Rebounds of deformed cavitation bubbles

Presented here are experiments clarifying how the deformation of cavitation bubbles affects their rebound. Rebound bubbles carry the remaining energy of a bubble following its initial collapse, which dissipates energy mainly through shock waves, jets, and heat. The rebound bubble undergoes its own collapse, generating such violent events anew, which can be even more damaging or effective than at first bubble collapse. However, modeling rebound bubbles is an ongoing challenge because of the lack of knowledge on the exact factors affecting their formation. Here we use single-laser-induced cavitation bubbles and deform them by variable gravity or by a neighboring free surface to quantify the effect of bubble deformation on the rebound bubbles. Within a wide range of deformations, the energy of the rebound bubble follows a logarithmic increase with the bubble's initial dipole deformation, regardless of the origin of this deformation.

Figure 1

Schematic of the experimental setup and direction with respect to aircraft. The dimensions are given in millimeters.

Figure 2

Bubble radius evolution in normalized coordinates [radius $R$ normalized to maximum bubble radius $R_0$ and time $T$ normalized to Rayleigh collapse time $T_C=0.915R_0{(\rho /\mathrm{\Delta }p)}^{1/2}]$ as extracted from the high-speed images for bubbles collapsing (a) spherically in microgravity (0 $g$) with variable driving pressures and (b) at variable gravity levels: 0, 1, and 1.8 $g$, where $g=9.81$ ${\mathrm{ms}}^{-2}$, with $R_0\approx 3.9\pm 0.2$ mm and at a driving pressure $\mathrm{\Delta }p=33$ kPa.

Figure 3

(a) Visualization of the first three oscillations of a bubble deformed by the gravity-induced pressure gradient. The interframe time is 250 $\mu \mathrm{s}$, exposure time 100 ns, and the maximum bubble radius is 4.4 mm ($\mathrm{\Delta }p=11$ kPa, $\zeta =0.0059$, $g=1.6\times 9.81$ ${\mathrm{ms}}^{-2}$). (b) Full raw pressure signal corresponding to the bubble in panel (a), as measured by the hydrophone and recorded by the oscilloscope. (c) Enlargement of the shock wave signals, aligned in time by their maximum amplitude to superimpose the peaks.

Figure 4

(a) Energy of the first rebound bubble normalized to the initial bubble energy $E_{\mathrm{R}1}/E_0$, and (b) energy of second rebound bubble normalized to the first rebound energy $E_{\mathrm{R}2}/E_{\mathrm{R}1}$, as a function of the anisotropy parameter $\zeta$. The bubbles are deformed by the gravity-induced pressure gradient (with $R_0=1.2–6.2\mathrm{mm}$, $\mathrm{\Delta }p=8–83\mathrm{kPa}$, and $g=0.0–2.1$ ${\mathrm{ms}}^{-2}$) and by a near free surface (with $R_0=1.3–4.8\mathrm{mm}$, $\mathrm{\Delta }p=50–96\mathrm{kPa}$, and $h=2–32\mathrm{mm}$). The dashed lines display the logarithmic best fit $E_{\mathrm{R}1}/E_0\approx 0.1ln\zeta +0.7$. Each data point corresponds to a single collapse event.

Figure 5

(a) Shock wave and rebound energy, normalized to initial bubble energy $E_0$ as a function of $\zeta$, for a bubble deformed by a neighboring free surface (shock energy data replotted from Ref. [47]). (b) Rebound collapse shock wave energy, normalized to initial bubble energy $E_0$, as a function of $\zeta$ for bubbles deformed by gravity and by a neighboring free surface. The equivalent stand-off parameter $\gamma$ is shown on the top axes for comparison. Each data point corresponds to a single collapse event. Some of the measurement uncertainties are shown by the error bars.