An asymptotic study of the behavior of a cavitation bubble in a variable pressure field

In order to investigate the relative importance of different phenomena involved in the dynamics of the growth of cavitation bubbles and their subsequent collapse or oscillations; namely, surface tension, viscosity and inertia reaction of gas inside the bubble; a classification of different initial dimensions is established. A dimensionless formulation leads to the definition of three characteristic quantities involving only the fluid properties: a limit radius, a maximum pressure and a characteristic frequency. Matched asymptotic expansions depending upon the position of initial data with respect to the three characteristic fluid quantities are then used. The fundamental importance of the thermodynamic behavior of the gas inside the bubble in all cases, and the role played by viscosity when resonance can occur, are shown.