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Aumaître S, Behringer RP, Cazaubiel A, Clément E, Crassous J, Durian DJ, Falcon E, Fauve S, Fischer D, Garcimartín A, Garrabos Y, Hou M, Jia X, Lecoutre C, Luding S, Maza D, Noirhomme M, Opsomer E, Palencia F, Pöschel T, Schockmel J, Sperl M, Stannarius R, Vandewalle N, Yu P. An instrument for studying granular media in low-gravity environment. Rev Sci Instrum 2018; 89:075103. [PMID: 30068123 DOI: 10.1063/1.5034061] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A new experimental facility has been designed and constructed to study driven granular media in a low-gravity environment. This versatile instrument, fully automatized, with a modular design based on several interchangeable experimental cells, allows us to investigate research topics ranging from dilute to dense regimes of granular media such as granular gas, segregation, convection, sound propagation, jamming, and rheology-all without the disturbance by gravitational stresses active on Earth. Here, we present the main parameters, protocols, and performance characteristics of the instrument. The current scientific objectives are then briefly described and, as a proof of concept, some first selected results obtained in low gravity during parabolic flight campaigns are presented.
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Affiliation(s)
- S Aumaître
- SPEC, DSM, CEA-Saclay, CNRS URA 2464, F-91191 Gif-sur-Yvette, France
| | - R P Behringer
- Department of Physics, Duke University, Durham, North Carolina 27708-0305, USA
| | - A Cazaubiel
- Université Paris Diderot, SPC, MSC, UMR 7057 CNRS, F-75013 Paris, France
| | - E Clément
- PMMH, ESPCI, UMR 7636 CNRS, F-75005 Paris, France
| | - J Crassous
- Université Rennes 1, IPR, UMR 6251 CNRS, F-35042 Rennes, France
| | - D J Durian
- University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - E Falcon
- Université Paris Diderot, SPC, MSC, UMR 7057 CNRS, F-75013 Paris, France
| | - S Fauve
- École Normale Supérieure, LPS, CNRS, UMR 8550, F-75005 Paris, France
| | - D Fischer
- IEP, Otto von Guericke Universität, D-39106 Magdeburg, Germany
| | - A Garcimartín
- DFMA, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Y Garrabos
- CNRS, ICMCB, Université de Bordeaux, UMR 5026, F-33600 Pessac, France
| | - M Hou
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - X Jia
- Institut Langevin, ESPCI Paris, PSL, CNRS, F-75005 Paris, France
| | - C Lecoutre
- CNRS, ICMCB, Université de Bordeaux, UMR 5026, F-33600 Pessac, France
| | - S Luding
- MSM, University of Twente, 7500 AE Enschede, The Netherlands
| | - D Maza
- DFMA, Universidad de Navarra, E-31080 Pamplona, Spain
| | - M Noirhomme
- GRASP, Institute of Physics B5a, University of Liège, B-4000 Liège, Belgium
| | - E Opsomer
- GRASP, Institute of Physics B5a, University of Liège, B-4000 Liège, Belgium
| | - F Palencia
- CNRS, ICMCB, Université de Bordeaux, UMR 5026, F-33600 Pessac, France
| | - T Pöschel
- Friedrich-Alexander Universität, IMS, D-91052 Erlangen, Germany
| | - J Schockmel
- GRASP, Institute of Physics B5a, University of Liège, B-4000 Liège, Belgium
| | - M Sperl
- Institut für Materialphysik im Weltraum, DLR, D-51170 Köln, Germany
| | - R Stannarius
- IEP, Otto von Guericke Universität, D-39106 Magdeburg, Germany
| | - N Vandewalle
- GRASP, Institute of Physics B5a, University of Liège, B-4000 Liège, Belgium
| | - P Yu
- MSM, University of Twente, 7500 AE Enschede, The Netherlands
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Sarkar S, Bi D, Zhang J, Ren J, Behringer RP, Chakraborty B. Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space. Phys Rev E 2016; 93:042901. [PMID: 27176374 DOI: 10.1103/physreve.93.042901] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Indexed: 11/07/2022]
Abstract
Solids are distinguished from fluids by their ability to resist shear. In equilibrium systems, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern that is persistent, which in turn results from minimizing the free energy. In this work, we focus on a class of systems where this paradigm is challenged. We show that shear-driven jamming in dry granular materials is a collective process controlled by the constraints of mechanical equilibrium. We argue that these constraints can lead to a persistent pattern in a dual space that encodes the statistics of contact forces and the topology of the contact network. The shear-jamming transition is marked by the appearance of this persistent pattern. We investigate the structure and behavior of patterns both in real space and the dual space as the system evolves through the rigidity transition for a range of packing fractions and in two different shear protocols. We show that, in the protocol that creates homogeneous jammed states without shear bands, measures of shear jamming do not depend on strain and packing fraction independently but obey a scaling form with a packing-fraction-dependent characteristic strain that goes to zero at the isotropic jamming point ϕ_{J}. We demonstrate that it is possible to define a protocol-independent order parameter in this dual space, which provides a quantitative measure of the rigidity of shear-jammed states.
