Impact on Soft Sand: Void Collapse and Jet Formation

Very fine sand is prepared in a well-defined and fully decompactified state by letting gas bubble through it. After turning off the gas stream, a steel ball is dropped on the sand. On impact of the ball, sand is blown away in all directions (“splash”) and an impact crater forms. When this cavity collapses, a granular jet emerges and is driven straight into the air. A second jet goes downwards into the air bubble entrained during the process, thus pushing surface material deep into the ground. The air bubble rises slowly towards the surface, causing a granular eruption. In addition to the experiments and the discrete particle simulations we present a simple continuum theory to account for the void collapse leading to the formation of the upward and downward jets.

Figure 1

Jet formation after the impact ($v_0=2.43\mathrm{m}/\mathrm{s}$) of a steel ball of $R_0=1.25\mathrm{c}\mathrm{m}$ on loose very fine sand. The jet in this experiment exceeds the release height of the ball. Frames 2–4: splash; frames 5–6: a jet emerges; frame 7: clustering within the jet; frames 8–9: granular eruption at the surface.

Figure 2

(a) Jet height as a function of release height of the ball in our experiments (solid bullets with error bars) and in those of Ref. 2 [for spheres in a granulate of a different diameter: $d_s=0.08\mathrm{m}\mathrm{m}$ (pluses), $d_s=0.118\mathrm{m}\mathrm{m}$ (triangles), $d_s=0.176\mathrm{m}\mathrm{m}$ (solid squares)]. The jets of Ref. 2 never reach the release height, because the granulate is less fine and much less decompactified. In our experiments jets are produced even at zero impact height [21] and there is no scaling relation as in Ref. [2]. (b) Sketch of the void collapse. When the accelerated sand grains from the sidewalls of the cylindrical cavity collide on the axis of the cavity, two jets are formed: one downward into the entrained air bubble formed above the sphere, and one upward straight into the air.

Figure 3

A cut through the quasi-2D discrete particle simulation. Frames 1–3: the impact of the disk on the particles; frames 4–6: the collapse of the void; frame 7: the upward jet (which is less pronounced than in the 3D experiments).

Figure 4

A cross section of the 3D-void collapse following from our Rayleigh-type model, for the same impact velocity and ball radius as in Fig. 1. The void is pressed together by the hydrostatic pressure from the side, leading to a singularity and an upward and downward jet.