Dynamics Of Granular Media Research Articles

Granular internal dynamics in a silo discharged with a conveyor belt

The dynamics of granular media within a silo in which the grain velocities are controlled by a conveyor belt has been experimentally investigated. To this end, the building of coarse-grained field maps of different magnitudes has allowed a deep analysis of the flow properties as a function of two parameters: the orifice size and the belt velocity. First, the internal dynamics of the particles within the silo has been fully characterized by the solid fraction, the velocity of the particles and the kinetic stress. Then, the analysis of the vertical profiles of the same magnitude (plus the acceleration) has allowed connection of the internal dynamics with the flow rate. In particular, we show that the gamma parameter – which accounts for the integration of the normalized acceleration along the vertical direction – can successfully discriminate the kind of flow established within the silo (from the quasistatic regime to the free discharge) depending on the outlet size and belt velocity.

Magnetization dynamics of granular heat-assisted magnetic recording media by means of a multiscale model

Heat assisted magnetic recording (HAMR) technology represents the most promising candidate to replace the current perpendicular recording paradigm to achieve higher storage densities. To better understand HAMR dynamics in granular media we need to describe accurately the magnetisation dynamics up to temperatures close to the Curie point. To this end we propose a multiscale approach based on the micromagnetic Landau-Lifshitz-Bloch (LLB) equation of motion parametrised using atomistic calculations. The LLB formalism describes the magnetisation dynamics at finite temperature and allows to efficiently simulate large system sizes and long time scales. Atomistic simulations provide the required temperature dependent input quantities for the LLB equation, such as the equilibrium magnetisation and the anisotropy, and can be used to capture the detailed magnetisation dynamics. The multiscale approach makes possible to overcome the computational limitations of atomistic models in dealing with large systems, such as a recording track, while incorporating the basic physics of the HAMR process. We investigate the magnetisation dynamics of a single FePt grain as function of the properties of the temperature profile and applied field and test the micromagnetic results against atomistic calculations. Our results prove the appropriateness and potential of the approach proposed here where the granular model is able to reproduce the atomistic simulations and capture the main properties of a HAMR medium.

On the Mechanism of Laboratory Earthquake Nucleation Highlighted by Acoustic Emission

Dynamics of granular media is the key to understanding behavior of many natural systems. In this work we concentrate on studying regularities of deformation of a gouge-filled fault. Confined granular layer – model fault – subjected to an external stress may display sudden slip owing to rearrangement of the granular layer. In nature fast slip along a fault results in an earthquake. To understand fault behavior better, we have conducted a comprehensive analysis of acoustic emission (AE) data that accompany stick-slip in granular media. Here we reveal and trace the emergence of two populations of AE. The first one is characterized by a waveform with a harsh onset, while the second one exhibits a gradual amplitude rise and a tremor-like waveform. During a regular stick-slip the statistical properties of the first population remains intact. The second one is very sensitive to alterations of stress conditions, and its scaling parameters correlate with the change of mechanical characteristics of the fault. Probably, AE populations were identified corresponding to two gouge-filled fault subsystems – a load-bearing granular network and an ensemble of relatively unloaded grains in the granular layer. The detected regularities point to a compound self-organization processes in fault zones and suggest that the final stage of earthquake preparation can be revealed in analyzing the scaling characteristics of seismic-acoustic data.

GPU-accelerated smoothed particle hydrodynamics modeling of granular flow

In this paper, the dynamical behavior of granular media is investigated numerically using smoothed particle hydrodynamics (SPH) with an elastoplastic and a phase-change constitutive model. A GPU-accelerated SPH code for granular flow modeling is implemented and validated using four test cases: (1) the collapse of an axisymmetric sand pile; (2) the impact force of sand on a rigid wall; (3) the head-on collisions of dense granular jets; and, (4) the impact of a granular jet with a wave structure on the granular film. The results of SPH simulations with the two models are compared to available experimental and numerical results. The validation showed that the dynamics of granular media are well predicted using the SPH methodology with an appropriate material model. An SPH simulation of granular flow run on a rather outdated GPU was already about 160 times as efficient as the same simulation run on a mainstream single CPU.

Crackling to periodic dynamics in granular media.

We study the local and global dynamics of sheared granular materials in a stick-slip experiment, using a slider and a spring. The system crackles, with intermittent slip avalanches, or exhibits irregular or periodic dynamics, depending on the shear rate and loading stiffness. The global force on the slider during shearing captures the transitions from the crackling to the periodic regime. We deduce a dynamic phase diagram as a function of the shear rate and the loading stiffness and associated scaling laws. Using photoelastic particles, we also capture the grain-scale stress evolution, and investigate the microscopic behavior in the different regimes.

