Boundary effects on the maximal angle of stability of a granular packing

We have studied the maximal angle of stability of a granular packing confined between two walls. The effect of the walls is to increase the angle dramatically. The decay of the angle with the distance between the walls is exponential with a characteristic length which is a function of the beads diameter. The effect of the roughness of the walls has been also studied. Received 1 April 1999     

Rolling as a “continuing collision”

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles , which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allows to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction. Received 5 May 1999     

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     

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in [#!bcre!#] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability. Received: 30 January 1998 / Revised: 12 May 1998 / Accepted: 8 June 1998     

Dynamics of aeolian sand ripples

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context, we first review existing models. This paper is a continuation of two previous papers (Z. Csahók et al., Physica D 128, 87 (1999); A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first one is based on symmetries and the second on a hydrodynamical model. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher-order nonlinear term in the equation leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations. Received 20 January 2000     

A nonlinear model for aeolian sand ripples

Starting from the phenomenological model for sand ripple formation developed in [#!Bouchaud98!#], we proposed a new interpretation in the light of recent experiments. Furthermore, we derive, close to the threshold of ripple instability, a nonlinear equation for the spatio-temporal evolution of the sand bed profile, which to leading order has a quadratic nonlinearity. This equation is identical to that derived recently on the basis of geometry and conservation law [#!Csahok98!#]. Our derivation connects the coefficients of the nonlinear equation to the underlying physical mechanisms (reptation length...). This equation reveals ripple structures which then undergo a coarsening process, as observed in wind tunnel experiment. Small, fast moving ripples are absorbed by larger, slower forms resulting in a growth of the mean wavelength. Received 5 January 1999     

Shapes of heaps and in silos

Experimental investigations on the shape of a heap formed in a Hele Shaw cell either on a flat base or in a two-dimensional silo are presented. We have focused our attention on the shape dependence on mass flux and initial energy of particles poured into the cell. Two kinds of granular media are considered: glass beads and sand and we shall point out their different behaviors. We described the variations of the angle of repose and of the size of the tail as a function of the experimental parameters. We also report the time evolution of the angle of repose during the formation of the heap. Received 28 September 1998 and Received in final form 20 January 1999     

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     

Convection in horizontally shaken granular material

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucially on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with varying inelasticity. Received 3 March 1999     

Force distribution in an inhomogeneous sandpile

The force perturbation field in a two-dimensional pile of frictionless gravity-loaded discs or spheres arising from lattice distortions is derived to first order. The starting point is the model proposed by Liffman et al. (Powder Technology (1992) pp. 255-267) and Hong (Phys. Rev. E 47, 760-762 (1993)) in which discs of uniform size are arranged on a regular lattice: this predicts a uniform normal stress distribution at the base of the pile. The analysis is applied to two problems: (i) deformable (rather than rigid) grains that undergo Hertzian deformation at the points of contact; (ii) a pile containing a gradient in particle size from the centre to the free surfaces. The former results in the classical pressure dip at the centre; the latter also produces a dip if the larger particles are at the centre. Received 29 January 1998 and Received in final form 7 September 1998     

Pressure screening and fluctuations at the bottom of a granular column

We report sets of precise and reproducible measurements on the static pressure at the bottom of a granular column. We make a quantitative analysis of the pressure saturation when the column height is increased. We evidence a great sensitivity of the measurements with the global packing fraction and the eventual presence of shear bands at the boundaries. We also show the limit of the classical Janssen model and discuss these experimental results under the scope of recently proposed theoretical frameworks. Received 7 September 1998 and Received in final form 28 January 1999     

Behavior of one inelastic ball bouncing repeatedly off the ground

An experimental study of the behavior of one bead bouncing repeatedly off a static flat horizontal surface is presented. We observe that the number of bounces made by the bead is finite. When the duration between two successive bounces becomes of the order of the impact duration, the bead no longer bounces but oscillates on the elastically deformed surface before coming to rest. This transition is explained with a modified Hertz interaction law in which gravity is taken into account during the interaction. For each bounce, measurement of both the duration of collision and the restitution coefficient have been done. The effective restitution coefficient is essentially constant and close to 1 during almost all bounces before decreasing to zero when the impact velocity vanishes. This is due to an interplay between gravity and viscoelastic dissipation. Received: 2 December 1997 / Accepted: 5 March 1998     