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Affiliation(s)
- Sumantra Sarkar
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Dapeng Bi
- Department of Physics, Syracuse University, Syracuse, New York 13224, USA.,Center for Studies in Physics and Biology, Rockefeller University, New York, New York 10065, USA
| | - Jie Zhang
- Institute of Natural Sciences and Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jie Ren
- Department of Physics, Duke University, Durham, North Carolina, USA
| | - R P Behringer
- Department of Physics, Duke University, Durham, North Carolina, USA
| | - Bulbul Chakraborty
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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Abstract
The zero temperature properties of frictionless soft spheres near the jamming point have been extensively studied both numerically and theoretically; these studies provide a reliable base for the interpretation of experiments. However, recent work by Ikeda et al. showed that, in a parameter space of the temperature and packing fraction, experiments to date on colloids have been rather far from the theoretical scaling regime. An important question is then whether theoretical results concerning point-J are applicable to any physical/experimental system, including granular media, which we consider here. On the surface, such a-thermal, frictional systems might appear even further from the idealized case of thermal soft spheres. In this work we address this question via experiments on shaken granular materials near jamming. We have systematically investigated such systems over a number of years using hard metallic grains. The important feature of the present work is the use of much softer grains, cut from photoelastic materials, making it possible to determine forces at the grain scale, the details of the contact networks and the motion of individual grains. Using this new type of particle, we first show that the contact network exhibits remarkable dynamics. We find strong heterogeneities, which are maximum at the packing fraction ϕ*, distinct from and smaller than the packing fraction ϕ(†), where the average number of contacts per particle, z, starts to increase. In the limit of zero mechanical excitation, these two packing fractions converge at point J. We also determine dynamics on time scales ranging from a small fraction of the shaking cycle to thousands of cycles. We can then map the observed system behavior onto results from simulations of ideal thermal soft spheres. Our results indicate that the ideal jamming point indeed illuminates the world of granular media.
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Affiliation(s)
- C Coulais
- SPHYNX/SPEC, CEA-Saclay, URA 2464 CNRS, 91 191 Gif-sur-Yvette, France
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4
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Abstract
Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern. In this work, we focus on the emergence of shear rigidity in a class of solids where this paradigm is challenged. Dry granular materials have no energetically or entropically preferred density modulations. We show that, in contrast to traditional solids, the emergence of shear rigidity in these granular solids is a collective process, which is controlled solely by boundary forces, the constraints of force and torque balance, and the positivity of the contact forces. We develop a theoretical framework based on these constraints, which connects rigidity to broken translational symmetry in the space of forces, not positions of grains. We apply our theory to experimentally generated shear-jammed states and show that these states are indeed characterized by a persistent, non-uniform density modulation in force space, which emerges at the shear-jamming transition.
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Affiliation(s)
- Sumantra Sarkar
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
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5
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Abstract
Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, and fractional Brownian motion provide examples. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collections of grains and the dynamics of a collections of molecules; in particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. Nonlinear Dynamics, Mathematics, Molecular Dynamics, and Condensed Matter Physics as well as traditional Engineering fields have all contributed to recent insights for these phenomena.
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Kondic L, Fang X, Losert W, O'Hern CS, Behringer RP. Microstructure evolution during impact on granular matter. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 85:011305. [PMID: 22400563 DOI: 10.1103/physreve.85.011305] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2011] [Indexed: 05/31/2023]
Abstract
We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself.
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Affiliation(s)
- L Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
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Abstract
A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu-Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort. In the Liu-Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea, the nature of the jamming transition for frictional grains is less clear. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order-disorder transition.
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Affiliation(s)
- Dapeng Bi
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
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8
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Affiliation(s)
- J Tang
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
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Wambaugh JF, Hartley RR, Behringer RP. Force networks and elasticity in granular silos. Eur Phys J E Soft Matter 2010; 32:135-145. [PMID: 20582447 DOI: 10.1140/epje/i2010-10608-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2009] [Accepted: 05/28/2010] [Indexed: 05/29/2023]
Abstract
We have made experimental observations of the force networks within a two-dimensional granular silo similar to the classical system of Janssen. Models like that of Janssen predict that pressure within a silo saturates with depth as the result of vertical forces being redirected to the walls of the silo where they can then be carried by friction. We use photoelastic particles to obtain information not available in previous silo experiments --the internal force structure. We directly compare various predictions with the results obtained by averaging ensembles of experimentally obtained force networks. We identify several differences between the mean behavior in our system and that predicted by Janssen-like models: We find that the redirection parameter describing how the force network transfers vertical forces to the walls varies with depth. We find that changes in the preparation of the material can cause the pressure within the silo to either saturate or to continue building with depth. Most strikingly, we observe a nonlinear response to overloads applied to the top of the material in the silo. For larger overloads we observe the previously reported "giant overshoot" effect where overload pressure decays only after an initial increase (G. Ovarlez et al., Phys. Rev. E 67, 060302(R) (2003)). For smaller overloads we find that additional pressure propagates to great depth. Analysis of the differences between the inter-grain contact and force networks suggests that, for our system, when the load and the particle weight are comparable, particle elasticity acts to stabilize the force network, allowing deep propagation. For larger loads, the force network rearranges, resulting in the expected, Janssen-like behavior. Thus, a meso-scale network phenomenon results in an observable nonlinearity in the mean pressure profile.
