Creating a dry variety of quicksand

Lohse, Detlef; Rauhé, Remco; Bergmann, Raymond; Meer, Devaraj van der

doi:10.1038/432689a

Cited by 132 publications

(153 citation statements)

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“…As in ref. 9, for 4-cm-diameter spheres of varying mass released from rest at the surface of a bed of 40 μm sand grains, a seems equal to −g plus a Coulomb friction term proportional to depth; however, this is only the limiting behaviour as we find in the main plot that the acceleration at z = 0 increases with impact speed. Third, the absolute final penetration depth, d, is plotted in Fig.…”

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confidence: 99%

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Unified force law for granular impact cratering

2007

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Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events 1-5 and to probe the unusual nature of the granular state of matter [6][7][8][9][10] . Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed 6 ; linear in speed 7 ; constant, proportional to the initial impact speed 8 ; and proportional to depth 9,10 . This is reminiscent of high-speed ballistics impact in the nineteenth and twentieth centuries, when a plethora of empirical rules were proposed 11,12 . To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 μs precision. For a 1-inch-diameter steel sphere dropped from a wide range of heights into noncohesive glass beads, we reproduce previous observations 6-10 either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between the projectile and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus, we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, although fundamentally different from that of liquids and solids, can be simply understood.To measure dynamics, we use a line-scan digital CCD (chargecoupled device) camera to image a finely striped transparent rod attached vertically to the top of the projectile (see the Methods section). The instantaneous speed is the key quantity, deduced from the displacement of the striped pattern between successive frames. The temporal precision is 20 μs, set by the 50 kHz frame rate of the line-scan camera. The position resolution is 100 nm, set by the 3.8 μm per pixel magnification divided by the square root of the number of pixels. These combine to give a velocity resolution of 0.5 cm s −1 . Besides measurement fidelity, another advantage of our method is that it applies even to very deep impacts-as long as the striped rod does not submerge.Our complete dynamics data set is shown in Fig. 1, which shows position z, velocity v, and acceleration a, versus time t, for initial impact speeds, v 0 , ranging from 0 to −400 cm s −1 . Time is measured from initial impact; position is measured upwards from the granular surface, opposite to gravity. A striking feature is that, although the final position is approached smoothly, the velocity vanishes abruptly with a discontinuity in acceleration. Similar behaviour is evident in data from an embedded accelerometer (P. B. Umbanhowar, private communication, 2004; J. C. Amato, private communication, 2005). This is counter to the viscous approach to a stable equilibrium, where acceleration vanishes continuously, but it permits the stopping time, t stop , to be easily gauged from the velocity versus time data. Note that t stop actually decreases with increasing impact speed; surprisingly, deeper penetration requires less time. Evidently, granular matter is very different from ordinary ...

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Unified force law for granular impact cratering

2007

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“…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. When an object impacts on a bed of fine, loose grains, it is quickly engulfed and a surprisingly vigorous jet shoots upward from the surface of the sand [1][2][3][4], similar to what happens in a liquid [5][6][7]. Royer et al [4] found a granular jet created at reduced ambient pressure to be smaller than at atmospheric pressure, highlighting the relevant role that interstitial air plays in systems with very small grains (<100 m) [8][9][10].…”

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“…For the experiments presented here we adapted the setup used in [2,3] to allow for the evacuation of air. It consists of a deep bed ( 40 cm) of sand grains between 20 and 60 m in size and with shapes of equivalent eccentricities between 0.2 and 0.6.…”

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Role of Air in Granular Jet Formation

et al. 2007

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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.

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Dynamics and scaling of explosion cratering in granular media

et al. 2018

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Granular cratering is a ubiquitous phenomenon occurring in various natural and industrial contexts. Although impactinduced granular cratering has been extensively studied, fewer experiments have been conducted on granular cratering via low-energy explosions. Here, we study the dynamics and scaling of explosion granular cratering by injecting short pulses of pressurized air in quasi-two-dimensional granular media. Through an analysis of the dynamics of explosion processes at different explosion pressures, explosion durations, and burial depths, we identify two regimes, the bubbling and the eruption regimes, in explosion granular cratering. Our experiments explore the distinctive dynamics and crater morphologies of these regimes and show the energy scaling of the size of explosion craters. We compare high-energy and low-energy explosion cratering as well as explosion and impact cratering in terms of their energy scalings. Our work illustrates complex granular flows in explosion cratering and provides new insights into the general scaling of granular cratering processes. The burial depth is fixed at d b 5 3.2 cm. The dashed line indicates a power-law scaling V b~E 1.2 . [Color figure can be viewed at wileyonlinelibrary.com.] 8

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Creating a dry variety of quicksand

Cited by 132 publications

References 11 publications

Unified force law for granular impact cratering

Unified force law for granular impact cratering

Role of Air in Granular Jet Formation

Dynamics and scaling of explosion cratering in granular media

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