Cavitation in a liquid-filled cavity surrounded by an elastic medium: Intercoupling of cavitation events in neighboring cavities

The subject of the present theoretical study is the dynamics of a cavitation bubble in a spherical liquid-filled cavity surrounded by an infinite elastic solid. Two objectives are pursued. The first is to derive equations for the velocity and pressure fields throughout the liquid filling the cavity and equations for the stress and strain fields throughout the solid medium surrounding the cavity. This derivation is based on the results of our previous paper [A. A. Doinikov et al., Phys. Rev. E 97, 013108 (2018)], where equations for the evolution of a bubble inside a cavity were derived. The second objective is to apply the equations obtained at the first step of the study to ascertain if the cavitation process in one cavity can trigger the nucleation in a neighboring cavity. To this end, we consider a neighboring cavity in which a cavitation bubble is absent. We derive equations that describe the disturbance of the liquid pressure inside the second cavity, assuming this disturbance to be caused by the cavitation process in the first cavity. The developed theory is then used to perform numerical simulations. The results of the simulations show that the magnitude of the background negative pressure inside the second cavity increases at the second half period of the pressure disturbance, which in turn enhances the probability of nucleation in the second cavity.

Figure 1

Geometry of the system under study. A cavitation bubble arises in a liquid-filled cavity due to a high initial negative pressure $P_{l0}$ in the liquid. The bubble grows and undergoes a damped oscillation until its radius reaches an equilibrium value. The bubble growth leads to the relaxation of the pressure in the liquid and the stress in the solid. The bubble oscillation generates acoustic waves, which propagate through the liquid, penetrate into the solid, and go away.

Figure 2

Two cavities with a separation distance $d$ between their centers. The second (right) cavity does not contain a cavitation bubble and is kept at rest until the disturbance wave from the first (left) cavity reaches it.

Figure 3

Liquid pressure as a function of time at different spatial points.

Figure 4

Spatial distribution of the pressure in the liquid between $R_b$ and $R_c$ for different time moments. For $t\to \infty$, the pressure tends to −5.3 kPa throughout the liquid.

Figure 5

Stress in the solid as a function of time at different spatial points. The stress at $r=R_c$ is shown in the separate plot because of a great difference in magnitude.

Figure 6

Spatial distribution of the stress in the solid for different time moments. For $r\to \infty$, the stress tends to $-P_{\infty }=-101.3$ kPa. The stress at $t=100\mu \mathrm{s}$ is shown in a separate plot because of a great difference in magnitude.

Figure 7

Peak positive and negative values of the stress in the solid as a function of the distance from the cavity surface. The dashed curve shows the best fit to the upper curve, which is given by Eq. (69).

Figure 8

Disturbance of the liquid pressure at the center of the second cavity at different radii of the second cavity. $R_{c10}=100\mu \mathrm{m}$, $d=500\mu \mathrm{m}$. The solid curves show the pressure at the center of the second cavity. The dashed curves show the pressure that is produced at the surface of the second cavity by the emitted wave from the first cavity. The second half period of the pressure disturbance can trigger the nucleation in the second cavity, increasing the magnitude of the background negative pressure within the second cavity.

Figure 9

The time position of the first negative peak of the pressure disturbance at the center of the second cavity as a function of the equilibrium radius of the first cavity $R_{c10}$ for different values of the initial negative pressure within the first cavity $P_{l01}$. $R_{c20}=50\mu \mathrm{m}$, $d=500\mu \mathrm{m}$.

Figure 10

The ratio of the time position of the first negative peak to the period of the fundamental frequency component of the disturbance wave produced by the first cavity. The parameters are as in Fig. 9.