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Affiliation(s)
- J F Wambaugh
- Department of Physics, Duke University, Durham, NC 27708, USA.
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Lois G, Zhang J, Majmudar TS, Henkes S, Chakraborty B, O'Hern CS, Behringer RP. Stress correlations in granular materials: an entropic formulation. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 80:060303. [PMID: 20365107 DOI: 10.1103/physreve.80.060303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2009] [Revised: 10/12/2009] [Indexed: 05/29/2023]
Abstract
We study the response of dry granular materials to external stress using experiment, simulation, and theory. We derive a Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the nature of the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively.
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Affiliation(s)
- G Lois
- Department of Mechanical Engineering, Yale University, New Haven, Connecticut 06520-8284, USA
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11
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Kondic L, Dybenko OM, Behringer RP. Probing dense granular materials by space-time dependent perturbations. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:041304. [PMID: 19518221 DOI: 10.1103/physreve.79.041304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2008] [Revised: 03/11/2009] [Indexed: 05/27/2023]
Abstract
The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to probe this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the space-time scales of the perturbation. The features of the response provide a test bed for models that predict statistical and continuum space-time properties. We illustrate this connection between microscale physics and macroscale behavior by comparing the system response to a simple elastic model with damping.
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Affiliation(s)
- L Kondic
- Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
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12
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Behringer RP, Bi D, Chakraborty B, Henkes S, Hartley RR. Why do granular materials stiffen with shear rate? Test of novel stress-based statistics. Phys Rev Lett 2008; 101:268301. [PMID: 19437678 DOI: 10.1103/physrevlett.101.268301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Recent experiments exhibit a rate dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, gamma. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence of (ln(gamma))(1/2).
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Affiliation(s)
- R P Behringer
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA
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13
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Utter B, Behringer RP. Experimental measures of affine and nonaffine deformation in granular shear. Phys Rev Lett 2008; 100:208302. [PMID: 18518583 DOI: 10.1103/physrevlett.100.208302] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2007] [Revised: 10/02/2007] [Indexed: 05/26/2023]
Abstract
Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces a mean azimuthal flow, smooth affine deformations, and irreversible so-called nonaffine particle displacements. We find that these processes are all of comparable magnitude and depend on the local shear rate. We compute the parameter of Falk and Langer characterizing nonaffine motion, Dmin2, and find that it is reasonably well described in terms of collections of single particles making locally nearly isotropic random steps, delta ri. Distributions for single particle nonaffine displacements, delta ri, satisfy P1(delta ri) proportional, variantexp[-|delta ri/Delta r|alpha] (alpha < or approximately 2).
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Affiliation(s)
- Brian Utter
- Department of Physics and Center for Nonlinear and Complex Systems, Box 90305, Duke University, Durham, North Carolina 27708, USA
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Matas JP, Uehara J, Behringer RP. Gas-driven subharmonic waves in a vibrated two-phase granular material. Eur Phys J E Soft Matter 2008; 25:431-438. [PMID: 18421417 DOI: 10.1140/epje/i2007-10310-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2007] [Accepted: 03/07/2008] [Indexed: 05/26/2023]
Abstract
Vibrated powders exhibit striking phenomena: subharmonic waves, oscillons, convection, heaping, and even bubbling. We demonstrate novel rectangular profile subharmonic waves for vibrated granular material, that occur uniquely in the two-phase case of grains, and a fluid, such as air. These waves differ substantially from those for the gas-free case, exhibit different dispersion relations, and occur for specific shaking parameters and air pressure, understandable with gas-particle flow models. These waves occur when the gas diffusively penetrates the granular layer in a time comparable to the shaker period. As the pressure is lowered towards P =0, the granular-gas system exhibits a Knudsen regime. This instability provides an opportunity to quantitatively test models of two-phase flow.
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Affiliation(s)
- J-P Matas
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708-0305, USA.
