Gas-Mediated Impact Dynamics in Fine-Grained Granular Materials

Noncohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material. We find a crossover from nearly incompressible, fluidlike behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated. We discuss these results in light of recent proposals for the drag force in granular media.

Figure 1

Pressure dependence of impact dynamics. Composite x-ray images at 12 kPa (a) 5 ms, (b) 40 ms, and (c) 57 ms after impact. Images at 0.7 kPa (d) 5 ms, (e) 12 ms, and (f) 28 ms after impact.

Figure 2

(a) Sphere depth $z_s$ versus time after impact ($t=0\mathrm{s}$). (b) Velocity $v_s(t)$ computed from curves in (a). (c) Velocity $v_s(z_s)$ versus depth. All panels top to bottom: $P=0.7$, 4.9, 8.7, 12, and 101 kPa.

Figure 3

Compaction front preceding sphere. Change in packing fraction $\Delta \varphi$ measured along the path of the sphere at depths (left to right) $z_m=1.0$, 2.0, and 3.0 cm plotted against distance from sphere tip $z_s$ to $z_m$.

Figure 4

Bed dynamics. (a) Rise of bed surface $\delta h$. Arrows mark $t_m$ for three pressures. Double-sided arrows denote rise needed to conserve bed volume . Resolution of $\delta h$ was limited by pixel size to $\sim 0.5\mathrm{mm}$. (b) Maximum change in packing fraction in front of sphere (○) and ratio of potential energy needed to raise bed by $\delta h_{\max }$ to kinetic energy lost by sphere at time $t_m$ (■). Error bars for $\Delta {\varphi }_{\max }$ are due to fluctuations in $\Delta \varphi$, and for $\Delta U_b/\Delta K_s$ due to uncertainty in $t_m$.