Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (γ= 2/(3-q)) between the anomalous diffusion exponent γ and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.     

Monodisperse dry granular flows on inclined planes: Role of roughness

Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that there exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the slope angle. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 m to 2 mm. The relative roughness corresponding to the maximum of the friction can be predicted with a geometrical model of stability of one single bead on the plane. The main parameters are the size of the bumps and the size of the flowing beads. In order to obtain a higher precision, the model also takes into account the spacing between the bumps of the rough plane. Experimental results and model are in good agreement for all the planes we studied. Other parameters, like the sphericity of the beads, or irregularities in the thickness of the layer of glued particles, are shown to be of influence on the friction.     

Coefficient of tangential restitution for viscoelastic spheres

The collision of frictional granular particles may be described by an interaction force whose normal component is that of viscoelastic spheres while the tangential part is described by the model by Cundall and Strack (Géotechnique 29, 47 (1979)) being the most popular tangential collision model in Molecular Dynamics simulations. Albeit being a rather complicated model, governed by 5 phenomenological parameters and 2 independent initial conditions, we find that it is described by 3 independent parameters only. Surprisingly, in a wide range of parameters the corresponding coefficient of tangential restitution, epsilont, is well described by the simple Coulomb law with a cut-off at epsilont = 0. A more complex behavior of the coefficient of restitution as a function on the normal and tangential components of the impact velocity, gn and gt, including negative values of epsilont, is found only for very small ratio gt/gn. For the analysis presented here we neglect dissipation of the interaction in normal direction.     

Granular flow from a silo: Discrete-particle simulations in three dimensions

Molecular (or granular) dynamics methods are used to study the gravity-driven flow of granular material through a horizontal aperture in three dimensions. The grains are spherical and modeled using a short-range repulsive interaction, together with normal and tangential frictional damping forces. The material is contained in a rough-walled cylindrical container with a circular hole in its base, and to permit flow measurements under steady-state conditions a continuous feed approach is employed in which exiting grains are replaced at the upper surface of the material. The dependence of flow velocity and discharge rate on aperture diameter is found to agree with experiment; other quantities such as the kinetic energy and pressure distributions are also examined. Received 5 June 2000 and Received in final form 21 September 2000     

Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.     

Development of an optical trap for microparticle clouds in dilute gases

Long-duration experiments with clouds of microparticles are planned for the ICAPS facility on board the International Space Station ISS. The scientific objectives of such experiments are widespread and are ranging from the simulation of aerosol behaviour in Earths atmosphere to the formation of planets in the early solar system. It is, however, even under microgravity conditions, impossible to sustain a cloud of free-floating, microscopic particles for an extended period of time, due to thermal diffusion and due to unavoidable external accelerations. Therefore, a trap for dust clouds is required which prevents the diffusion of the particles, which provides a source of relative velocities between the dust grains and which can also concentrate the dust to higher number densities that are otherwise not achievable. We are planning to use the photophoretic effect for such a particle trap. First short-duration microgravity experiments on the photophoretic motion of microscopic particles show that such an optical particle-cloud trap is feasible. First tests of a two-dimensional trap were performed in the Bremen drop tower.     

Effective temperature and jamming transition in dense, gently sheared granular assemblies

We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the shear rate for slow enough shear suggesting that it is the effective temperature of the jammed packing. However, we also show that the agreement of the effective temperature for different observables is only approximate, for very long times, suggesting that this defintion may not capture the full thermodynamics of the system. On the other hand, we find good agreement between the dynamical effective temperature and a compactivity calculated assuming that all jammed states are equiprobable. Therefore, this definition of temperature may capture an instance of the ergodic hypothesis for granular materials as proposed by theoretical formalisms for jamming. Finally, our simulations indicate that the average shear stress and apparent shear viscosity follow the usual relation with the shear rate for complex fluids. Our results show that the application of shear induces jamming in packings whose particles interact by tangential forces.     