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Behringer RP, Daniels KE, Majmudar TS, Sperl M. Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system. Philos Trans A Math Phys Eng Sci 2008; 366:493-504. [PMID: 17698474 DOI: 10.1098/rsta.2007.2106] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
In this work, we first review some general properties of dense granular materials. We are particularly concerned with a statistical description of these materials, and it is in this light that we briefly describe results from four representative studies. These are: experiment 1: determining local force statistics, vector forces, force distributions and correlations for static granular systems; experiment 2: characterizing the jamming transition, for a static two-dimensional system; experiment 3: characterizing plastic failure in dense granular materials; and experiment 4: a dynamical transition where the material 'freezes' in the presence of apparent heating for a sheared and shaken system.
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Affiliation(s)
- R P Behringer
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708-0320, USA.
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16
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Abstract
Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number Z at a critical volume fraction phi(c). Above phi(c), Z and the pressure P are predicted to increase as power laws in phi-phi(c). In experiments using photoelastic disks we corroborate a rapid increase in Z at phi(c) and power-law behavior above phi(c) for Z and P. Specifically we find a power-law increase as a function of phi-phi(c) for Z-Z(c) with an exponent beta around 0.5, and for P with an exponent psi around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.
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Affiliation(s)
- T S Majmudar
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA
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17
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Dutt M, Behringer RP. Effects of surface friction on a two-dimensional granular system: numerical model of a granular collider experiment. Phys Rev E 2007; 75:021305. [PMID: 17358335 DOI: 10.1103/physreve.75.021305] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2005] [Revised: 09/25/2006] [Indexed: 11/07/2022]
Abstract
We present numerical results from a simulation of a granular collider experiment [B. Painter, M. Dutt, and R. P. Behringer, Physica D 175, 43 (2003)] using a numerical model which accounts for substrate frictional effects [M. Dutt and R. P. Behringer, Phys. Rev. E 70, 061304 (2004)]. We find the gradual birth and growth of a central cluster for the final state of the particles that depends on the system size, the substrate frictional dissipation, and the initial average kinetic energy. For systems where a central cluster is observed in the final state, the autocorrelation function C(r) of the interparticle spacing satisfies a Gaussian functional form C(r)=Ae-(r/sigma)2. We also find that the fluctuation speed distributions adhere to a Maxwell-Boltzmann distribution for times in the vicinity of collapse. Our results strongly indicate that the principal mechanism responsible for the energy and momentum dissipation is the particle-substrate kinetic friction. Our findings reiterate the importance of considering the effects of substrate friction in particle-substrate systems, as shown by the agreement between our numerical results with experimental findings of Painter, Dutt, and Behringer.
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Affiliation(s)
- Meenakshi Dutt
- Department of Physics, Duke University, Durham, North Carolina 27708-0305, USA
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18
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Majmudar TS, Behringer RP. Contact force measurements and stress-induced anisotropy in granular materials. Nature 2005; 435:1079-82. [PMID: 15973358 DOI: 10.1038/nature03805] [Citation(s) in RCA: 374] [Impact Index Per Article: 19.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2005] [Accepted: 05/06/2005] [Indexed: 11/09/2022]
Abstract
Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.
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Affiliation(s)
- T S Majmudar
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina, 27708-0305, USA
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19
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Atman APF, Brunet P, Geng J, Reydellet G, Claudin P, Behringer RP, Clément E. From the stress response function (back) to the sand pile "dip". Eur Phys J E Soft Matter 2005; 17:93-100. [PMID: 15864732 DOI: 10.1140/epje/i2005-10002-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2005] [Accepted: 03/08/2005] [Indexed: 05/02/2023]
Abstract
We relate the pressure "dip" observed at the bottom of a sand pile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sand pile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing --albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.
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Affiliation(s)
- A P F Atman
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, ESPCI, 10 rue Vauquelin, 75231, Paris Cedex 05, France
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Abstract
We study the drag force experienced by an object slowly moving at constant velocity through a two-dimensional granular material consisting of bidisperse disks. The drag force is dominated by force chain structures in the bulk of the system, thus showing strong fluctuations. We consider the effect of three important control parameters for the system: the packing fraction, the drag velocity and the size of the tracer particle. We find that the mean drag force increases as a power law (exponent of 1.5) in the reduced packing fraction, (gamma- gamma(c) ) / gamma(c) , as gamma passes through a critical packing fraction, gamma(c) . By comparison, the mean drag grows slowly (basically logarithmic) with the drag velocity, showing a weak rate dependence. We also find that the mean drag force depends nonlinearly on the diameter, a of the tracer particle when a is comparable to the surrounding particles' size. However, the system nevertheless exhibits strong statistical invariance in the sense that many physical quantities collapse onto a single curve under appropriate scaling: force distributions P (f) collapse with appropriate scaling by the mean force, the power spectra P (omega) collapse when scaled by the drag velocity, and the avalanche size and duration distributions collapse when scaled by the mean avalanche size and duration. We also show that the system can be understood using simple failure models, which reproduce many experimental observations. These observations include the following: a power law variation of the spectrum with frequency characterized by an exponent alpha=-2 , exponential distributions for both the avalanche size and duration, and an exponential fall-off at large forces for the force distributions. These experimental data and simulations indicate that fluctuations in the drag force seem to be associated with the force chain formation and breaking in the system. Moreover, our simulations suggest that the logarithmic increase of the mean drag force with rate can be accounted for if slow relaxation of the force chain networks is included.
