Velocity statistics in excited granular media

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) ~ exp(-|v/v_c|^1.5), in agreement with a recent theory. The characteristic velocity v_c is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy.Comment: 27 pages, 13 figures, to appear in Chaos, September 99, revised 3 figures and tex

Diffusion of a granular pulse in a rotating drum

The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to elucidate the effect of the confining end-plate of the drum. We then show that the diffusion is neither subdiffusive nor superdiffusive but normal. This is demonstrated by rescaling the concentration profiles obtained at various stages and by studying the time evolution of the mean squared deviation. Finally we study the self-diffusion of both large and small grains and we show that it is normal and that the diffusion coefficient is independent of the grain size

Bubble kinematics in a sheared foam

We characterize the kinematics of bubbles in a sheared two-dimensional foam using statistical measures. We consider the distributions of both bubble velocities and displacements. The results are discussed in the context of the expected behavior for a thermal system and simulations of the bubble model. There is general agreement between the experiments and the simulation, but notable differences in the velocity distributions point to interesting elements of the sheared foam not captured by prevalent models

The Behavior of Granular Materials under Cyclic Shear

The design and development of a parallel plate shear cell for the study of large scale shear flows in granular materials is presented. The parallel plate geometry allows for shear studies without the effects of curvature found in the more common Couette experiments. A system of independently movable slats creates a well with side walls that deform in response to the motions of grains within the pack. This allows for true parallel plate shear with minimal interference from the containing geometry. The motions of the side walls also allow for a direct measurement of the velocity profile across the granular pack. Results are presented for applying this system to the study of transients in granular shear and for shear-induced crystallization. Initial shear profiles are found to vary from packing to packing, ranging from a linear profile across the entire system to an exponential decay with a width of approximately 6 bead diameters. As the system is sheared, the velocity profile becomes much sharper, resembling an exponential decay with a width of roughly 3 bead diameters. Further shearing produces velocity profiles which can no longer be fit to an exponential decay, but are better represented as a Gaussian decay or error function profile. Cyclic shear is found to produce large scale ordering of the granular pack, which has a profound impact on the shear profile. There exist periods of time in which there is slipping between layers as well as periods of time in which the layered particles lock together resulting in very little relative motion.Comment: 10 pages including 12 figure

Understanding the dynamics of segregation bands of simulated granular material in a rotating drum

Axial segregation of a binary mixture of grains in a rotating drum is studied using Molecular Dynamics (MD) simulations. A force scheme leading to a constant restitution coefficient is used and shows that axial segregation is possible between two species of grains made of identical material differing by size. Oscillatory motion of bands is investigated and the influence of the frictional properties elucidated. The mechanism of bands merging is explained using direct imaging of individual grains

Creep motion in a granular pile exhibiting steady surface flow

We investigate experimentally granular piles exhibiting steady surface flow. Below the surface flow, it has been believed exisitence of a `frozen' bulk region, but our results show absence of such a frozen bulk. We report here that even the particles in deep layers in the bulk exhibit very slow flow and that such motion can be detected at an arbitrary depth. The mean velocity of the creep motion decays exponentially with depth, and the characteristic decay length is approximately equal to the particle-size and independent of the flow rate. It is expected that the creep motion we have seeen is observable in all sheared granular systems.Comment: 3 pages, 4 figure

Breakdown of Energy Equipartition in a 2D Binary Vibrated Granular Gas

We report experiments on the equipartition of kinetic energy between grains made of two different materials in a mixture of grains vibrated in 2 dimensions. In general, the two types of grains do not attain the same granular temperature, Tg = 1/2m v^2. However, the ratio of the two temperatures is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but is not sensitive to the inelasticity of grains. Also, this ratio is insensitive to compositional variables of the mixture such as the number fraction of each component and the total number density. We conclude that a single granular temperature, as traditionally defined, does not characterize a multi-component mixture.Comment: 4 pages, 5 figures, submitted to Physical Review Letters, updated reference

Deformation and flow of a two-dimensional foam under continuous shear

We investigate the flow properties of a two-dimensional aqueous foam submitted to a quasistatic shear in a Couette geometry. A strong localization of the flow (shear banding) at the edge of the moving wall is evidenced, characterized by an exponential decay of the average tangential velocity. Moreover, the analysis of the rapid velocity fluctuations reveals self-similar dynamical structures consisting of clusters of bubbles rolling as rigid bodies. To relate the instantaneous (elastic) and time-averaged (plastic) components of the strain, we develop a stochastic model where irreversible rearrangements are activated by local stress fluctuations originating from the rubbing of the wall. This model gives a complete description of our observations and is also consistent with data obtained on granular shear bands by other groups.Comment: 5 pages, 2 figure