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Unifying Impacts in Granular Matter from Quicksand to Cornstarch J Unifying Impacts in Granular Matter from Quicksand to Cornstarch J. John Soundar Jerome, Nicolas Vandenberghe, Yoël Forterre To cite this version: J. John Soundar Jerome, Nicolas Vandenberghe, Yoël Forterre. Unifying Impacts in Granular Matter from Quicksand to Cornstarch. Physical Review Letters, American Physical Society, 2016, 117 (9), 10.1103/PhysRevLett.117.098003. hal-01431977 HAL Id: hal-01431977 https://hal.archives-ouvertes.fr/hal-01431977 Submitted on 11 Jan 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. week ending PRL 117, 098003 (2016) PHYSICAL REVIEW LETTERS 26 AUGUST 2016 Unifying Impacts in Granular Matter from Quicksand to Cornstarch † J. John Soundar Jerome,1,2, Nicolas Vandenberghe,2 and Yoël Forterre1,* 1Aix Marseille Univ, CNRS, IUSTI, 13013 Marseille, France 2Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, 13013 Marseille, France (Received 15 March 2016; published 23 August 2016) A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact hardening in shear-thickening suspensions like cornstarch. DOI: 10.1103/PhysRevLett.117.098003 Impacts on particulate media like granular materials immersed in an incompressible fluid (water, viscous oil). and suspensions present an astonishingly rich phenom- The initial packing fraction of the suspension ϕ0 (the ratio enology [1,2]. Along with its astrophysical [3] and ballis- of the volume of the glass beads to the total volume) is tics applications [4], impact dynamics is an object of active controlled by first fluidizing the mixture and then compacting research to understand the high-speed response of granular the sediment, before removing the excess liquid [see Fig. 1(a) matter [5]. In dry granular media, impact by a solid object and the Supplemental Material [29]]. For a granular pile of results in the formation of a corona of granular ejecta and a frictional spherical particles, ϕ0 typically takes values solidlike plastic deformation leading to a permanent crater between 0.55 and 0.62 [22]. The suspension is kept fully [6–11]. For fine powders in air, granular jets and cavity saturated so that surface tension effects can be neglected. collapse occur during impact [12,13]. Subsequent studies Remarkably, two very distinct impact regimes are obs- showed that the ambient pressure of the interstitial fluid erved depending on the initial packing fraction [Figs. 1(b), (air) is an important element for the observed fluidlike 1(c)]. For initially loose packing (ϕ0 ¼ 0.560), the ball behavior [14–16], while for denser packing the impact readily sinks in the suspension, giving rise to a collapsing penetration is much reduced [17]. However, the question of cavity and a central jet (see movie 1 in the Supplemental the physical mechanisms and control parameters that give Material [29]). Such fluidlike behavior is strikingly similar to rise to such a wide variety of phenomena is still largely that observed when a rigid sphere hits a dry loose powder open. Recently, studies on shear-thickening suspensions under atmospheric pressure [12,13]. By contrast, for dense (cornstarch) showed another kind of behavior. Above a packing (ϕ0 ¼ 0.604), the ball stops abruptly within a critical velocity, an impacting object immediately stops few milliseconds as it hits the surface (see movie 2 in the [18], or in some cases generates cracks [19], as if hitting a Supplemental Material [29]). This solidlike behavior is solid. This phenomenon has been related to the propagation reminiscent of the impact-activated solidification observed of dynamic jamming fronts in the bulk [18]. However, the in a shear-thickening suspension like cornstarch [18]. arrest mechanism remains unclear and explanations so It strongly depends on the grain size and viscosity of the far overlook the role of the coupling between the inter- interstitial fluid between the particles. Using coarser particles stitial fluid and the grains, which can strongly affect the in the same fluid tends to suppress the extreme deceleration, transient behavior of saturated granular materials [20–22]. which can be restored by increasing the fluid viscosity Understanding the origin of impact-activated