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Affiliation(s)
- Junfei Geng
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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Abstract
We describe a probe of diffusivity (D) and mobility (B) for a dense 2D granular system. We introduce random motion by stirring, and characterize D by particle tracking. To measure B we measure the force needed to push a particle through the medium at fixed velocity, v, using three sizes of tracer particle. We find simple Brownian diffusion, but B depends strongly on v because the force needed to push a tracer through a sample is nearly independent of v. Data for D/B depend on the tracer particle size.
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Affiliation(s)
- Junfei Geng
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708-0305, USA
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Dutt M, Behringer RP. Effects of surface friction on a two-dimensional granular system: cooling bound system. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 70:061304. [PMID: 15697352 DOI: 10.1103/physreve.70.061304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2004] [Indexed: 05/24/2023]
Abstract
Experiments performed by Phys. Rev. E 62, 2380 (2000)] on two-particle collisions and dynamics emphasized the importance of the role played by substrate friction, in particular kinetic friction, on the particle dynamics after collisions on a substrate. We present a numerical model which accounts for collisional and surface frictional dissipation and their influence on particle dynamics for a quasi-two-dimensional cooling initially dilute granular material. This model makes the simplifying assumption that the collision dynamics is determined solely by the incoming velocity and angular velocities of the colliding particles. We apply this model to a numerical simulation of a monolayer of monodisperse particles moving on a substrate, enclosed between inelastic walls. We find that surface friction-in particular, kinetic friction-plays a dominant role in determining the dynamics of quasi-two-dimensional multiparticle systems where the particles are in continuous contact with a substrate. Results from simulations performed for different system sizes indicate that surface friction and the inelastic walls lead to clustering of the particles in and near the vicinity of the walls. We find that the rate of decrease of average total kinetic energy is the highest when the majority of the particles have just collided and are experiencing kinetic frictional forces and torques. We also find from our calculations that, on average, particle-wall collisions lead to more dissipation than particle-particle collisions for a single particle for fixed restitutional parameters.
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Affiliation(s)
- Meenakshi Dutt
- Department of Physics and Center of Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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Abstract
As dense granular materials are sheared, a shear band and an anisotropic force network form. The approach to steady-state behavior depends on the history of the packing and the existing force and contact network. We present experiments on shearing of dense granular matter in a 2D Couette geometry in which we probe the history and evolution of shear bands by measuring particle trajectories and stresses during transients. We find that when shearing is stopped and restarted in the same direction, steady-state behavior is immediately reached, in agreement with the typical assumption that the system is quasistatic. Although some relaxation of the force network is observed when shearing is stopped, quasistatic behavior is maintained because the contact network remains essentially unchanged. When the direction of shear is reversed, a transient occurs in which stresses initially decrease, changes in the force network reach further into the bulk, and particles far from the wheel become more mobile. This occurs because the force network is fragile to changes transverse to the force network established under previous shear; particles must rearrange before becoming jammed again, thereby providing resistance to shear in the reversed direction. The strong force network is re-established after displacing the shearing surface approximately equal 3d, where d is the mean grain diameter. Steady-state velocity profiles are reached after a shear of < or approximately equal 30 d. Particles immediately outside of the shear band move on average less than 1 diameter before becoming jammed again. We also examine particle rotation during this transient and find that mean particle spin decreases during the transient, which is related to the fact that grains are not interlocked as strongly.
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Affiliation(s)
- B Utter
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, NC 27708, USA.
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Abstract
Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear flows in a two-dimensional Couette geometry. We find that self-diffusivities D are proportional to the local shear rate gamma; with diffusivities along the direction of the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D approximately gamma;a(2), where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is suppressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Lévy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce nondiffusive effects, on average the system appears simply diffusive.
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Affiliation(s)
- Brian Utter
- Department of Physics and Center for Nonlinear and Complex Systems, Box 90305, Duke University, Durham, North Carolina 27708, USA.
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Lätzel M, Luding S, Herrmann HJ, Howell DW, Behringer RP. Comparing simulation and experiment of a 2D granular Couette shear device. Eur Phys J E Soft Matter 2003; 11:325-333. [PMID: 15011035 DOI: 10.1140/epje/i2002-10160-7] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We present experiments along with molecular-dynamics (MD) simulations of a two-dimensional (2D) granular material in a Couette cell undergoing slow shearing. The grains are disks confined between an inner, rotating wheel and a fixed outer ring. The simulation results are compared to experimental studies and quantitative agreement is found. Tracking the positions and orientations of individual particles allows us to obtain density distributions, velocity and particle rotation rates for the system. The key issue of this paper is to show the extent to which quantitative agreement between an experiment and MD simulations is possible. Besides many differences in model details and the experiment, the qualitative features are nicely reproduced. We discuss the quantitative agreement/disagreement, give possible reasons, and outline further research perspectives.
