Energy Loss at Propagating Jamming Fronts in Granular Gas Clusters

We explore the initial moments of impact between two dense granular clusters in a two-dimensional geometry. The particles are composed of solid ${\mathrm{CO}}_2$ and are levitated on a hot surface. Upon collision, the propagation of a dynamic “jamming front” produces a distinct regime for energy dissipation in a granular gas in which the translational kinetic energy decreases by over 90%. Experiments and associated simulations show that the initial loss of kinetic energy obeys a power law in time $\Delta E=-K{t}^{3/2}$, a form that can be predicted from kinetic arguments.

Figure 1

(a) Schematic of the experimental apparatus. An anodized aluminum plate with tilted boundaries is heated to $\approx 100°\mathrm{C}$. Two clusters of solid ${\mathrm{CO}}_2$ particles impact in the middle of the plate. Silicone rubber strips prevent the particles from falling off the plate edges. The collision is filmed with a high-speed camera from above. (b) Sublimated gas from beneath a particle creates a high-pressure region which supports its weight. This leads to nearly frictionless translational motion. (c) Ratio of final to initial kinetic energy versus relative initial velocity for single-particle collisions. There is a spread of values for the energy loss, even for similar relative velocities.

Figure 2

(a) Images of the particles from an experiment during the initial moments of the collision. (b) Snapshots from a simulation of the collision between two elliptical clusters, each composed of 5000 particles. The initial area fraction inside each cluster is ${\varphi }_0=0.71$. In both sets of images, the color indicates the magnitude of the velocity, as denoted by the scale bar on the bottom. Upon impact, a jamming front spreads quickly and eventually encompasses all of the particles when $\tau \equiv t/t_{\mathrm{jam}}=1$.

Figure 3

Relative loss of kinetic energy $\Sigma \equiv -\Delta E/E(t=0)$ versus $\tau \equiv t/t_{\mathrm{jam}}$ immediately after impact for four experimental data sets (black dots) and the simulation of elliptical clusters (solid red line). The dashed line is the prediction [Eq. (4)] using parameters from the simulation. The inset compares five simulations using the same initial conditions but with different dissipative forces. Two have viscous forces that are $5\times \mathrm{\text{stronger}}$ and $5\times \mathrm{\text{weaker}}$ than in the main figure, and two others have friction coefficients of $\mu =0.1$ and $\mu =0.9$. The results are virtually identical in all cases.