Millimetric granular craters from pulsed laser ablation

This Rapid Communication reports on an experimental study of granular craters formed by a mechanism, namely, optical energy, via a pulsed laser focused onto the surface of a granular bed. This represents an insight into granular cratering for two reasons; first, there is no physical contact between the initiation mechanism and the granular media (as typical for impact or explosion craters). Second, the resulting craters are millimetric in scale, which facilitates a test of energy scalings down to a previously unobserved lengthscale. Indeed, we observe a range of energy scalings conforming to $D_c\sim E^{\beta }$ with $\beta \approx 0.31\text{–}0.43$ depending on the characteristics of the granular media.

Figure 1

(a) Schematic representation of the experimental setup used, showing the synchronized laser and high-speed imaging system, along with the optics used to direct and focus the laser pulse onto the granular bed. (b) Images of the granular surface for coarse sand (left) and glass beads (right) with 1 mm scale bar.

Figure 2

(a) Image sequence showing the laser pulse and subsequent crater formation. The scale bar is 5 mm long and the images, relative to the trigger signal, are taken at $t=-0.04$, 0.04, 0.08, 1.6, 3.6, 5.6, 7.7, and 11.8 ms. (b) A five-frame streak image ($dt=0.1$ ms) showing particle tracks of individual grains and the curtain neck diameter, $D\approx 6$ mm. In both realizations, the laser pulse energy was 38 mJ and the grain size was 178 $\mu \mathrm{m}$. (c) Examples of the final crater in fine glass beads $d=31\mu \mathrm{m}$ (left) and coarse sand (right) with 2 mm scale bar.

Figure 3

Final crater diameter plotted as a function of the laser pulse energy for the four different granular media, indicated in the legend. The solid lines are the best power-law fits, $D_C\propto {(E-E^{*})}^{\beta }$. A characteristic error bar is shown in the top left corner.

Figure 4

(a) Temporal evolution of the ejecta curtain diameter for 31-$\mu \mathrm{m}$ glass beads For $t\lesssim 8$ ms, the ejecta growth is well described by a power law, $D=\alpha t^{0.24}$. (b) Dependence of the numerical prefactor on energy, $\alpha =0.98{(E-E^{*})}^{0.33}$ with $E^{*}=0.83$ mJ.