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Affiliation(s)
- M Lätzel
- Institute for Computer Applications 1, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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Hartley RR, Behringer RP. Logarithmic rate dependence of force networks in sheared granular materials. Nature 2003; 421:928-31. [PMID: 12606996 DOI: 10.1038/nature01394] [Citation(s) in RCA: 157] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2002] [Accepted: 12/30/2002] [Indexed: 11/09/2022]
Abstract
Many models of slow, dense granular flows assume that the internal stresses are independent of the shearing rate. In contrast, logarithmic rate dependence is found in solid-on-solid friction, geological settings and elsewhere. Here we investigate the rate dependence of stress in a slowly sheared two-dimensional system of photoelastic disks, in which we are able to determine forces on the granular scale. We find that the mean (time-averaged) stress displays a logarithmic dependence on the shear rate for plastic (irreversible) deformations. However, there is no perceivable dependence on the driving rate for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate leads to an increase in the strength of the force network and stress fluctuations. Qualitatively, this behaviour resembles the changes associated with an increase in density. Increases in the shearing rate also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is suddenly stopped, stress relaxations occur with a logarithmic functional form over long timescales. This slow collective relaxation of the stress network provides a mechanism for rate-dependent strengthening.
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Affiliation(s)
- R R Hartley
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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Metcalfe G, Tennakoon SGK, Kondic L, Schaeffer DG, Behringer RP. Granular friction, Coulomb failure, and the fluid-solid transition for horizontally shaken granular materials. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 65:031302. [PMID: 11909041 DOI: 10.1103/physreve.65.031302] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2000] [Revised: 11/07/2001] [Indexed: 11/07/2022]
Abstract
We present the results of an extensive series of experiments, molecular dynamics simulations, and models that address horizontal shaking of a layer of granular material. The goal of this work was to better understand the transition between the "fluid" and "solid" states of granular materials. In the experiments, the material-consisting of glass spheres, smooth and rough sand-was contained in a container of rectangular cross section, and subjected to horizontal shaking of the form x=A sin(omega(t)). The base of the container was porous, so that it was possible to reduce the effective weight of the sample by means of a vertical gas flow. The acceleration of the shaking could be precisely controlled by means of an accelerometer mounted onboard the shaker, plus feedback control and lockin detection. The relevant control parameter for this system was the dimensionless acceleration, Gamma=Aomega(2)/g, where g was the acceleration of gravity. As Gamma was varied, the layer underwent a backward bifurcation between a solidlike state that was stationary in the frame of the shaker and a fluidlike state that typically consisted of a sloshing layer of maximum depth H riding on top of a solid layer. That is, with increasing Gamma, the solid state made a transition to the fluid state at Gamma(cu) and once the system was in the fluid state, a decrease in Gamma left the system in the fluidized state until Gamma reached Gamma(cd)<Gamma(cu). In the fluidized state, the flow consisted of back and forth sloshing at the shaker frequency, plus a slower convective flow along the shaking direction and additionally in the horizontal direction transverse to the shaking direction. Molecular dynamics simulations show that the last of these flows is associated with shear and dilation at the vertical sidewalls. For Gamma<Gamma(cu) and in the solid state, there was a "gas" of free particles sliding on the surface of the material. These constituted much less than one layer's worth of particles in all cases. If these "sliders" were suppressed by placing a thin strip of plastic on the surface, the hysteresis was removed, and the transition to fluidization occurred at a slightly lower value than Gamma(cd) for the free surface case. The hysteresis was also suppressed if a vertical gas flow from the base was sufficient to support roughly 40% of the weight of the sample. Both the transition to the fluid state from the solid and the reverse transition from the fluid to the solid were characterized by similar divergent time scales. If Gamma was increased above Gamma(cu) by a fractional amount epsilon=(Gamma-Gamma(cu))/Gamma(cu), where epsilon was small, there was a characteristic time tau=Aepsilon(-beta) for the transition from solid to fluid to occur, where beta is 1.00+/-0.06. Similarly, if Gamma was decreased below Gamma(cd) in the fluidized state by an amount epsilon=(Gamma-Gamma(cd))/Gamma(cd), there was also a transient time tau=Bepsilon(-beta), where beta is again indistinguishable from 1.00. In addition, the amplitudes A and B are essentially identical. By placing a small "impurity" on top of the layer, consisting of a heavier particle, we found that the exponent beta varied as the impurity mass squared and changed by a factor of 3. A simple Coulomb friction model with friction coefficients mu(k)<mu(s) for the fluid and solid states predicts a reversible rather than hysteretic transition to the fluid state, similar to what we observe with the addition of the small overload from a plastic strip. In an improved model, we provide a relaxational mechanism that allows the friction coefficient to change continuously between the low and high values. This model produces the hysteresis seen in experiments.