Restructuring of force networks

The compaction of granular packings or soils is a collective process which for higher densities becomes increasingly slower reaching glassy behaviour. We present a study of this problem from various points of view, in particular we will represent the evolving force network that percolates through the system by an inverse fiber rupture model. Received 15 March 2002 and Received in final form 29 July 2002     

Discrete Element Method studies of the collision of one rapid sphere on 2D and 3D packings

We performed numerical simulations of one-bead collision on the surface of a static granular medium. The simulations have been done for two- and three-dimensional packings of beads. The effect of the incident bead velocity, the shot angle, the mechanical parameters and the packing structure are analyzed for ordered and disordered 2D packings and only disordered 3D packings. The 2D results are in good agreement with experimental available data. The 3D simulations give good preliminaries results about the shock-wave propagation through the stacking and provides new insights in the ejection process (“splash function”).     

Grain segregation mechanism in aeolian sand ripples

Many sedimentary rocks are formed by migration of sand ripples. Thin layers of coarse and fine sand are present in these rocks, and understanding how layers in sandstone are created has been a longstanding question. Here, we propose a mechanism for the origin of the most common layered sedimentary structures such as inverse graded climbing ripple lamination and cross-stratification patterns. The mechanism involves a competition between three segregation processes: (i) size-segregation and (ii) shape-segregation during transport and rolling, and (iii) size segregation due to different hopping lengths of the small and large grains. We develop a discrete model of grain dynamics which incorporates the coupling between moving grains and the static sand surface, as well as the different properties of grains, such as size and roughness, in order to test the plausibility of this physical mechanism. Received 19 July 1999 and Received in final form 4 August 1999     

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     

Dynamics of density waves in a two dimensional funnel on an inclined plane

We report here experiments on two-dimensional funnel flow of diameter glass beads on an inclined plane. We have investigated the properties of the flow according to the outlet size D of the funnel and the gravity. We have identified three different regimes. For small funnel outlet sizes, there is no significant change in flow density: the flow is rather steady and homogeneous. For intermediate outlet sizes (), the flow is intermittent, consisting of spatially ordered density waves propagating upwards. At bigger outlet sizes, density waves do not exhibit any ordering and the flow dynamics becomes chaotic. In addition, we find that the flow dynamics is independent of the funnel opening angle except close to the channel flow configuration. Finally, it is stressed that the interactions between the beads and the inclined plane play a crucial role in the mechanism of formation of density waves. Received: 9 July 1998 / Received in final form and Accepted: 18 September 1998     

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.     

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     

Spatial versus quantum confinement in porous amorphous silicon nanostructures

Light-emitting porous amorphous silicon has been produced by anodization in HF of hydrogenated amorphous silicon films. The maximal thickness of the porous films is limited by the onset of an instability which results in the formation of large channels short-circuiting the amorphous layer. This is due to the high resistivity of the amorphous silicon films as compared to that of the electrolyte. Confinement effects on the electron wavefunction are analyzed in situ using photoluminescence measurements in hydrofluoric acid and compared to those observed in porous crystalline silicon. For crystalline silicon, a huge blue shift of the photoluminescence is observable upon reducing the size of the structures by photo-etch, showing clear evidence of quantum confinement effects in this material. No shift has been observed when carrying out the same experiment with amorphous silicon. This indicates that the extent of the wavefunction in the bandtail states involved in luminescence is too small to be sensitive to confinement down to the minimum sizes of our porous material ( 3 nm). Measurements of the width and the temperature dependence of the photoluminescence demonstrate that the Urbach energy does not change upon increasing the porosity, i.e., upon decreasing the size of the a-Si:H nanostructures, in contradiction with what has been reported in ultrathin a-Si:H multilayers. Received: 3 August 1998