Initiation and evolution of current ripples on a flat sand bed under turbulent water flow

We investigate the formation and dynamics of sand ripples under a turbulent water flow. Our experiments were conducted in an open flume with spherical glass beads between 100 and 500μm in diameter. The flow Reynolds number is of the order of 10 000 and the particle Reynolds number of the order of 1 to 10. We study the development of ripples by measuring their wavelength and amplitude in course of time and investigate the influence of the grain size and the flow properties. In particular, we demonstrate two different regimes according to the grain size. For fine grains, a slow coarsening process (i.e., a logarithmic increase of the wavelength and amplitude) takes place, while for coarser grains, this process occurs at a much faster rate (i.e., with a linear growth) and stops after a finite time. In the later case, a stable pattern is eventually observed. Besides, we carefully analyze the wavelength of ripples in the first stages of the instability as a function of the grain size and the shear velocity of the flow, and compare our results with other available experimental data and with theoretical predictions based on linear stability analyses.     

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.     

About the influence of friction and polydispersity on the jamming behavior of bead assemblies

We study the jamming of bead assemblies placed in a cylindrical container whose bottom is pierced with a circular hole. Their jamming behavior is quantified here by the median jamming diameter, that is the diameter of the hole for which the jamming probability is 0.5. Median jamming diameters of monodisperse assemblies are obtained numerically using the Distinct Element Method and experimentally with steel beads. We obtain good agreement between numerical and experimental results. The influence of friction is then investigated. In particular, the formation of concentric bead rings is observed for low frictions. We identify this phenomenon as a boundary effect and study its influence on jamming. Relying on measures obtained from simulation runs, the median jamming diameter of bidisperse bead assemblies is finally found to depend only on the volume-average diameter of their constituting beads. We formulate this as a tentative law and validate it using bidisperse assemblies of steel beads.     

Ripple formation in weakly turbulent flow

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.     

Random inelasticity and velocity fluctuations in a driven granular gas

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the “stochastic thermostat” model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high-velocity stretched-exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics. Received: 27 May 2002 / Accepted: 6 May 2003 / Published online: 27 May 2003 RID="a" ID="a"e-mail: Alain.Barrat@th.u-psud.fr     

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”).     

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.     

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.     

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.     

Experimental study of the porosity of loose stacks of stiff cylindrical fibres: Influence of the aspect ratio of fibres

The aim of this work is to study the porosity of three-dimensional and two-dimensional packing of stiff cylindrical fibres according to their aspect ratio. First, we have carried out an experimental study of the porosity for 3D and 2D packing. In this last case, the elementary representative surfaces have been determined. Then, an attempt of interpretation of the porosity variations for 2D stacks has been realized on the basis of the excluded volume theory and a variation law has been proposed. To conclude, we have studied the relevance of a simplified packing model based on a single geometry of the defects. Received 12 April 1999 and Received in final form 4 August 1999     

Energy fluctuations in vibrated and driven granular gases

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results that have previously been observed numerically and that had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit suggests that they are also due to the finite size of the system.     

Selection of dune shapes and velocities Part 2: A two-dimensional modelling

We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes. The latter, by contrast to the former, do not present a slip face. Their shape and velocity can be predicted as a function of their size. We recover that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no dune solution exists. It rises the problem of dune nucleation: how can dunes appear if any bump below this minimal mass gets eroded and disappears? The linear stability analysis of a flat sand bed shows that it is unstable at large wavelengths: dune can in fact nucleate from a small sand mass if the proto-dune is sufficiently long. Received 22 December 2001 / Received in final form 31 May 2002 Published online 31 July 2002     

Dynamical invariants in the deterministic fixed-energy sandpile

The non-ergodic behavior of the deterministic Fixed Energy Sandpile (DFES), with Bak-Tang-Wiesenfeld (BTW) rule, is explained by the complete characterization of a class of dynamical invariants (or toppling invariants). The link between such constants of motion and the discrete Laplacians properties on graphs is algebraically and numerically clarified. In particular, it is possible to build up an explicit algorithm determining the complete set of independent toppling invariants. The partition of the configuration space into dynamically invariant sets, and the further refinement of such a partition into basins of attraction for orbits, are also studied. The total number of invariant sets equals the graphs complexity. In the case of two dimensional lattices, it is possible to estimate a very regular exponential growth of this number vs. the size. Looking at other features, the toppling invariants exhibit a highly irregular behavior. The usual constraint on the energy positiveness introduces a transition in the frozen phase. In correspondence to this transition, a dynamical crossover related to the halting times is observed. The analysis of the configuration space shows that the DFES has a different structure with respect to dissipative BTW and stochastic sandpiles models, supporting the conjecture that it lies in a distinct class of universality.