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Affiliation(s)
- Guy Metcalfe
- CSIRO Thermal and Fluids Engineering, Melbourne, VIC 3190, Australia
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Geng J, Longhi E, Behringer RP, Howell DW. Memory in two-dimensional heap experiments. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64:060301. [PMID: 11736161 DOI: 10.1103/physreve.64.060301] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2001] [Indexed: 05/23/2023]
Abstract
The measurement of force distributions in sandpiles provides a useful way to test concepts and models of the way forces propagate within noncohesive granular materials. Recent theory [J.-P. Bouchaud, M.E. Cates, and P. Claudin, J. Phys. I 5, 639 (1995); M. E. Cates, J. P. Wittmer, J.-P. Bouchaud, and P. Claudin, Phil. Trans. Roy. Soc. 356, 2535 (1998)] by Bouchaud et al. implies that the internal structure of a heap (and therefore the force pathway) is a strong function of the construction history. In general, it is difficult to obtain information that could test this idea from three-dimensional granular experiments except at boundaries. However, two-dimensional systems, such as those used here, can yield information on forces and particle arrangements in the interior of a sample. We obtain position and force information through the use of photoelastic particles. These experiments show that the history of the heap formation has a dramatic effect on the arrangement of particles (texture) and a weaker but clear effect on the forces within the sample. Specifically, heaps prepared by pouring from a point source show strong anisotropy in the contact angle distribution. Depending on additional details, they show a stress dip near the center. Heaps formed from a broad source show relatively little contact angle anisotropy and no indication of a stress dip.
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Affiliation(s)
- J Geng
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708-0305, USA
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29
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Geng J, Howell D, Longhi E, Behringer RP, Reydellet G, Vanel L, Clément E, Luding S. Footprints in sand: the response of a granular material to local perturbations. Phys Rev Lett 2001; 87:035506. [PMID: 11461569 DOI: 10.1103/physrevlett.87.035506] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2000] [Indexed: 05/23/2023]
Abstract
We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We use 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.
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Affiliation(s)
- J Geng
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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30
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Painter B, Behringer RP. Substrate interactions, effects of symmetry breaking, and convection in a 2D horizontally shaken granular system. Phys Rev Lett 2000; 85:3396-3399. [PMID: 11030905 DOI: 10.1103/physrevlett.85.3396] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2000] [Indexed: 05/23/2023]
Abstract
We describe experiments on a horizontally shaken [x = Asin(omegat)] single layer of hard spheres rolling on a nearly horizontal surface. We identify a novel substrate-mediated convective flow which occurs when the system is tilted slightly so that the weak gravitational force, g-->(eff), acting on the particles is not parallel to the driving direction. As the shaking amplitude is increased, the system progresses through four regimes: solid-flat, solid-inclined, convective, and disordered. The control parameter is the driving velocity, Aomega, rather than the usual Aomega(2) of vertically shaken 3D systems. At the onset of convection, the critical velocity is V(c) approximately sqrt[2g(eff)d].
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Affiliation(s)
- B Painter
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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31
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Painter B, Behringer RP. Dynamics of two-particle granular collisions on a surface. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 62:2380-2387. [PMID: 11088718 DOI: 10.1103/physreve.62.2380] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2000] [Indexed: 05/23/2023]
Abstract
We experimentally examine the dynamics of two-particle collisions occurring on a surface. We find that in two-particle collisions a standard coefficient of restitution model may not capture crucial dynamics of the system. Instead, for a typical collision, the particles involved slide relative to the substrate for a substantial time following the collision; during this time they experience very high frictional forces. The frictional forces lead to energy losses that are typically larger by a factor of 5-6 than the losses due to particle inelasticity. In addition, momentum can be transferred to the substrate, so that the momentum of the two particles is not necessarily conserved. Finally, we measure the angular momenta of particles immediately following the collision, and find that angular momentum can be lost to the substrate following the collision as well.
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Affiliation(s)
- B Painter
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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Vanel L, Howell D, Clark D, Behringer RP, Clément E. Memories in sand: experimental tests of construction history on stress distributions under sandpiles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 60:R5040-3. [PMID: 11970451 DOI: 10.1103/physreve.60.r5040] [Citation(s) in RCA: 102] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/1999] [Indexed: 11/07/2022]
Abstract
We report experiments on piles of cohesionless granular materials showing the effect of construction history on static stress distributions. Stresses under piles are monitored by sensitive capacitive techniques. The piles are formed either by pouring granular material from a funnel with a small outlet (localized source), or from a large sieve (homogeneous rain). Localized sources yield stress profiles with a clear stress dip near the center of the pile; the homogeneous rain profiles have no stress dip. We show that the stress profiles scale linearly with the pile height. Experiments on wedge-shaped piles show similar but weaker effects.
