The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divises (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

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On dense granular flows.

A granular material is a collection of a large number of discrete solid particles. Generally, the interstices between the particles are filled with a fluid such as air or water, and thus, technically, a granular flow is a multiphase process. However, if the particles are closely packed or if they are much denser than the interstitial fluid, the particles alone-and not the fluid or the fluid-particle interactions-will play the greatest role in momentum transport within the material, in which case the interstitial fluid can be ignored in describing the flow behavior. Granular-material fl ows are generally taken to fall into this limiting category and thus may be considered dispersed single-phase rather than multiphase flows. This review addresses the fluidlike behavior of granular solids and, in particular, those flows for which the material is rapidly sheared. I outline what is currently known about rapid granular flows, discuss the various modeling techniques used to describe the motion of the bulk material, and point out many questions that remain to be answered. Depending on the local stress conditions, a granular material may behave as either an elastic solid or a fluid. When a granular material is showing its elastic-solid behavior, it can support the large loads of building foundations or form i nto hills with finite slopes. However, much of the load is supported across frictional bonds between the particles, and, as such, the system's strength is limited to the loads that those bonds can support. When enough of the bonds have been overcome, the system will fail and begin to flow. The initial failure will consist of many-particle blocks moving relative to one another along shear bands that roughly follow stress characteristics through the material. If the motion occurs slowly, particles will stay in contact and interact frictionally with their neighbors over long periods of time. The failure will continue in this

Rapid granular flows

This report describes the MFIX (Multiphase Flow with Interphase exchanges) computer model. MFIX is a general-purpose hydrodynamic model that describes chemical reactions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors. MFIX calculations give detailed information on pressure, temperature, composition, and velocity distributions in the reactors. With such information, the engineer can visualize the conditions in the reactor, conduct parametric studies and what-if experiments, and, thereby, assist in the design process. The MFIX model, developed at the Morgantown Energy Technology Center (METC), has the following capabilities: mass and momentum balance equations for gas and multiple solids phases; a gas phase and two solids phase energy equations; an arbitrary number of species balance equations for each of the phases; granular stress equations based on kinetic theory and frictional flow theory; a user-defined chemistry subroutine; three-dimensional Cartesian or cylindrical coordinate systems; nonuniform mesh size; impermeable and semi-permeable internal surfaces; user-friendly input data file; multiple, single-precision, binary, direct-access, output files that minimize disk storage and accelerate data retrieval; and extensive error reporting. This report, which is Volume 1 of the code documentation, describes the hydrodynamic theory used in the model: the conservation equations,more » constitutive relations, and the initial and boundary conditions. The literature on the hydrodynamic theory is briefly surveyed, and the bases for the different parts of the model are highlighted.« less

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MFIX documentation theory guide

Granular materials display a variety of behaviors that are in many ways different from those of other substances. They cannot be easily classified as either solids or liquids. This has prompted the generation of analogies between the physics found in a simple sandpile and that found in complicated microscopic systems, such as flux motion in superconductors or spin glasses. Recently, the unusual behavior of granular systems has led to a number of new theories and to a new era of experimentation on granular systems.

https://science.sciencemag.org/content/sci/255/5051/1523.full.pdf

Physics of the Granular State

Experimental observations and numerical simulations of the large force inhomogeneities present in stationary bead packs are presented. Forces much larger than the mean occurred but were exponentially rare. An exactly soluble model reproduced many aspects of the experiments and simulations. In this model, the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead in the pile.

R.M. Nedderman

Papers

The flow of granular materials—I: Discharge rates from hoppers

The flow of granular materials—II Velocity distributions in slow flow

Die entry pressure drops in paste extrusion

The effect of viscosity on the flooding conditions in wetted wall columns

The motion and frequency of large disturbance waves in annular two-phase flow of air-water mixtures