solidification (see movie 3 in the Supplemental Material [29]). in these systems should help to clarify the physics of shear- To explain such a drastic change between the impact thickening fluids—a still debated topic [23–27]. behavior of the loose and dense suspension, we rely on a The objective of this Letter is to address these issues pore-pressure feedback mechanism: a coupling between the and elucidate the role of the interstitial fluid and the deformation of the granular medium and the pressure of the initial volume fraction on the impact dynamics in dense interstitial fluid between the grains [20,21]. As first described suspensions. To avoid difficulties associated with colloidal by Reynolds [30], when a dense granular packing starts to interactions between particles (like in shear-thickening sus- flow, it must dilate. Since the medium is saturated with an pensions) or fluid compressibility (like in powders in air), we incompressible fluid, the fluid is sucked in, as evidenced study here the impact of a freely falling rigid sphere on a by the bright zone developing beneath the impacting sphere model granular suspension [28] made up of macroscopic, in the dense case [Fig. 1(b)]. Therefore, when the ball hits heavy particles (glass beads in the range 0.1–1mm) the pile, the interstitial fluid pressure (pore–pressure) drops 0031-9007=16=117(9)=098003(5) 098003-1 © 2016 American Physical Society week ending PRL 117, 098003 (2016) PHYSICAL REVIEW LETTERS 26 AUGUST 2016 18 cm (a) (b) Loose case = 0.560 0 1 cm g 27 cm Porous - 10 ms0 ms 2 ms 4 ms 20 ms 125 ms plate Pump Dense case = 0.604 0 1 cm tap h 0 - 10 ms0 ms 2 ms 4 ms 20 ms 125 ms (c) = 0.560 1 0 D 0.3 0 D 0 0.8 V / 0.2 g -50 / 0.60 s v 0.6 V = 0.604 0.59 0.1 0 0.4 -100 0.58 0 0 Speed 0.2 , Accel. 0.57 d p -150 Penetration / 0 0.56 -0.1 f f 0102030 -1 01 23 4 -1 01 23 4 -1 01 23 4 # tap Time t (ms) Time t (ms) Time t (ms) 3 FIG. 1. Liquid-solid transition after impact on a suspension of heavy particles (glass beads of density ρp ¼ 2500 kg=m and diameter d ¼ 170 μm in water). (a) Protocol used to prepare the nonbuoyant suspension at a given initial packing fraction ϕ0 (h0 ¼ 9–10 cm depending on the number of taps). (b) Image sequence of a solid sphere (glass marble of diameter D ¼ 25.2 mm, density 3 ρs ¼ 2500 kg=m , speed V ¼ 2.35 m=s) impacting the suspension in the loose (top) or dense (bottom) case. (c) Corresponding penetration, speed, and acceleration of the impacting sphere as a function of time. Time t ¼ 0 gives the instant when the sphere hits the granular bed surface. instantaneously, which in turn presses the grains against each other, thereby enhancing the friction. Thus, the medium is (a) (b) transiently solidified. A loosely packed granular bed, on the Hydrophone 1.4 1.2 0=0.560 other hand, tends to compact when it deforms. Therefore, a Low-frequency 1.2 0.8 (kPa) sensor (kPa) P 2 mm f 1.0 0.4 rise in pore pressure is produced during impact that can P 0.8 0 balance the weight of the grains. This suppresses the contact 0246 0.6 Time (s) network, resulting in local or global fluidization. z 0.4 P>0 Grid We proceed a direct verification of this mechanism by 0.2 developing a high-frequency measurement of the interstitial 0 Pore pressure, fluid pressure inside the suspension, just under the impact (c) 5 0=0.604 [Fig. 2(a)] (see Fig. S1 and the Supplemental Material 10 [29]). In the loose case [Fig. 2(b), upper panel], the pore 0 (kPa) 0 f pressure shows a sudden positive peak after impact. The P -5 -101 measured peak pressure (∼1 kPa) is of the order of the -10 ΔP<0 (kPa) -10 (kPa) 2 P -10 effective weight of the suspension above the sensor [31], -20 P Δ indicating a fluidization of the medium. At longer times -15 02468 -30 z (cm) sedimentation proceeds and the pressure slowly relaxes c 0.56 0.58 0.6 Pore pressure, -0.05 0 0.05 0.1 to zero. By contrast, in the dense case [Fig. 2(b) lower Volume fraction 0 Time (s) panel], the peak pressure is negative and its magnitude (10–100 kPa) is much higher than the confining pressure FIG. 2. (a) Experimental setup to measure pore pressure at due to gravity, indicating that particles are strongly pressed different heights z in the suspension.
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