Model for the growth and the oscillation of a cavitation bubble in a spherical liquid-filled cavity enclosed in an elastic medium

Equations are derived that describe the growth and subsequent damped oscillation of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid. It is assumed that the nucleation and the growth of the bubble are caused by an initial negative pressure in the cavity. The liquid is treated as viscous and compressible. The obtained equations allow one to model, by numerical computation, the growth and the oscillation of the bubble in the cavity and the oscillation of the cavity surface. It is shown that the equilibrium radius reached by the growing bubble decreases when the absolute magnitude of the initial negative pressure decreases. It is also found that the natural frequency of the bubble oscillation increases with increasing bubble radius. This result is of special interest because in an unbounded liquid, the natural frequency of a bubble is known to behave oppositely, namely it decreases with increasing bubble radius.