Impact of granular drops

We investigate the spreading and splashing of granular drops during impact with a solid target. The granular drops are formed from roughly spherical balls of sand mixed with water, which is used as a binder to hold the ball together during free-fall. We measure the instantaneous spread diameter for different impact speeds and find that the normalized spread diameter $d/D$ grows as ${(tV/D)}^{1/2}$. The speeds of the grains ejected during the “splash” are measured and they rarely exceed twice that of the impact speed.

Figure 1

Impact of (a) a 26 mm granular drop onto a thick glass plate and (b) a 3.6 mm water droplet onto a hydrophobic glass plate. The times shown are in milliseconds. The impact speed in both cases is $V\approx 2.6$ m/s.

Figure 2

Maximum spread (a) and drop height (b) versus time. Scaled data are shown in (c) and (d), respectively, where the spread diameters and heights are normalized by the initial drop diameter $D$, and time is normalized by the timescale $D/V$. The solid black line in (c) indicates a slope of $1/2$. Error bars encompass multiple trials [not shown in (c) and (d)].

Figure 3

Images with highlighted boundaries (a) just before impact and (b) just before grain ejection. The change in area inside the boundaries determines the change in solids packing during impact.

Figure 4

(a) Snapshots of the velocity field rendered after particle tracking, taken at times $t=-0.4$, 4.5, and 9.5 ms from impact. $D=26$ mm, $V=3.3$ m/s. (b) Maximum instantaneous particle velocity versus time from impact.

Figure 5

(a) Peak grain velocities versus time from impact. Data shown in each plot is averaged over five different realizations. The vertical lines indicate the moment of first contact (dashed) and first ejection of grains (dotted). (b) Maximum grain velocity versus impact speed. The dashed line indicates a slope of 2.