Flow Of Granular Media Research Articles

Non-coaxial plastic flow of granular materials through stress probing analysis

The current study investigates the non-coaxial plastic flow in granular media where the principal directions of incremental plastic strain differ from those of the current stress (and of the current fabric tensor). The stress probing technique is used with Discrete Element Method simulations to capture the plastic response of a 2D granular assembly to loading increments along different directions in stress space, including non-coaxial ones. A general form for the plastic flow is suggested, based on multi-mechanism plasticity theory which is demonstrated to be capable of capturing the essential characteristics of the non-coaxial plastic flow. Deviations between DEM results and model predictions are associated with the incrementally nonlinear nature of the response. The analysis of the results indicate that, at a given stress state, the plastic yielding direction is not coaxial with the current stress. The significance of the non-coaxial plastic flow is shown to be around 20% for lower deviatoric stresses, but this value diminishes as the peak stress is achieved, hinting to the dominance of a single mechanism at failure. The study concludes by comparing the developed model with two well-known non-coaxial models in the literature, where the performance of the developed model is found to be close to the double-shearing theory.

Finding Flow in Granular Media

Finding Flow in Granular Media

Physics of particulate flows: From sand avalanche to active suspensions in plants

Abstract Flows of granular media in air or in a liquid have been a research field for physicists for several decades. Sometimes solid, sometimes liquid, these particulate materials exhibit peculiar behaviors, which have motivated many studies at the frontiers between nonlinear physics, soft matter physics and fluid mechanics. This paper presents a summary of the recent advances in the field, with a focus on the development of continuous approaches, which make it possible to treat granular media as a complex fluid and to develop a granular hydrodynamics. We also discuss how the better understanding of granular flows we have today may help to address more complex materials, such as colloidal suspensions or some biological systems.

Discharge flow of granular media from silos with a lateral orifice and injection of air

Few studies concern the prediction of the mass flow rate of a granular media discharged from a silo with a lateral orifice. However, this situation can have pratical interest considering a tank of granular material with a leak on its side. We studied experimentally the discharge of a vertical silo filled by spherical glass beads. We consider rectangular silos with a rectangular orifice. The impact of size, aspect ratio and position of the orifice and the effect of an additional air flow were studied. The measured parameters are the mass flow rate and the pressure along the silo, whereas the controlled parameters are the size of particles, and the flow rate of air. We identified two regimes of discharge according to the aspect ratio (of width to height) of the rectangular orifice. Increasing the air flow rate induces an increase of the granular media flow rate. Using a simple physical model to describe the grains and gas flow, we put in evidence the role played by the air pressure gradient at the outlet. Then we compared the experimental results with continuum Navier-Stokes simulations with the granular μ (I)-rheology. We showed that the continuum μ (I)-rheology describes well our discharge flow of granular media from silos, taking into account the effect of the position of the orifice as well as the coupling with the gas flow.

Kinetic theory for strong uniform shear flow of granular media at high density

We discuss the uniform shear flow of a fluidized granular bed composed of monodisperse Hertzian spheres. Considering high densities around the glass transition density of inelastic Hertzian spheres, we report kinetic theory expressions for the Newtonian viscosity as well as the Bagnold coefficient. We discuss the dependence of the transport coefficients on density and coefficient of restitution.

Influence of particle size in silo discharge

Recently Janda et al. [Phys. Rev. Lett. 108 , 248001 (2012)] reported an experimental study where it was measured the velocity and volume fraction fields of 1 mm diameter stainless steel beads in the exit of a two-dimensional silo. In that work, they proposed a new expression to predict the flow of granular media in silos which does not explicitly include the particle size as a parameter. Here, we study if effectively, there is not such influence of the particle size in the flux equations as well as investigate any possible effect in the velocity and volume fraction fields. To this end, we have performed high speed motion measurements of these magnitudes in a two-dimensional silo filled with 4 mm diameter beads of stainless steel, the same material than the previous works. A developed tracking program has been implemented to obtain at the same time both, the velocity and volume fraction. The final objective of this work has been to extend and generalize the theoretical framework of Janda et al. for all sizes of particles. We have found that the obtained functionalities are the same than in the 1 mm case, but the exponents and other fitting parameters are different.

On the validity of the flow rule postulate for geomaterials

SUMMARYThis paper is concerned with a fundamental assumption in the theory of plasticity: the direction of plastic strain increments is independent of the loading (stress) increment direction. This assumption, also known as plastic flow rule postulate, works quite well for metal‐like materials. However, geomaterials such as sand present deformational mechanisms that are distinctive from those of metals when they are loaded. As such, we hereby examine the validity of this postulate for granular media accounting for their discrete nature. This is accomplished by analysing the mechanical behaviour of a cubic assembly of polydispersed spherical articles using a particle flow code. An extension to Gudehus' response envelope to three‐dimensional conditions is used to study the incremental character and influence of loading direction on the behaviour of these materials. It is found that plastic flow in granular media is governed by both current state variables and incremental loading direction and magnitude, especially under non‐axisymmetric stress conditions. The flow rule postulate of plasticity remains valid only in axisymmetric and biaxial conditions. We also verified that the plastic response might be significantly influenced by the stress path (or history) taken prior to loading. These findings raise the question of whether or not classic elastoplastic models based on the above postulate will have serious shortcomings, especially in true‐triaxial conditions. Copyright © 2013 John Wiley & Sons, Ltd.

