Single-bubble and multibubble cavitation in water triggered by laser-driven focusing shock waves

In this study a single laser pulse spatially shaped into a ring is focused into a thin water layer, creating an annular cavitation bubble and cylindrical shock waves: an outer shock that diverges away from the excitation laser ring and an inner shock that focuses towards the center. A few nanoseconds after the converging shock reaches the focus and diverges away from the center, a single bubble nucleates at the center. The inner diverging shock then reaches the surface of the annular laser-induced bubble and reflects at the boundary, initiating nucleation of a tertiary bubble cloud. In the present experiments, we have performed time-resolved imaging of shock propagation and bubble wall motion. Our experimental observations of single-bubble cavitation and collapse and appearance of ring-shaped bubble clouds are consistent with our numerical simulations that solve a one-dimensional Euler equation in cylindrical coordinates. The numerical results agree qualitatively with the experimental observations of the appearance and growth of large bubble clouds at the smallest laser excitation rings. Our technique of shock-driven bubble cavitation opens interesting perspectives for the investigation of shock-induced single-bubble or multibubble cavitation phenomena in thin liquids.

Figure 1

Experimental setup. An axicon combined with a lens is used to focus a laser excitation pulse as a ring at the sample location. The sample is illuminated by a probe pulse and imaged with high magnification on a multiframe camera. After laser absorption by the liquid sample, two in-plane counterpropagating shock waves are launched and remain mostly confined within the liquid layer.

Figure 2

(a) Single-shot frames recorded for an excitation pulse of 0.5 mJ and a laser ring of $95\mu \mathrm{m}$ radius. The bubble formation at the vicinity of the annular bubble and the collapse dynamics of the central bubble are clearly apparent on this sequence of time-resolved images. (b) Zoomed-in images taken from (a) highlighting the dynamics of the central bubble.

Figure 3

Bubble walls trajectories extracted from the frames displayed in Fig. 2. The two stages of the central bubble wall trajectory (expansion and collapse) have analogies with the classical Rayleigh-Plesset bubble dynamics well established in single-bubble sonoluminescence [20].

Figure 4

Selection of single-shot stroboscopic time-resolved images recorded for different laser ring radii $R=68\mu \mathrm{m}$ (a), $92\mu \mathrm{m}$ (b). The central image taken at 35 ns and 50 ns in each sequence indicate the instant of inner shock focus. Each individual frame has a width of $410\mu \mathrm{m}$. See Appendix pp2 for more radii.

Figure 5

Selection of stroboscopic time-resolved images recorded such as in Fig. 4, at different radii, at times where the bubble cloud is the largest. The inner bubble cloud appears after reflection of the inner shock at the annular laser-induced bubble. Qualitatively, the bubble cloud appears to fill most of the inner part of the annular bubble at small laser ring radius. Each individual frame has a width of $410\mu \mathrm{m}$.

Figure 6

Numerical simulations of the inner shock trajectories for several laser ring radii of $R_{\mathrm{sim}}=55,70,80,90,105\mu \mathrm{m}$ and an initial pressure of 2 GPa. The symbols correspond to the inner shock trajectories extracted from Fig. 4 for different laser ring radii.

Figure 7

Numerical simulations of the spatial pressure profiles at different times during shock propagation of both inner and outer shock waves, departing from the laser ring coordinate $r=R=50\mu \mathrm{m}$. (a) Both spatiotemporal pressure profiles until the time of shock focusing. (b) The spatiotemporal pressure profiles of both inner and outer shock waves at later times after shock focusing. The appearance of a tensile tail on the inner shock spatial profile, right after shock focusing, arises from the acoustic discontinuity at the center.

Figure 8

(left axis) Maximum tension pressure as a function of the laser ring radius $R$, these are reached at the center ($r=0\mu \mathrm{m}$) shortly after the inner shock focuses. (right axis) Maximum positive pressure as the inner shock rebounds and reaches original position $r=R$.

Figure 9

Bubble radii as a function of time for a selection of three most visible bubbles (blue, red, and yellow) from the tertiary bubble cloud, extracted from Fig. 2.

Figure 10

Single-shot stroboscopic time-resolved images recorded for different laser ring radii $R=55$, 68, 80, 92, $105\mu \mathrm{m}$. Each individual frame has a width of $410\mu \mathrm{m}$. The central column shows the instant of inner shock focus.

Figure 11

Stroboscopic time-resolved images recorded such as in Fig. 10, at longer timescales. A bubble cloud appear after reflection of the inner shock at the annular laser-induced bubble. The dashed frames highlight the instant when the bubble cloud appears to be largest. Each individual frame has a width of $410\mu \mathrm{m}$.

Figure 12

Plot of the maximum pressure evolution at long distances and analytical fit following $a/r$ with $a=1250$ Pa.