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     

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999     

Kinematic segregation of granular mixtures in sandpiles

We study the segregation of granular mixtures in two-dimensional silos using a recently proposed set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this dynamical segregation process, called kinematic sieving, free-surface segregation or percolation, into the theoretical formalism and calculate the profiles of the rolling species and the concentration of grains in the bulk in the steady state. Our solution shows the segregation of the mixture with the large grains being found at the bottom of the pile in qualitative agreement with experiments. Received: 6 July 1998 / Revised and Accepted: 13 August 1998     

Humidity effects on the stability of a sandpile

Humidity is well-known to significantly affect the mechanical properties, static as well as dynamic, of granular materials. We present the method of humidification of granular media from an under-saturated vapor that we designed in order to experimentally quantify such moisture-induced effects under accurately-controlled humidity conditions. We report the quantitative measurements of the maximum angle of stability of a pile made of small glass beads, as a function of the relative vapor pressure, up to close to saturation. The results obtained with liquids differing in their wetting properties on glass, namely water and heptane, are presented. It is shown that the wetting properties of the liquid on the grains have a strong influence on the cohesion of the non-saturated granular medium. Received 26 October 1998 and Received in final form 30 March 1999     

Force fluctuations in a vertically pushed granular column

We present series of experiments on the resistance force encountered by a bottom piston pushing a vertical granular column confined in a two-dimensional cell. We show that, due to the presence of friction at the boundaries and between the grains, the signal shows many complex features. At slow driving velocities, we observe a transition to a stick-slip dynamic instability. Depending on the granular material used, the elementary stick-slip events may either be well characterized or largely distributed. We present a statistical study on the waiting time between events and the distribution of energy release as a function of the spring stiffness and the driving velocity. Received 5 August 1998 and Received in final form 22 October 1998     

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised. Received 17 April 2000 and Received in final form 7 June 2000     

Influence of roughness and dilatancy for dense granular flow along an inclined wall

In a previous work [#!ref1!#], the flow velocity of a steady two-dimensional granular flow along an inclined wall was investigated. The scaling law for the velocity field was found in good agreement with recent experimental results. The purpose of the present paper is to reformulate in more systematic manner and in a somewhat more general context the equations of mass and momentum conservation for dense granular flow, and also to present some new results with particular emphasis on roughness influence and dynamic dilatancy. Theoretical results are found in good agreement with experiments. Received 19 July 1999 and Received in final form 14 October 1999     

Time of avalanche mixing of granular materials in a half filled drum

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference δ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time τ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when δ is an integer part of π. Introduction of fluctuations of δ suppresses the singularities of τ(δ) and smoothes the dependence τ(δ). Received 27 October 2000 and Received in final form 13 March 2001     

Surface flows of granular mixtures

We present the generalization of the minimal model for surface flows of granular mixtures, proposed by Boutreux and de Gennes [J. Phys. I France 6, 1295 (1996)]. The minimal model was valid for grains differing only in their surface properties. The present model also takes into account differences in the size of the grains. We apply the model to study segregation in two-dimensional silos of mixtures of grains differing in size and/or surface properties. When the difference in size is small, the model predicts that a continuous segregation appears in the static phase during the filling of a silo. When the difference in size is wide, we take into account the segregation of the grains in the rolling phase, and the model predicts complete segregation and stratification in agreement with experimental observations. Received 9 September 1998 and Received in final form 4 November 1998     

Gas-driven subharmonic waves in a vibrated two-phase granular material

Vibrated powders exhibit striking phenomena: subharmonic waves, oscillons, convection, heaping, and even bubbling. We demonstrate novel rectangular profile subharmonic waves for vibrated granular material, that occur uniquely in the two-phase case of grains, and a fluid, such as air. These waves differ substantially from those for the gas-free case, exhibit different dispersion relations, and occur for specific shaking parameters and air pressure, understandable with gas-particle flow models. These waves occur when the gas diffusively penetrates the granular layer in a time comparable to the shaker period. As the pressure is lowered towards P =0, the granular-gas system exhibits a Knudsen regime. This instability provides an opportunity to quantitatively test models of two-phase flow.     

