Role of Air in Granular Jet Formation

Abstract

A steel ball impacting on a bed of very loose, fine sand results in a surprisingly vigorous jet which shoots up from the surface of the sand [D. Lohse et al., Phys. Rev. Lett. 93, 198003 (2004)]. When the ambient pressure p is reduced, the jet is found to be less vigorous [R. Royer et al., Nature Phys. 1, 164 (2005)]. In this Letter we show that p also affects the rate of penetration of the ball: Higher pressure increases the rate of penetration, which makes the cavity created by the ball close deeper into the sand bed, where the hydrostatic pressure is stronger, thereby producing a more energetic collapse and jetting. The origin of the deeper penetration under normal ambient pressure is found to lie in the extra sand fluidization caused by the air flow induced by the falling ball.

Penetration in bimodal, polydisperse granular material

“…However, it is unclear how the rattlers affect the dynamical response of the granular material to impact, for example, or how they affect the interstitial forces between grains. Our study here indicates that the inclusion of fine grains into a bed of larger grains brings in the influence of ambient air and local fluidization, which has been observed previously for dense spheres impacting onto granular beds [23][24][25] and in falling granular streams [29,30]. The influence of ambient air only appears to be significant for finer grains (Geldart group A), such as the smallest particles used here with d p = 31 μm, and is typically not present for larger grains (Geldart group B, typically with mean diameter between 40 and 500 μm), such as the larger grains used here with d p = 178 and 520 μm, according to Geldart's classification [31].…”

“…Air-mediated effects (e.g., Refs. [24,25]) may also be important for the finest grains at low packing fraction, since it is known that the interstitial air plays a significant role on the drag on a sphere. This was best demonstrated by Royer et al using x-ray imaging [26], showing drag increases as the ambient pressure decreases.…”

Dynamics of grain ejection by sphere impact on a granular bed

“…The penetration dynamics of the impacting sphere and the grain ejection have been shown to be very different when the granular material is not dense but loose: A spectacular thin granular jet can raise very high after the impact as first demonstrated in Refs [2,17,18]. The effects on this granular jet of the interstitial fluid [19,20] and of the initial packing fraction of the target [21] have then been studied. In the dense case, no granular jet but a growing granular corona is seen after the impact.…”

Suction of splash after impact on dry quick sand

“…Finally, the cavity closes and all the grains continue to fly ballistically. We will show in the following sections that, indeed, the pressure drag stops being significant between 20 and 30 ms after impact, which coincides with the time at which the cavity begins to close [15].…”

“…The experimental set up is the same used and described in references [3,15,16]. It consists of a 1 m high, transparent, perspex container of 14 × 14 cm 2 cross section and is half filled with fine grains.…”