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Affiliation(s)
- L Vanel
- Laboratoire des Milieux Désordonnés et Hétérogènes, CNRS UMR No. 7603, Case 86, Université Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex, France
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Abstract
Dense slowly evolving or static granular materials exhibit strong force fluctuations even though the spatial disorder of the grains is relatively weak. Typically, forces are carried preferentially along a network of "force chains." These consist of linearly aligned grains with larger-than-average force. A growing body of work has explored the nature of these fluctuations. We first briefly review recent work concerning stress fluctuations. We then focus on a series of experiments in both two- and three-dimension [(2D) and (3D)] to characterize force fluctuations in slowly sheared systems. Both sets of experiments show strong temporal fluctuations in the local stress/force; the length scales of these fluctuations extend up to 10(2) grains. In 2D, we use photoelastic disks that permit visualization of the internal force structure. From this we can make comparisons to recent models and calculations that predict the distributions of forces. Typically, these models indicate that the distributions should fall off exponentially at large force. We find in the experiments that the force distributions change systematically as we change the mean packing fraction, gamma. For gamma's typical of dense packings of nondeformable grains, we see distributions that are consistent with an exponential decrease at large forces. For both lower and higher gamma, the observed force distributions appear to differ from this prediction, with a more Gaussian distribution at larger gamma and perhaps a power law at lower gamma. For high gamma, the distributions differ from this prediction because the grains begin to deform, allowing more grains to carry the applied force, and causing the distributions to have a local maximum at nonzero force. It is less clear why the distributions differ from the models at lower gamma. An exploration in gamma has led to the discovery of an interesting continuous or "critical" transition (the strengthening/softening transition) in which the mean stress is the order parameter, and the mean packing fraction, gamma, must be adjusted to a value gamma(c) to reach the "critical point." We also follow the motion of individual disks and obtain detailed statistical information on the kinematics, including velocities and particle rotations or spin. Distributions for the azimuthal velocity, V(theta), and spin, S, of the particles are nearly rate invariant, which is consistent with conventional wisdom. Near gamma(c), the grain motion becomes intermittent causing the mean velocity of grains to slow down. Also, the length of stress chains grows as gamma-->gamma(c). The 3D experiments show statistical rate invariance for the stress in the sense that when the power spectra and spectral frequencies of the stress time series are appropriately scaled by the shear rate, Omega, all spectra collapse onto a single curve for given particle and sample sizes. The frequency dependence of the spectra can be characterized by two different power laws, P proportional, variant omega(-alpha), in the high and low frequency regimes: alpha approximately 2 at high omega; alpha<2 at low omega. The force distributions computed from the 3D stress time series are at least qualitatively consistent with exponential fall-off at large stresses. (c) 1999 American Institute of Physics.
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Affiliation(s)
- Daniel W. Howell
- Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305
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35
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Shattuck MD, Behringer RP, Johnson GA, Georgiadis JG. Onset and Stability of Convection in Porous Media: Visualization by Magnetic Resonance Imaging. Phys Rev Lett 1995; 75:1934-1937. [PMID: 10059166 DOI: 10.1103/physrevlett.75.1934] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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36
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Olafsen JS, Behringer RP. Temporal response of the thermal boundary resistance in superfluid helium. Phys Rev B Condens Matter 1995; 52:61-63. [PMID: 9979569 DOI: 10.1103/physrevb.52.61] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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39
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Metcalfe G, Behringer RP. Transition to large aspect ratio convection. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1994; 49:R3572-R3575. [PMID: 9961787 DOI: 10.1103/physreve.49.r3572] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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40
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41
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Anderson KE, Shattuck MD, Behringer RP. Novel cross-roll state in a cylindrical convection cell with thermally conducting sidewalls. Phys Rev A 1992; 46:R6143-R6146. [PMID: 9907998 DOI: 10.1103/physreva.46.r6143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Metcalfe GP, Behringer RP. Convection in 3He-superfluid-4He mixtures: Measurement of the superfluid effects. Phys Rev A 1990; 41:5735-5738. [PMID: 9902969 DOI: 10.1103/physreva.41.5735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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45
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46
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Gao H, Behringer RP. Onset of time dependence at the secondary instability of a convecting binary mixture: Implications for wave-number selection. Phys Rev A Gen Phys 1987; 35:3993-3996. [PMID: 9898638 DOI: 10.1103/physreva.35.3993] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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48
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Shaumeyer JN, Behringer RP. Unexpected observation in measurements of transport coefficients in 3He-4He mixtures near T lambda. Phys Rev B Condens Matter 1986; 33:3553-3555. [PMID: 9938751 DOI: 10.1103/physrevb.33.3553] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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49
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