Radiation dynamics of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid

A specific cavitation phenomenon occurs inside the stems of trees. The internal pressure in tree conduits can drop down to significant negative values, which causes the nucleation of bubbles. The bubbles exhibit high-frequency oscillations just after their nucleation. In the present study, this phenomenon is modeled by taking into account acoustic waves produced by bubble oscillations. A dispersion equation is derived, which is then used to calculate the resonance frequency and the attenuation coefficient of the bubble oscillations. Radiation damping is found to be predominant in comparison with viscous damping, except for very small bubbles. A typical number of oscillation cycles before the complete damping of the oscillation is found to be of the order of 10, as observed for cavitation bubbles in biomimetic synthetic trees.

Figure 1

(a) The system under study: the nucleation of a cavitation bubble in a liquid-filled cavity that leads to the relaxation of tension in the liquid. (b) Acoustic waves induced by the bubble pulsation after nucleation.

Figure 2

Comparison of exact numerical solutions calculated by Eq. (24) (solid) with approximate analytical solutions calculated by Eq. (33) (long dashed) and Eq. (43) (short dashed). The dash-dotted lines show numerical solutions at $\eta =0$.

Figure 3

Dependence on the shear modulus $\mu$. The resonance frequency increases monotonically with $\mu$ while the attenuation coefficient passes through a maximum.

Figure 4

Dependence on the solid density ${\rho }_s$. The resonance frequency decreases with ${\rho }_s$ while the attenuation coefficient increases.