Microstructure characterization of granular materials

This paper presents techniques and algorithms to compute microstructure properties of irregular-shaped granulate assemblies utilizing 3D images. The techniques are capable of extracting microstructure properties of particles such as centeroid, particle size distribution, shape indices (i.e., sphericiy and angularity), number of contacts (i.e., distribution of coordination numbers), contact network, packing efficiency, distribution of local void ratio and radial distribution function. Such properties are critical parameters for micromechanical-based numerical models to capture micro- and macromechanical behavior of geomaterials. X-ray microtomography was used to reconstruct high-resolution 3D image of a natural sand system to represent granular materials. Microstructure properties of the sand system were computed and compared with properties of a computer-simulated image of periodic random spheres. Findings indicate that the use of simplified systems of idealized spheres to model micro- and macromechanical behavior of granular systems can lead to inaccurate results due to the differences in the microstructure between both systems. Methods presented in this paper enabled capturing a more realistic microstructure that can be incorporated in micromechanical models to better simulate, understand, or explain macroscale behavior of granular materials based on their actual microstructure.     

Fluctuations in apparent mass at the bottom of granular columns due to different arrangements

We report the fluctuations in apparent mass at the bottom of granular columns due to various configurations. It is found that the fluctuations decrease with the increase in the ratio of diameters of silo to grain. For the arrangement of different grain layers in a column, the higher fluctuations appear when the larger grains are stacked at the bottom layer while reversing the order of grain-layers leads to smaller fluctuations. We attribute this behavior to the randomness in the direction of frictional forces between the grains and the confining wall. Moreover, due to polydisperse media, the development of inhomogeneous force transmission in grains may cause this to happen.     

Corona-discharge-based neutralization of charged granular insulating materials in contact with an electrode of opposite polarity

Charge neutralization is a key operation in many electrostatic processes. A wide-range of charge neutralizers have already been developed for various applications: eliminate shock and ignition hazards, avoid electrostatic discharges that might affect the operation of electronic equipment, reduce electrostatic adhesion forces that might stick granular materials in pneumatic conveyors, and so on. The aim of the present paper is to evaluate several methods of charge neutralization for charged granular insulating materials spread on an electrode energized from a voltage source of opposite polarity, a situation encountered – for instance – in two-metallic-belt tribo-aero-electrostatic separators, and which is not covered by commercially-available solutions. Three corona-discharge-based charge neutralization systems are studied: (i) DC-biased AC voltage applied to a corona dual-type electrode; (ii) DC-biased AC voltage applied to a triode-type electrode system; (iii) DC voltage applied to a corona dual-type electrode. The charged samples of polycarbonate granules are obtained at the outlet of a tribo-aero-electrostatic separator. The electric charge per mass ratio of each sample is measured before and after neutralization. The third of the above-mentioned charge neutralization solutions seems to be the most effective solution, but it requires an appropriate adjustment of the DC voltage applied to the corona dual-type electrode.     

Triboelectrification of granular insulating materials as affected by dielectric barrier discharge (DBD) treatment

The aim of this paper is to point out the influence of dielectric barrier discharge treatment on tribocharging of granular insulating materials. Particles of Polyvinyl Chloride (PVC) and Polypropylene (PP) were subjected to an AC dielectric barrier discharge (DBD) plasma treatment in ambient airprior to tribocharging in a vibratory device. The charge to mass ratio was measured for treated and untreated materials. Electrostatic separation of a mixture of granular materials (PVC and PP) to measure the effectiveness of DBD treatment was evaluated by processing treated and untreated PVC/PP granular mixtures in a free-fall electrostatic separator. The obtained results clearly indicate that DBD has the capability to influence surface charging proprieties of polymer granular materials. In case of short treatment time, typically less than 3 s, a marked increase in the charge to mass ratios was observed for both PVC (about 35%) and PP (roughly 45%). In the same way, the quantity of DBD-treated materials, recovered after electrostatic separation, was increased by about 104% and 30% for PVC and PP, respectively, as compared to untreated case. The DBD treatment time is a key factor to increase the tribo electric effect.     

Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

A dynamical systems approach to mixing and segregation of granular materials in tumblers

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.     

Capillary cohesion and mechanical strength of polydisperse granular materials

We investigate the macroscopic mechanical behaviour of wet polydisperse granular media. Capillary bonding between two grains of unequal diameters is described by a realistic force law implemented in a molecular-dynamics algorithm together with a protocol for the distribution of water in the bulk. Axial-compression tests are simulated for granular samples at different levels of water content, and compared to experiments performed in similar conditions. We find good agreement between numerical and experimental data in terms of the rupture strength as a function of water content. Our results show the importance of the distribution of water for the mechanical behaviour.     

