Shear- and vibration-induced order-disorder transitions in granular media

By molecular dynamics simulations we investigate the order-disorder transitions induced in granular media by an applied drive combining vibrations and shear. As the steady state is attained, the pack is found in disordered configurations for comparatively high intensities of the drive; conversely, ordering and packing fractions exceeding the random close packing are found when vibrations and shear are weak. As forcing amplitudes get smaller, we find diverging time scales in the dynamics, as the system enters a jamming region. Under this perspective, our picture supports the intuition that externally applied forcing has, in driven granular media, a role similar to temperature in thermal systems.     

The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation

In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) [13], and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results.     

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.     

The effect of blending granular aggregates of different origin on the strength of concrete

This work correlates the resistance of concrete cores with the physical properties of the granular material forming it. A basic physical characterization is conducted, taking into account the origin of the grains involved in the concrete mixture; that is, if they come from natural degradation (natural granular aggregates) or from a grinding process (crushed granular aggregates). Apparent and real densities, shape factors, packing densities, and specific surface areas of the grains are measured. The results are discussed as a function of size and origin of the grains. Several mixtures are prepared following a standard protocol and using different ratios of natural and crushed aggregates. For each ratio, six cores are prepared and uniaxial compression tests are performed. A non-monotonic relation between the resistance of concrete and the percentage of crushed aggregate present in it is obtained, with an optimum ratio depending on the physical properties of the grains.     

Numerical simulations in granular matter: The discharge of a 2D silo

In this paper I give a short and elementary review of numerical simulations in granular assemblies, giving the process of discharge of a 2D silo as an example. The strengths and limitations of different approaches are discussed, together with some comments on the specific issues related to the numerics of discontinuous dissipative collisions.      

Micromagnetic simulation of ferromagnetic resonance of perpendicular granular media: Influence of the intergranular exchange on the Landau-Lifshitz-Gilbert damping constant

A micromagnetic approach was used to simulate ferromagnetic resonance frequency (FMR) profiles of perpendicular granular CoCrPt-oxide thin films. From the obtained FMR line-width we computed the effective damping constant. The influence of the intergranular exchange on the effective damping was investigated, showing an increase in the damping constant with increase in intergranular exchange coupling. Moreover, the effective damping constant increases with decrease in mesh size of the model, and eventually saturates for mesh sizes of about 1 nm. These dependencies are explained in terms of different modes that can be excited in the granular medium due to interactions between the individual spins.     

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].     

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.     

Magnetic behavior of Co nanostructures deposited in porous Al2O3 templates

The magnetic behavior as a function of magnetic field and temperature of nanostructures of Co deposited on insulator templates of Al₂O₃ is presented. The results show that the granular Co was formed inside the pores and the characteristics of granular ferromagnetics, such as high saturation of the magnetization and paramagnetic behavior at high magnetic fields, were observed.     

Dispersive flow of disks through a two-dimensional Galton board

We report here an experimental and numerical study of the flow properties of disks driven by gravity through a hexagonal lattice of obstacles, i.e. a Galton board. During the fall, particles experience dissipative collisions that scatter them in random directions. A driven-diffusion regime can be achieved under certain conditions. A characteristic length of the motion and its dependence on geometrical parameters of the system is analyzed in the steady regime. The influence of collective effects on the dispersion process is investigated by comparison between single- and many-particle flows. The characterization of the dynamics and the diffusive properties of the flow in a system like a Galton board can be expanded to other granular systems, particularly static solid particle mixers and will give some insight in understanding granular mixing.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

Random Loose Packing in Granular Matter

We introduce and simulate a two-dimensional Edwards-style model of granular matter at vanishing pressure. The model incorporates some of the effects of gravity and friction, and exhibits a random loose packing density whose standard deviation vanishes with increasing system size, a phenomenon that should be verifiable for real granular matter. Research of the second named author was supported in part by NSF Grant DMS-0700120.     

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.     

Phase-dependent heat current of granular Josephson junction for different geometries

We theoretically investigate the phase-dependent heat transport of a temperature-biased granular Josephson junction in the presence of a perpendicular magnetic field. We illustrate the influence of geometry of the junction on the thermal current. The use of granular Josephson junction rather than bulk one makes significant changes in the heat current behavior. The heat current diffraction pattern of the rectangular, circular and annular geometries with no trapped fluxons demonstrates similar to the current of s-wave superconducting junction. By increasing the number of trapped fluxon, the pattern of current behaves such as d-wave superconducting junction. The feasibility of using granular superconductors, with different geometries, controlled by the magnetic field provides an appropriate tool to obtain the desired result for a specific application.     

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.     

Cellular model for the compaction of a vertically tapped granular column

A cellular model for the compaction of granular material is described. It takes into account horizontal redistribution as well as vertical transfer of particles. Parameters are the width of the horizontal redistribution and the settling probability. Numerical simulations of the behaviour of a granular column in a container are shown as an example, and the evolution of some characteristic features over time has been followed for some typical configurations. Experimental results for the time evolution of the density can be reproduced for a settling probability proportional to the unoccupied spaces for particles in the lower cells. Received 3 March 2000 and Received in final form 21 July 2000     

Wet granular materials

Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g. food processing, pharmaceuticals, ceramics, civil engineering, construction, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g. the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of cohesion. We also list several open problems that might motivate future studies in this exciting but mostly unexplored field.

Wet granular materials

All authors

Namiko Mitarai &; Franco Nori

https://doi.org/10.1080/00018730600626065

Published online:

01 February 2007

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