Granular flow down an inclined plane: Bagnold scaling and rheology

Silbert, Leonardo E.; Ertaş, Deniz; Grest, Gary S.; Halsey, Thomas C.; Levine, Dov; Plimpton, Steven J.

doi:10.1103/physreve.64.051302

Cited by 894 publications

(1,149 citation statements)

References 42 publications

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“…[23][24][25]. The system starts as an ensemble of up to 70,000 monodisperse spheres of diameter d inside a cylindrical reservoir (hopper).…”

Section: Resultsmentioning

confidence: 99%

“…The repulsive force between grains is modeled using a linear spring-dashpot with both normal and tangential damping as well as static friction, following [25]. In this model, the normal contact force is given by F n = k n δ n + γ n m ef fδn , where δ n = d − |r i − r j | is the overlap between the grains i and j, k n the normal stiffness, γ n is the damping constant for normal motion, m ef f = m/2 is the reduced mass, and m = 1 6 πρd 3 is the grain mass (ρ =2.5 kg/m 3 ).…”

Section: Discussionmentioning

confidence: 99%

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Droplet and cluster formation in freely falling granular streams

et al. 2011

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Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream's macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gas-like jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams

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“…[23][24][25]. The system starts as an ensemble of up to 70,000 monodisperse spheres of diameter d inside a cylindrical reservoir (hopper).…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Droplet and cluster formation in freely falling granular streams

et al. 2011

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“…Since the realistic modeling of particle deformation is complicated, a simplified contact force model based on a linear spring−dashpot combination is used in this work. 3 Details of the computational model used in these discrete element simulations are given in the Appendix. For all the DEM simulations reported, the mass and diameter of particles are set to 1, so the density of particles is 6/π.…”

Section: Discrete Element Methods Simulationsmentioning

confidence: 99%

“…The first approach, DEM (discrete element method), is a particle-level microscopic simulation method that represents multiparticle interaction on contact through a contact force model. 3 The computational cost of DEM restricts its use to relatively small system sizes and idealized geometries. The second approach is a continuum description of granular flows that results in averaged conservation equations for mass, momentum, and energy.…”

Section: Introductionmentioning

confidence: 99%

Granular Flow in Silo Discharge: Discrete Element Method Simulations and Model Assessment

Vidyapati

Subramaniam

2013

Ind. Eng. Chem. Res.

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Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle-wall friction coefficient and particle coefficient of restitution) and system parameters (orifice width) on the discharge rate is quantified. The spatial extent of different regimes (quasi-static, intermediate and inertial) of granular rheology are quantified using a regime map previously established from DEM data of homogeneously sheared granular flow. It is shown that all three regimes of granular rheology coexist during silo discharge, and the intermediate regime plays a significant role in discharge dynamics. A quantitative comparison between results of continuum and DEM simulations is performed by computing discharge rates, solid velocities, and solid stresses for a threedimensional (3D) flat-bottomed silo. It is found that the three constitutive models investigated in this study overpredict the discharge rate when compared to DEM data. Contour plots of the error in solid stress prediction are compared with the spatial extent of different regimes of granular rheology to deduce that it is inaccurate modeling of the intermediate regime that is responsible for overprediction of the discharge rate. ABSTRACT: Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle−wall friction coefficient and particle coefficient of restitution) and system parameters (orifice width) on the discharge rate is quantified. The spatial extent of different regimes (quasi-static, intermediate and inertial) of granular rheology are quantified using a regime map previously established from DEM data of homogeneously sheared granular flow. It is shown that all three regimes of granular rheology coexist during silo discharge, and the intermediate regime plays a significant role in discharge dynamics. A quantitative comparison between results of continuum and DEM simulations is performed by computing discharge rates, solid velocities, and solid stresses for a three-dimensional (3D) flat-bottomed silo. It is found that the three constitutive models investigated in this study overpredict the discharge rate when compared to DEM data. Contour plots of the error in solid stress prediction are compared with the spatial extent of different regimes of granular rheology to deduce that it is inaccurate modeling of the intermediate regime that is responsible for overprediction of the discharge rate. Disciplines Aerodynamics and Fluid Mechanics | Mechanical Engineering Comments Reprinted with permission from INTRODUCTIONModeling and prediction of granular flows in nature and in technological applications is a challenging problem of considerable socioeconomic i...

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“…This is important, because it implies that the results hold for arbitrary lateral velocity profiles, from plug flow, which is usually assumed in most avalanche models, to simple shear (Savage & Lun 1988) and nonlinear profiles (e.g. Silbert et al 2001). Equation (5.3) must be solved subject to an initial concentration profile φ 0 (z) and the no-flux boundary condition (2.24) at the surface and base of the avalanche…”

Section: Uniform Flowmentioning

confidence: 99%

Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

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Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the sizedistribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particlesize segregation and diffusive remixing of large and small particles in shallow gravitydriven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation-remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation-remixing equation reduces to a logistic type equation and the 'S'-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation-remixing equation to Burgers equation and using the Cole-Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent twodimensional solutions are also constructed for plug-flow in a semi-infinite chute.

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Granular flow down an inclined plane: Bagnold scaling and rheology

Cited by 894 publications

References 42 publications

Droplet and cluster formation in freely falling granular streams

Droplet and cluster formation in freely falling granular streams

Granular Flow in Silo Discharge: Discrete Element Method Simulations and Model Assessment

Particle-size segregation and diffusive remixing in shallow granular avalanches

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