The measure of friction angles for different types of granular material

The aim of this research is to deepen the knowledge of the role of friction on the dynamics of granular media; in particular the friction angle is taken into consideration as the physical parameter that drives stability, motion and deposition of a set of grains of any nature and size. The idea behind this work is a question: is the friction angle really that fundamental and obvious physical parameter which rules stability and motion of granular media as it seems from most works which deal with particle dynamics? The experimental study tries to answer this question with a series of laboratory tests, in which different natural and artificial granular materials have been investigated in dry condition by means of a tilting flume. The characteristic friction angles, both in deposition (repose) and stability limit (critical) conditions, were measured and checked against size, shape, density and roughness of the considered granular material. The flume tests have been preferred to “classical” geotechnical apparatuses (e.g. shear box) since the flume experimental conditions appear closer to the natural ones of many situations of slope stability interest (e.g. a scree slope). The results reveal that characteristic friction angles depend on size and shape of grains while mixtures of granules of different size show some sorting mechanism with less clear behaviour.

Simulation research of the buffering capacity of non-convex particle system under impact loading

The behavior of granular materials under the action of external force is a fundamental problem for the dynamics of granular media. This paper investigates the buffering capacity of three-dimensional non-convex granular beds subjected to vertical impact using the discrete element methods. The results display the particle shape significantly affects the buffering capacity of the equal mass granular bed. And the influence of aspect ratio of non-convex particles on buffering capacity exhibits an obvious non-monotonicity. The functional mechanism of inter-particle friction is discussed. It is showed that the shape of the non-convex particles has a great effect on the contact number of granular system and probability density functions of inter-particle forces.

Oscillation-induced sand dunes in a liquid-filled rotating cylinder.

The dynamics of granular medium in a liquid-filled horizontal cylinder with a time-varying rotation rate is experimentally studied. When the cylinder is purely rotated, the granular medium develops an annular layer near the cylindrical wall. The interface between fluid and sand is smooth and axisymmetric. The time variation of the rotation rate initiates the azimuthal oscillation of the liquid in the cylinder's frame of reference and provokes the onset of quasisteady relief in the form of regular dunes. The stability of the axisymmetric sand surface and dynamics of regular dunes are examined. It is found that the ripple formation is provoked by the quasisteady instability of the Stokes boundary layer. In the range of high Reynolds numbers, the ripple formation occurs at a constant critical Shields number θ_{c}≃0.05. The spatial period of the relief is not sensitive to the fluid viscosity and granule diameter; it is determined by the amplitude of oscillation and ratio between the oscillation frequency and mean rotation rate. Long-term experiments show that there are forward and backward azimuthal drifts of dunes. An initial analysis of the issues related to the dune migration is provided.

Wave propagation in a rotating randomly varying granular generalized thermoelastic medium

Elastic wave propagation has been explored in an infinite granular thermoelastic medium rotating with constant speed. The elastic and thermal parameters of the granular medium are taken to be randomly fluctuated so that the medium represents the randomly fluctuating inhomogeneous medium. The method of smooth perturbation has been used, which requires the inversion of a deterministic differential operator to find the solution of governing equations in the relevant media. The analysis is based on the dynamics of granular medium as propounded by N. Oshima. All field parameters are functions of space vector and time. A general dispersion equation for waves propagating in the rotating random granular generalized thermal elastic medium has been obtained. The compression and shear wave propagations have been studied. It has been pointed out that in the case of compression waves, the mean and auto-correlation function of the thermo-mechanical coupling parameter greatly influence the mean wave propagation. For shear waves, however, randomness has no effect on wave propagation. Effects of non-random granular elastic medium, randomness and rotation of the frame of reference are discernible from analyses of dispersion equations. The study may find applications in soil mechanics, seismology and oil-prospecting. Computational results have been shown.

