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.

Figure 1

Geometry of the system under study. (a) Growth of a cavitation bubble due to a negative pressure in the liquid. (b) Oscillation of the bubble around its equilibrium radius.

Figure 2

Comparison of the linearized equations derived in the present paper with the linear theory developed by Drysdale et al. [25].

Figure 3

(a) Growth and oscillation of the bubble. The dashed curve shows the exponential approximation of the bubble attenuation. (b) Oscillation of the cavity surface. (c) Comparison of the oscillations of the bubble and the cavity surface.

Figure 4

Normalized Fourier spectrum of the bubble oscillation shown in Fig. 3.

Figure 5

(a) Velocity of the bubble surface. (b) Velocity of the cavity surface.

Figure 6

Normal stress at the cavity surface.

Figure 7

Bubble growth and oscillation at different values of the initial negative liquid pressure.

Figure 8

Bubble growth and oscillation at different values of the shear modulus $\mu$.

Figure 9

Dependence of the attenuation coefficient $\alpha$ on the specific acoustic impedance of the solid $z_s={\rho }_s{c}_s$. The physical parameters are as in Fig. 8. The longitudinal wave speed $c_s$ is calculated by Eq. (71) varying the value of $\mu$.