Simulations of dense granular flow: Dynamic Arches and Spin Organization

We present a numerical model for a two dimensional (2D) granular assembly, falling in a rectangular container when the bottom is removed. We observe the occurrence of cracks splitting the initial pile into pieces, like in experiments. We study in detail various mechanisms connected to the `discontinuous decompaction' of this granular material. In particular, we focus on the history of one single long range crack, from its origin at one side wall, until it breaks the assembly into two pieces. This event is correlated to an increase in the number of collisions, i.e. strong pressure, and to a momentum wave originated by one particle. Eventually, strong friction reduces the falling velocity such that the crack may open below the slow, high pressure `dynamic arch'. Furthermore, we report the presence of large, organized structures of the particles' angular velocities in the dense parts of the granulate when the number of collisions is large.Comment: Submitted to J. Phys.

Simulations of Pattern Formation in Vibrated Granular Media

We present simulations of peak pattern formation in vibrated two-dimensional (2D) granulates and measure the dispersion relation of the pattern for various frequencies, accelerations, cell sizes, and layer heights. We report the first quantitative data from numerical simulations showing an interesting dependence of the pattern wavelength on the acceleration and the system size. Our results are related to recent experimental findings and theoretical predictions for gravity waves.Comment: 6 pages PS-file including figures, (version accepted at Europhys. Lett. 26.10.96

A 2-D asymmetric exclusion model for granular flows

A 2-D version of the asymmetric exclusion model for granular sheared flows is presented. The velocity profile exhibits two qualitatively different behaviors, dependent on control parameters. For low friction, the velocity profile follows an exponential decay while for large friction the profile is more accurately represented by a Gaussian law. The phase transition occurring between these two behavior is identified by the appearance of correlations in the cluster size distribution. Finally, a mean--field theory gives qualitative and quantitative good agreement with the numerical results.Comment: 13 pages, 5 figures; typos added, one definition change

Rapid granular flows on a rough incline: phase diagram, gas transition, and effects of air drag

We report experiments on the overall phase diagram of granular flows on an incline with emphasis on high inclination angles where the mean layer velocity approaches the terminal velocity of a single particle free falling in air. The granular flow was characterized by measurements of the surface velocity, the average layer height, and the mean density of the layer as functions of the hopper opening, the plane inclination angle and the downstream distance x of the flow. At high inclination angles the flow does not reach an x-invariant steady state over the length of the inclined plane. For low volume flow rates, a transition was detected between dense and very dilute (gas) flow regimes. We show using a vacuum flow channel that air did not qualitatively change the phase diagram and did not quantitatively modify mean flow velocities of the granular layer except for small changes in the very dilute gas-like phase.Comment: 10 pages, 16 figures, accepted to Phys. Rev.

Solid-fluid transition in a granular shear flow

The rheology of a granular shear flow is studied in a quasi-2d rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and non-accelerating. Streakline photography and image analysis are used to obtain particle velocities and positions. Different particle sizes and rotational speeds are considered. We find a sharp transition in the apparent viscosity ($\eta$) variation with rms velocity ($u$). In the fluid-like region above the depth corresponding to the transition point (higher rms velocities) there is a rapid increase in viscosity with decreasing rms velocity. Below the transition depth we find $\eta \propto u^{-1.5}$ for all the different cases studied and the material approaches an amorphous solid-like state deep in the layer. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The observed transition appears to be analogous to a glass transition.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Exact Solutions of a Model for Granular Avalanches

We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced: Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, velocities of the active region and of the sandpile profile.Comment: 7 pages, 2 figure

Thick surface flows of granular materials: The effect of the velocity profile on the avalanche amplitude

A few years ago, Bouchaud al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. Fr. I, 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion/accretion mechanism. Boutreux et al. [Phys. Rev. E, 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. In this article, we therefore modify the above models by introducing a velocity profile in the flow, and study the physical consequences of this modification in the simple situation of an avalanche in an open cell. We present a complete analytical description of the avalanche in the case of a linear velocity profile, and generalize the results for a power-law dependency. We show, in particular, that the amplitude of the avalanche is strongly affected by the velocity profile.Comment: 7 figures, accepted for publication in Phys. Rev.

Dynamics of granular avalanches caused by local perturbations

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed. Following previous studies, we use mass and momentum conservation to derive St-Venant like equations for the evolution of the thickness R of the mobile layer and the profile Z of the static bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in details the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for non-stationary avalanches triggered by a localized amount of mobile grains on a static bed of constant slope. We solve analytically the non-linear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.Comment: 25 pages, 12 figure

Pressure and Motion of Dry Sand -- Translation of Hagen's Paper from 1852

In a remarkable paper from 1852, Gotthilf Heinrich Ludwig Hagen measured and explained two fundamental aspects of granular matter: The first effect is the saturation of pressure with depth in a static granular system confined by silo walls -- generally known as the Janssen effect. The second part of his paper describes the dynamics observed during the flow out of the container -- today often called the Beverloo law -- and forms the foundation of the hourglass theory. The following is a translation of the original German paper from 1852.Comment: 4 pages, accepted for publication in Granular Matter, original article (German) can be found under http://www.phy.duke.edu/~msperl/Janssen

Stress transmission in granular matter

The transmission of forces through a disordered granular system is studied by means of a geometrical-topological approach that reduces the granular packing into a set of layers. This layered structure constitutes the skeleton through which the force chains set up. Given the granular packing, and the region where the force is applied, such a skeleton is uniquely defined. Within this framework, we write an equation for the transmission of the vertical forces that can be solved recursively layer by layer. We find that a special class of analytical solutions for this equation are L\'evi-stable distributions. We discuss the link between criticality and fragility and we show how the disordered packing naturally induces the formation of force-chains and arches. We point out that critical regimes, with power law distributions, are associated with the roughness of the topological layers. Whereas, fragility is associated with local changes in the force network induced by local granular rearrangements or by changes in the applied force. The results are compared with recent experimental observations in particulate matter and with computer simulations.Comment: 14 pages, Latex, 5 EPS figure