubbles useful in interpreting such phenomena. Subject Classification: 30.70, 30.60.