Outcomes of the collapse of a large bubble in water at high ambient pressures

Presented here are observations of the outcomes of the collapses of large single bubbles in ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ at high ambient pressures. Experiments were carried out in a high-pressure spherical resonator at ambient pressures of up to 30 MPa and acoustic pressures up to 35 MPa. Monitoring of the collapse events and their outcomes was accomplished using multiframe high-speed photography. Among the observations to be presented are the temporal and spatial evolution of light emissions produced by the collapse events, which were observed to last on the order of 30 ns and have time independent radii on the order of $30\mu \mathrm{m}$; the production of Rayleigh-Taylor jets which were observed to travel distances of up to $70\mu \mathrm{m}$ at speeds in excess of 4500 m/s; the entrainment of the light emitting regions in the jets' remnants; the production of spheroidal objects around the collapse points of the bubbles, far from any surface of the resonator; and the traversal and emergence of the Rayleigh-Taylor jets through the spherical objects. These spheroidal objects appear to behave as amorphous solids and form at locations where hydrodynamics predicts pressures in excess of the known transition pressures of water into the high-pressure crystalline ices, Ice-VI and Ice-VII.

Figure 1

Schematic of the experimental setup. CL, collimation lenses used to expand beam waist from 1 to 25 mm. HWP, half wave plate used to adjust the polarization angle of the light exiting the laser. PBS, polarizing beam splitter used in combination with the half wave plate to adjust downstream laser energy. FL, 125-mm focal length lens used to focus laser into the center of the spherical resonator.

Figure 2

Bubble wall velocity vs bubble radius for single cavitation bubbles (${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ data combined). The inset plot shows that the bubble wall velocity (normalized by $\sqrt{2P_{\infty }/3\rho }$) was linearly proportional to the quantity $\sqrt{R_m^3/R^3-1}$, where $P_{\infty }$ is the static pressure, $\rho$ is the density of the species of water used, and $R_m$ and $R$ are the bubble's maximum and instantaneous radii, respectively. The dotted line in the inset plot shows the theoretical relationship between these two quantities from Eq. (1).

Figure 3

Experimental details: frame dimensions = $1.75\times 1.32$ mm; frame exposure times = 5 ns; $P_{\infty }$=$$ 17.2 MPa. The gap between frames in Frames (b) and (h) was 0 ns, giving an effective frame rate of 200 Mfps. This image shows the final stages of a bubble's collapse [frames (b)–(e)], followed by the generation of a light emitting region therein [frames (f)–(h)]. Frame (a) was captured $16\mu \mathrm{s}$ prior to frame (b) to ensure that the event observed was from a single bubble collapse.

Figure 4

Experimental details: frame dimensions = $1.75\times 1.32$ mm; frame exposure times = 5 ns; $P_{\infty }=17.2\mathrm{MPa}$. The gap between frames in frames (b) and (h) was 0 ns, giving an effective frame rate of 200 Mfps. This image shows the early development and time evolution of a light emitting region in frames (b)–(g). The light emitting region in frames (b)–(g) is observed moving leftwards from its point of origin during its lifetime. Starting in frame (e) and progressing through frame (h) we see the thick, dark band surrounding the light-emitting region traveling radially outwards from the center. In frame (h) we see a ringlike structure revealed in the light region encircled by the thick, dark band as it crosses over it. Frame (a) was captured $16\mu \mathrm{s}$ prior to frame (b) to ensure that the event observed was from a single bubble collapse.

Figure 5

Experimental details: frame dimensions = $1.75\times 1.32$ mm; frame exposure times = 5 ns; $P_{\infty }=17.2\mathrm{MPa}$. The gap between frames in frames (b)–(h) was 0 ns, giving an effective frame rate of 200 Mfps. This image shows the time evolution of a light emitting region near the end of its life [frames (b)–(e) and (f)] and what remains in the fluid region after emissions have ceased [frames (f)–(h)]. During its lifetime the light-emitting region is observed to travel leftwards, entrained in what is revealed in frame (h) to be a Rayleigh-Taylor jet remnant. In frames (b)–(h) a ringlike structure is observed in the form of the thin, dark band in the light region encircled by the thick, dark band traveling outwards from the center. Frame (a) was captured $16\mu \mathrm{s}$ prior to frame (b) to ensure that the event observed was from a single bubble collapse.

Figure 6

Radius vs time plots of typical light emission events produced during collapses in ${\mathrm{H}}_{2}0$ at ambient pressures of 17.2 MPa.

Figure 7

This plot shows the maximum radius of the light-emitting region versus the maximum radius of the bubble that generated it.

Figure 8

Experimental details: frame dimensions = $1.75\times 1.32$ mm; $P_{\infty }=17.2\mathrm{MPa}$ in ${\mathrm{H}}_2\mathrm{O}$. Successive images of a collapsing bubble [(a)–(e)] and the aftermath [(f)–(h)] during the first acoustic cycle after nucleation. Each frame had an exposure time of 20 ns with a 30-ns gap in between frames, resulting in an effective framing rate of 20 Mfps. The dark region around the bubble before and after the collapse is due to the high pressure in the liquid bending light away from the camera. Note the persistent ring-like structures in frames (f)–(h).

Figure 9

Experimental details: frame dimensions = $1.75\times 1.32$ mm; $P_{\infty }=17.2\mathrm{MPa}$ in ${\mathrm{H}}_2\mathrm{O}$. Successive images of a collapsing bubble [(a)–(c)] and the aftermath [(d)–(h)] during the first acoustic cycle after nucleation. Each frame had an exposure time of 20 ns with a 100-ns gap in between frames, resulting in an effective framing rate of 8.33 Mfps. The remnants of a Rayleigh-Taylor jet are visible in frames (d)–(h).

Figure 10

Experimental details: frame dimensions = $1.75\times 1.32$ mm; $P_{\infty }$=$$ 20.7 MPa in ${\mathrm{D}}_2\mathrm{O}$. Evolution of spheroid with a frozen remnant jet and toroidal vortex during the second acoustic cycle following nucleation. Frames (a)–(d) had an exposure time of 5 ns, (e)–(h) had increasing exposure times of 10–60 ns, with a $2.5-\mu \mathrm{s}$ gap in between frames, resulting in an effective framing rate of 400 kfps.

Figure 11

Experimental details: frame dimensions = $1.75\times 1.32$ mm; $P_{\infty }=20.7\mathrm{MPa}$ in ${\mathrm{D}}_2\mathrm{O}$. Deformation of an existing spheroid [upper left in frame (a)] by expanding bubble during the second acoustic cycle following nucleation. Frame timings are identical to those described in the caption of Fig. 10. The collapse of the bubble creates a second spheroidal object visible in frame (h).

Figure 12

Plots showing the dependence of the sizes of the inner (a) and outer (b) ring structures on the initial maximum bubble radius at the ambient pressures used in experiments. The dotted lines are the predicted radii [from Eq. (3)], where the pressures first exceed the value, $P_t$, as given in the plots. It can be seen for the boundary of the inner ring (a) that $P_t$ is 18 GPa, and for the outer ring (b) that $P_t$ is 1.6 GPa. The three sets of lines in each plot show the dependence of the structure size on the initial maximum bubble radius at different ambient pressures, where the values $P_{\infty }$ of each line were chosen to correspond with the ambient pressures used in experiments.