The role of interstitial gas in determining the impact response of granular beds

Abstract

Abstract. -We examine the impact of a solid sphere into a fine-grained granular bed. Using high-speed X-ray radiography we track both the motion of the sphere and local changes in the bed packing fraction. Varying the initial packing density as well as the ambient gas pressure, we find a complete reversal in the effect of interstitial gas on the impact response of the bed: The dynamic coupling between gas and grains allows for easier penetration in initially loose beds but impedes penetration in more densely packed beds. High-speed imaging of the local packing density shows that these seemingly incongruous effects have a common origin in the resistance to bed packing changes caused by interstitial air.Introduction. -Granular materials often exhibit behavior intermediate between that of conventional solids and liquids. Probing the resulting combination of liquidand solid-like properties a number of recent studies investigated the impact of a large object into a bed of dry grains. These studies focused on issues such as the drag on the impacting object [1-6], crater formation [7-10] the corona-like splash formed immediately after the impactor hits the bed surface [10], and the subsequent jet of grains formed by the collapse of the cavity left by the impactor [11][12][13][14][15][16]. So far however, almost all work considered the limit of loosely packed, marginally stable beds that readily compact in response to perturbations. On the other hand, densely packed beds must dilate in order for grains to move out of the way of inserted objects. This implies different resistance not only for slow, quasi-static perturbations [17] but also suggests that there should be a significant change in the dynamics for faster impacts.An important feature of the impact dynamics in granular systems is the coupling between the interstitial gas, typically air, and the grain packing. For fine grained beds (grain diameters below ∼ 150 µm) this interaction can drastically change the impact dynamics. In particular, in

Penetration in bimodal, polydisperse granular material

“…This interesting observation is consistent with the data in Figs. 3(a), 3(b), and 3(c) and also fits with previous conclusions regarding the initial packing state relative to the critical packing state [8,23].…”

“…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].…”

“…In contrast, for the higher packing fractions in Figure 2(b), all three grain sizes exhibit very similar penetration depths, indicating that particle size becomes less important at higher initial packing fractions. We may interpret these observations in the context of a critical packing fraction, φ * ≈ 0.6, found by Umbanhower and Goldman [8] and Royer et al [23], whereby the impact can bring about local fluidization for φ > φ * , but local compaction for φ < φ * , which may partly explain the slightly deeper penetration for d 4,3 = 520 μm at φ = 0.64 than for d 4,3 = 31 μm at φ = 0.58 for the compacted grain in Fig. 2(b), the effect of S notwithstanding.…”

Novel experimentally observed phenomena in soft matter

“…The importance of the role of interstitial air in the formation of granular jets was established by high speed X-ray radiography and digital video imaging in [177,178]. These experiments report the presence of two jets when a projectile hits a bed of loosely packed sand: a thin, wispy jet whose size does not depend on the air pressure, and an air pressure-dependent thick jet.…”

“…8 shows the emergence of granular jets following the impact of a projectile on a sand bed under two different air pressure conditions. The complex interplay between interstitial gas, bed particles and the impacting sphere has been studied in detail in [178,179]. Videos of granular jets can be viewed at [180] and a review on sand jets can be found in [181].…”