The focus of light – theoretical calculation and experimental tomographic reconstruction

We present numerical calculations on the field distribution in the focus of an optical system with high numerical aperture. The diffraction integrals which are based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution. It is shown that this mode focusses down to a spot size significantly smaller as compared to the case of linear polarization. An experimental setup to measure the three-dimensional intensity distribution in the focal region is presented, which is based on the knife-edge method and on tomographic reconstruction. Received: 14 July 2000 / Published online: 30 November 2000     

Stress fluctuations and macroscopic stick-slip in granular materials

This paper deals with the quasi-static regime of deformation of granular matter. It investigates the size of the Representative Elementary Volume (REV), which is the minimum packing size above which the macroscopic mechanical behaviour of granular materials can be defined from averaging. The first part uses typical results from recent literature and finds that the minimum REV contains in general 10 grains; this result holds true either for most experiments or for Discrete Element Method (DEM) simulation. This appears to be quite small. However, the second part gives a counterexample, which has been found when investigating uniaxial compression of glass spheres which exhibit stick-slip; we show in this case that the minimum REV becomes 10⁷ grains. This makes the system not computable by DEM. Moreover, similarity between the Richter law of seism and the exponential statistics of stick-slip is stressed. Received 8 March 2002 and Received in final form 12 July 2002     

Shear Flow of a Granular Material

The shear flow of a granular material between parallel plates is treated by means of the Boltzmann equation with pseudo-Maxwellian grains. The moments for reverse reflection boundary conditions are found explicitly. The shearing stress is found to depend quadratically on the shear rate.     

Giant electrical fluctuations in metallic disordered packings

We have experimentally studied granular arches through electrical measurements. The packing is composed of 2d metallic pentagons and is submitted to small taps. Large electrical fluctuations are observed and they are distributed along power laws. This indicates the presence of long-time memory effects even the packing density remains constant around a value ρ = 0.72±0.02. Large electrical fluctuations should be associated with the breaking/creation of granular arches. Received 3 October 2000     

Vertically shaken column of spheres. Onset of fluidization

The onset of surface fluidization of granular material in a vertically vibrated container, z = A cosωt , is studied experimentally. Recently, for a column of spheres it has been theoretically found (see T. P?schel, T. Schwager, C. Salue na, Phys. Rev. E 62, 1361 (2000)) that the particles lose contact if a certain condition for the acceleration amplitude ≡Aω²/g = f (ω) holds. This result is in disagreement with other findings where the criterion = = const was found to be the criterion of fluidization. We show that for a column of spheres a critical acceleration is not a proper criterion for fluidization and compare the results with theory. Received 21 August 2000 and Received in final form 30 October 2000     

Surface flows of granular mixtures: II. Segregation with grains of different size

We present the generalization of a theoretical model for segregation of granular mixtures due to surface flows, published in J. Phys. I France 6, 1295 (1996). Our generalized model is valid for grains differing by their size and/or their surface properties; in the present paper, we describe the case of two species with the same surface properties but two different sizes. The rolling stream is assumed to be homogeneous. Exchanges between the grains at rest and the rolling stream are modelized via binary collisions. The model predicts that during the filling of a two-dimensional silo, continuous segregation appears inside the static phase: small (respectively large) grains tend to stop uphill (respectively downhill), although both species remain present everywhere. This fits the observations when the size difference between the species is small. When the size difference is large, a different regime is observed. We argue that in this case, segregation occurs directly inside the rolling stream. Received: 25 February 1998 / Received in final form and Accepted: 6 July 1998     

Fragmentation of grains in a two-dimensional packing

A numerical model of fragmentation of a two-dimensional granular medium under pressure is investigated. The fragmentation process is found to be strongly dependent on the type of force used as the criterion for breaking the grains. The fragmentation mode affects the process less dramatically. There is a power-law divergence in the pressure when the medium approaches the full packing limit, . Both log-normal and power-law fragment-size distributions are found. Gravity is demonstrated to be an important factor. Received: 14 December 1997 / Accepted: 17 March 1998     

Intermittent granular flow and clogging with internal avalanches

The dynamics of intermittent granular flow through an orifice at the bottom of a granular bin and the associated clogging due to formation of arches blocking the outlet, is studied numerically in two dimensions. When the hole size is less than the grain diameter, only a single grain is removed from the system so that the system self-organizes to a steady state and the distribution of the grain displacements decays as power laws. On the other hand, when hole sizes are within few times of the grain diameter, the outflow distributions are also observed to follow a power law. Received 21 July 1999 and Received in final form 17 September 1999     

Granular Rayleigh-Taylor instability: experiments and simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.     

Molecular dynamics of comminution in ball mills

We investigate autogenous fragmentation of dry granular material in rotating cylinders using two-dimensional molecular dynamics. By evaluation of spatial force distributions achieved numerically for various rotation velocities we argue that comminution occurs mainly due to the existence of force chains. A statistical analysis of these force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel [1] and Rolf [2]. For animated sequences of our simulations see http://summa.physik.hu-berlin.de/kies/mill/bm.html Received 19 January 2000