Experimental Surface Profile of Dense Granular Media in Cylindrical Couette Flow

Granular materials have widespread use in the industry. The flow of granular media requires careful studies through experiments to understand the rheology of these complex materials. The present work determines the surface profile of dense granular media subjected to cylindrical Couette flow. A translation stage is used to obtain measurement of depth varying with radial distance. A depth gauge attached to the translation stage is used to measure the surface profile. Glass beads (average diameter 0.8-1 mm) and mustard seeds (average diameter 1.2-1.4 mm) are used as model granular materials. Two different Couette gaps are used (4cm and 3cm). Cylinders with smooth surfaces, as well as coated with emery paper are used. The surface profile varies with material, surface roughness of the cylinders, and the gap between the two cylinders. The comparison of the various cases has been done by graphical representation. The probable reasons for the development of such a surface profile are given.

General capillary pressure and relative permeability expressions for through-plane fluid transport in thin fibrous sheets

The rate of fluid transport in partially saturated porous media depends on the media's instantaneous (function of saturation) relative permeability, k r( S), and capillary pressure, P c( S). Obtaining functional relationships for relative permeability and capillary pressure is only possible via experimentation or expensive microscale simulations, and needs to be repeated for different media having different fiber diameters, thicknesses, or porosities. In this concern, we conducted series of 3-D microscale simulations to investigate the effect of the above parameters on the relative permeability and capillary pressure of fibrous porous sheets. The results of our parameter study are utilized to develop general expressions for k r( S) and P c( S). Our general expressions are based on the existing empirical correlations of two-phase flow in granular media, and can easily be included in macroscale fluid transport equations to predict the rate of fluid release from partially saturated fibrous sheets in a time and cost-effective manner.

応力主軸回転を受ける粒状体の塑性ひずみ増分応答の考察

応力主軸回転を受ける粒状体の塑性ひずみ増分応答の考察

Stability of couette flow in granular media

Stability of couette flow in granular media

Molecular dynamics studies of grain segregation in sheared flow

Size segregation is a widely observed consequence of sheared flow in granular media, in which the larger grains rise to the upper surface of the bulk, despite the fact that all grains have the same material density. A two-dimensional molecular dynamics study of the phenomenon is described in this paper. The grains are represented by inelastic disks and the flow occurs down an inclined slope with a rough base. The simulations readily reproduce the segregation effect; the results of a series of measurements of various aspects of this so-called ``inverse grading'' are reported.

Nonlinear bubble dynamics in a slowly driven foam.

Sudden topological rearrangement of neighboring bubbles in a foam occur during coarsening, and can also be induced by applied forces. Diffusing-wave spectroscopy measurements are presented of such dynamics before, during, and after an imposed shear strain. The rate of rearrangements is proportional to the strain rate, and the shape of the correlation functions shows that they are spatially and temporally uncorrelated. Macroscopic deformation is thus accomplished by a nonlinear microscopic process reminiscent of dynamics in the propagation of earthquake faults or the flow of granular media.

A new technique for differentiating between diffusion and flow in granular media using magnetic resonance imaging

We have shown that a simple nuclear magnetic resonance spin-tagging sequence for spatial encoding of the longitudinal magnetization, combined with an imaging sequence, can be used to measure flow and diffusion in granular materials. Using this technique, experiments have been performed to study flow and diffusion profiles during convection induced by the vertical shaking of a container (39 mm diameter) filled with a granular medium. We have shown that maximum diffusion and displacements occur in a thin boundary layer near the container’s walls. The observed flow profiles are predominantly flat with relatively small positive displacements across the container with the exception of the boundary layer, where increasingly negative displacements are observed as the container’s edges are approached.

Density waves in the flows of granular media.

We study density waves in the flows of granular particles through vertical tubes and hoppers using both analytic methods and molecular dynamics (MD) simulations. We construct equations of motion for quasi one-dimensional systems. The equations, combined with the Bagnold's law for friction, are used to describe the time evolutions of the density and the velocity fields for narrow tubes and hoppers. The solutions of the equations can have two types of density waves, kinetic and dynamic. For tubes, we can show the existence of kinetic waves, and obtain the condition for dynamic waves for tubes from the equations. For hoppers, we obtain the solutions of the equations up to the first order of the opening angle, which also show the existence of kinetic waves. We reproduce density waves in the MD simulations for tubes. The waves are believed to be kinetic based on a few evidences, including a well defined flux-density curve. In MD simulations of flows in hoppers, we find density waves, which are also believed to be kinetic.

Flow of granular media through a plane parallel/converging bunker

Some experimental results of an investigation of the kinematics of sand in a plane bunker model are presented. A non-steady pattern of rupture bands is shown to develop from the discharge outlet towards the traction-free boundary of the material in the initial stage of flow. In the advanced phase of discharge the rupture band pattern undergoes repetitive fluctuations due to the formation of new shear bands and the diminishing of existing ones. The advanced stage of flow is described approximately by a steady velocity field. The theoretical description is based upon the flow theory of isotropic rigid/perfectly plastic material. The solution for incompressible material seems to accurately predict the experimental measurements of the velocity (displacement) vectors and the location of the discontinuities.