Continuum models in dynamics of granular media. Review

Mechanical models and equations of state used for solving dynamic problems in mechanics of granular media are reviewed. We study elastic, hypoelastic, hyperelastic, elastoplastic, and hydrodynamic models. Within the framework of hyperelasticity several generalized models, including the modified Arruda-Boyce model and some other hyperelastic models, are examined to investigate the formation of hysteresis loops during cyclic loading. We find that due to the switching mechanism the hysteresis loops can also be studied using the concept of hyperelasticity. The elastic-plastic models with one or several plastic flow surfaces, as well as the models with continuously distributed flow surfaces (microplasticity), are analyzed. Some newly developed models without plastic flow surfaces are considered (hypoplasticity, barodesy). Special attention is given to the elastic-plastic models with isotropic hardening and the models used to analyze the formation of hysteresis loops. The elastic-plastic models for studying non-degenerate hysteresis loops under cyclic loading conditions are examined as well. The comparative analysis of elastic, hyperelastic, hypoelastic and various elastic-plastic models reveals that under quasistatic cyclic loading conditions the cam-clay and other critical state models that take into account both the hardening and softening phenomena in real granular materials appear to be the most suitable ones for modeling hysteresis loops in cohesionless granular materials. However, the study of non-stationary dynamical processes requires finding appropriate models. For such problems, the combination of hyperelastic and hypoelastic models provides a simple adequate tool for taking into account the nucleation effects associated with the formation of local discontinuities. This is mainly due to the capabilities of hyper- and hypoelastic models to account for variations in elastic parameters and, consequently, in elastic wave velocities under wave propagation. In the future we plan to combine hyper- or hypo-elastic models with cam-clay or other critical state models.

Simulation of the projectile dynamics in granular media

The three-dimensional (3D) dynamics of a projectile in granular media is simulated using DEM (discrete element method). Periodic boundary conditions are adopted, and the effects of gravity, contact forces, damping and friction are taken into account. The 3D simulation results fit the experiment results very well. Simulation results show that the heaver the projectile, the deeper the penetration depth. The impact depth grows linearly when the projectile quality increases. And when the density of granular media decreases, the penetration depth also increases. Splash of granular particles is also observed in the impact simulation.

Elementary excitation modes in a granular glass above jamming

The dynamics of granular media in the jammed, glassy region is described in terms of "modes", by applying a Principal Component Analysis (PCA) to the covariance matrix of the position of individual grains. We first demonstrate that this description is justified and gives sensible results in a regime of time/densities such that a metastable state can be observed on long enough timescale to define the reference configuration. For small enough times/system sizes, or at high enough packing fractions, the spectral properties of the covariance matrix reveals large, collective fluctuation modes that cannot be explained by a Random Matrix benchmark where these correlations are discarded. We then present a first attempt to find a link between the softest modes of the covariance matrix during a certain "quiet" time interval and the spatial structure of the rearrangement event that ends this quiet period. The motion during these cracks is indeed well explained by the soft modes of the dynamics before the crack, but the number of cracks preceded by a "quiet" period strongly reduces when the system unjams, questioning the relevance of a description in terms of modes close to the jamming transition, at least for frictional grains.

Directed and undirected multiurn models in a one-dimensional ring

The flea model by Ehrenfest describes the jumps of a fixed number of fleas between two dogs. In each time step a randomly selected flea jumps on the other dog. We study directed and undirected multiurn models in a one-dimensional ring. The introduced models represent generalizations of three recently proposed multiurn models which themselves are generalizations of Ehrenfest's model. The models are solved analytically. For the directed case we find oscillations of the average number of balls or fleas in a certain urn before the system reaches its equilibrium state. The discussed models may serve as basic models of dynamics of granular media in connected periodic compartment systems.

Resource Letter GP-1: Granular physics or nonlinear dynamics in a sandbox

This Resource Letter provides a guide to the literature on the statics and dynamics of granular media. Journal article and book references are provided for the following topics: Packing, Angle of Repose, Avalanches and Granular Flow, Hoppers and Jamming, Vertically Vibrated Induced Phenomena, Avalanche Stratification, and Axial Segregation.

NMR imaging of materials

Nuclear magnetic resonance (NMR) and NMR imaging (MRI) are being used more and more to characterize the heterogeneity and the distribution of relevant properties in materials like gels, polymers, elastomers, and catalysts. Moreover, spatially resolved NMR can be used for the investigations of particle dynamics in granular media and parameters of mass transport, a topic of interest in chemical engineering. The possibility to enhance the nuclear polarization by laser-polarized 129Xe and 3He can be combined with MRI of materials. This method opens up the possibility to obtain NMR parameter images of material surfaces.

Entropy for Relaxation Dynamics in Granular Media

We investigate the role of entropic concepts for the relaxation dynamics in granular systems. In particular, we show how, in the framework of a mean-field model introduced for compaction phenomenon, there exists a free-energy-like functional which decreases along the trajectories of the dynamics and which allows one to account for the asymptotic behavior: e.g., density profile, segregation phenomena. Also we are able to perform the continuous limit of the above mentioned model which turns out to be a diffusive limit. In this framework one can single out two separate physical ingredients: the free-energy-like functional that defines the phase space and the asymptotic states and a diffusion coefficient $D(\ensuremath{\rho})$ accounting for the velocity of approach to the asymptotic stationary states.