Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory

Jenkins, James T.; Berzi, Diego

doi:10.1007/s10035-010-0169-8

Cited by 127 publications

(169 citation statements)

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“…It is well known that flows of thin layers of grains down an inclined surface exhibit a size effect whereby thinner layers require more tilt to begin flowing (50), and it is possible that the nonlocal fluidity approach justifies this behavior as a consequence of the lower boundary condition. Approaches based on kinetic theory have had success attributing this phenomenon to the effect of the bottom wall (27), which is encouraging.…”

Section: Resultsmentioning

confidence: 82%

“…Approaches include integral equations representing a self-activated process (23), theories of partial fluidization governed by a Ginzberg-Landau order parameter (24), Cosserat plasticity-based models (25), extensions of kinetic theory to the slow-flow regime (26,27), and the stochastic flow rule (28). Each of these models displays a "diffusive" character-although invoking different physical hypotheses, each accomplishes the essential qualitative goal of spreading sharply varying flow features on the basis of grain size.…”

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confidence: 99%

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A predictive, size-dependent continuum model for dense granular flows

Henann

Kamrin

2013

Proc. Natl. Acad. Sci. U.S.A.

292

330

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Dense granular materials display a complicated set of flow properties, which differentiate them from ordinary fluids. Despite their ubiquity, no model has been developed that captures or predicts the complexities of granular flow, posing an obstacle in industrial and geophysical applications. Here we propose a 3D constitutive model for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal rheology-inspired by efforts for emulsions-in which flow at a point is affected by the local stress as well as the flow in neighboring material. The microscopic physical basis for this approach borrows from recent principles in soft glassy rheology. The sizedependence is captured using a single material parameter, and the resulting model is able to quantitatively describe dense granular flows in an array of different geometries. Of particular importance, it passes the stringent test of capturing all aspects of the highly nontrivial flows observed in split-bottom cells-a geometry that has resisted modeling efforts for nearly a decade. A key benefit of the model is its simple-to-implement and highly predictive final form, as needed for many real-world applications. G ranular materials are ubiquitous in day-to-day life, as well as central to important industries, such as geotechnical, energy, pharmaceutical, and food processing. In fact, granular matter is second only to water as the most handled industrial material (1), but unlike water, dense granular flows are substantially more complex (2-10). In particular, slowly flowing granular media form clear, experimentally robust features, most notably, shear bands, which can have a variety of possible widths and decay nontrivially into the surrounding quasi-rigid material. However, these behaviors remain poorly understood and have not been rationalized with a universal continuum model, posing a costly problem in industry. Quantitatively describing and predicting dense, well-developed granular flows with a constitutive model that may be applied in arbitrary configurations remains a major open challenge.For many years, mechanicians and materials engineers have approached granular materials modeling from a soil mechanics perspective, grounded in the principles of continuum solid mechanics, invoking various yield criteria and plastic flow relations (11, 12). In contrast, over the past two decades, a resurgence of interest in granular media has arisen among physicists, primarily drawing upon statistical and fluid dynamical approaches (13,14). More recently, drawing upon both schools of thought, granular rheologists have made progress combining a fluid-like, ratedependent flow approach with an appropriate yield criterion. Backed by numerous experiments and a coherent dimensional argument, the key result is the dimensionless relation μ = μ(I), consistent with the seminal work of Bagnold (15), which has become a well-regarded basis for modeling well-developed granular flows in simple shear (9, 16), where μ = τ/P fo...

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Section: Resultsmentioning

confidence: 82%

mentioning

confidence: 99%

A predictive, size-dependent continuum model for dense granular flows

Henann

Kamrin

2013

Proc. Natl. Acad. Sci. U.S.A.

292

330

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“…Jenkins further extended the theory in [28] to very dissipative frictional particles, with a coefficient of restitution less than 0.7. Later, a detailed comparison with new experiments was performed, showing agreement for flows on low inclinations [25].…”

Section: Shallow-layer Modelsmentioning

confidence: 90%

Closure relations for shallow granular flows from particle simulations

et al. 2012

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The discrete particle method (DPM) is used to model granular flows down an inclined chute with varying basal roughness, thickness and inclination. We observe three major regimes: arresting flows, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed: for small inclinations the flow can be highly energetic and strongly layered in depth; whereas, for large inclinations it can be non-uniform and oscillating. For steady uniform flows, depth profiles of density, velocity and stress are obtained using an improved coarse-graining method, which provides accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations obtained from micro-scale DPM simulations of steady flows. We obtain functional relations for effective basal friction, velocity shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal roughness. Granular avalanche flows are common in both the natural environments and industry. They occur across many orders of magnitude. Examples range from rock slides, containing upwards of 1,000 m 3 of material; to the flow of sinter, pellets and coke into a blast furnace for iron-ore melting; down to the flow of sand in an hour-glass. The dynamics of these flows are influenced by many factors such as: polydispersity; variations in density; non-uniform shape; complex basal topography; surface contact properties; coexistence of static, steady and accelerating material; and, flow obstacles and constrictions. KeywordsDiscrete particle methods (DPMs) are an extremely powerful way to investigate the effects of these and other factors. With the rapid recent improvement in computational power the full simulation of the flow in a small hour glass of millions of particles is now feasible. However, complete DPM simulations of large-scale geophysical mass flow will, probably, never be possible.One of the main goals of the present research is to simulate large scale and complex industrial flows using granular shallow-layer equations. In this paper we will take the first step of using the DPM [9,34,42,43,46] to simulate small granular flows of mono-dispersed spherical particles in steady flow situations. We will use a refined and novel analysis to investigate three particular aspects of shallow chute flows: (i) how to obtain meaningful macro-scale fields from the DPM simulation, (ii) how to assess the flow dependence on the basal roughness, and (iii) how to validate the assumptions made in depth-averaged theory.The DPM simulations presented here will enable the construction of the mapping between the micro-scale and 123

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“…We also make the assumption that plastic flow proceeds at constant volume, so that J p = det F p = 1, J = J e , and tr L p = trD p = 0. This is a standard assumption in the modeling of steady granular flow [32,25,33,34,4,14,15] and provides considerable simplification. This is equivalent to assuming that the material is always in its "critical state" [35], and all transient plastic volumetric dilatation or compaction (which is an important aspect of granular deformation [36,37]) has subsided.…”

Section: Summary Of the Modelmentioning

confidence: 99%

A finite element implementation of the nonlocal granular rheology

Henann¹,

Kamrin²

2016

Numerical Meth Engineering

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SUMMARYInhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models have been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finiteelement-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom -the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (i) linear shear with gravity, (ii) annular shear flow without gravity, and (iii) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh-independent.

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Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory

Cited by 127 publications

References 29 publications

A predictive, size-dependent continuum model for dense granular flows

A predictive, size-dependent continuum model for dense granular flows

Closure relations for shallow granular flows from particle simulations

A finite element implementation of the nonlocal granular rheology

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