Langevin equation approach to granular flow in a narrow pipe

The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.     

不同条件下颗粒物质的粘弹性响应

研制了能承受100 MPa压强的测量装置,并用该装置对加压下制备的紧密沙堆进行粘弹性响应测量,得球形镍颗粒沙堆在周期性竖直振荡下储能模量G′与压强p 的关系. 实验结果表明,反映沙堆整体弹性特征的储能模G′与压强p 的关系为G′~p0.45;不同形状颗粒体系的粘弹性响应行为不同.     

Pore Stabilization in Cohesive Granular Systems

Cohesive powders tend to form porous aggregates which can be compacted by applying an external pressure. This process is modelled using the Contact Dynamics method supplemented with a cohesion law and rolling friction. Starting with ballistic deposits of varying density, we investigate how the porosity of the compacted sample depends on the cohesion strength and the friction coefficients. This allows to explain different pore stabilization mechanisms. The final porosity depends on the cohesion force scaled by the external pressure and on the lateral distance between branches of the ballistic deposit. Even if cohesion is switched off, pores can be stabilized by Coulomb friction alone. This effect is weak for round particles, as long as the friction coefficient is smaller than 1. However, for non-spherical particles the effect is much stronger.     

Interrupted shear of granular media

The response of a granular material during a stop-and-go shear experiment is investigated using an annular shear cell and silicagel powders of different particle sizes. The experimental results are examined on the basis of the Dieterich-Rice-Ruina model for solid friction. In addition to making this analogy with solid friction, we describe a new instability that is observed when restarting shear, where the powder bed is found to slip and compact for short hold times but only dilates for long hold times. The minimum hold time to restore a non-slip behaviour has been investigated for different size particles and normal loadings. The observed dependencies show analogies between this behaviour and the sliding rearrangements seen above the stick-slip threshold.     

MRI investigation of granular interface rheology using a new cylinder shear apparatus

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample. This study describes the influence of the roughness of the shearing interface and of the transverse confining walls on the granular interface rheology.     

Strength and failure of cemented granular matter

Cemented granular materials (CGMs) consist of densely packed solid particles and a pore-filling solid matrix sticking to the particles. We use a sub-particle lattice discretization method to investigate the particle-scale origins of strength and failure properties of CGMs. We show that jamming of the particles leads to highly inhomogeneous stress fields. The stress probability density functions are increasingly wider for a decreasing matrix volume fraction, the stresses being more and more concentrated in the interparticle contact zones with an exponential distribution as in cohesionless granular media. Under uniaxial loading, pronounced asymmetry can occur between tension and compression both in strength and in the initial stiffness as a result of the presence of bare contacts (with no matrix interposed) between the particles. Damage growth is analyzed by considering the evolution of stiffness degradation and the number of broken bonds in the particle phase. A brutal degradation appears in tension as a consequence of brittle fracture in contrast to the more progressive nature of damage growth in compression. We also carry out a detailed parametric study in order to assess the combined influence of the matrix volume fraction and particle-matrix adherence. Three regimes of crack propagation can be distinguished corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We find that particle damage scales well with the relative toughness of the particle-matrix interface with respect to the particle toughness. This relative toughness is a function of both matrix volume fraction and particle-matrix adherence and it appears therefore to be the unique control parameter governing transition from soft to hard behavior.     

Size dependence of effective mass in granular columns

An experimental setup is developed to measure accurately and reproducibly the effective mass as well as its fluctuations at the bottom of the granular columns. It is found that the saturated mass M_s obeys a third power function of the diameter of the silos. The data obtained are in agreement with the modified Janssen model proposed by Vanel and Clement [L. Vanel, E. Clement, Eur. Phys. J. B 11 (1999) 525-533].     

Time resolved particle dynamics in granular convection

We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists mainly of vertical jumps, and a global ordered drift. The analysis of the system movement as a whole reveals that the observed bifurcation in the flight time is not adequately described by the Inelastic Bouncing Ball Model. Near the bifurcation point, friction plays an important role, and the branches of the bifurcation do not diverge as the control parameter is increased. By fitting the grains trajectories near the wall it is possible to quantify the effective acceleration acting on them. A comparison of the mass centre flying time and the flying time determined for the grains near the wall exposes the underlying mechanism that causes the downward flow.     

Modeling force transmission in granular materials

The probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.     

Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the Boltzmann equation. A line of nontrivial fixed-point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively. Received 16 January 2002     

Correlations and aggregate statistics in granular packs

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Vorono? cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.