Stochastic model for the motion of a particle on an inclined rough plane and the onset of viscous friction

Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.

Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction

The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed.

Rolling friction on a granular medium

We present experimental results for the rolling of spheres on a granular bed. We use two sets of glass and steel spheres with varying diameters and a high-speed camera to follow the motion of the spheres. Despite the complex phenomena occurring during the rolling, the results show a friction coefficient nearly independent of the velocity (0.45-0.5 for glass and 0.6-0.65 for steel). It is found that for a given sphere density, the large spheres reach a longer distance, a result that may also help explain the rock sorting along natural stone accumulations at the foot of mountain slopes.

Dynamics of a grain on a sandpile model

The dynamics of a macroscopic grain rolling on an inclined plane composed of fixed identical grains is investigated both experimentally and theoretically. As real sand, the system exhibits an hysteretic transition between static and dynamical states: for angles smaller than straight phi(d), the roller always stops, for angles larger than straight phi(s), it spontaneously starts rolling down. But for angles between straight phi(d) and straight phi(s), it can be either at rest or in motion with a constant velocity. It is shown that the limit velocity is given by the equilibrium between gravity driving and dissipation by the shocks. Moreover, the rough plane acts as a periodic potential trap whose width and depth decrease when the angle is increased: the static angle straight phi(s) corresponds to the angle for which the trap disappears; the dynamical angle straight phi(d) to that for which the limit velocity is sufficient to escape from the trap. Finally, a continuous description of the force globally acting on the grain is proposed, which preserves this hysteretic behavior.

Motion of grains down a bumpy surface

We summarize in this article an extensive experimental and theoretical effort carried out to understand the behavior of a single ball when rolling down a bumpy surface. This may appear to be a simple problem but in fact is one that displays a rich variety of different behaviors which allow us to understand better dissipative systems such as granular media. Studies performed previously have shown that the motion of the single ball on the rough surface can be characterized by three different dynamic regimes according to the different values of the two control parameters, the inclination angle theta and the ratio Phi=R/r, where R is the radius of the rolling ball and r the radius of the glass beads which make up the rough surface. The three regimes are a decelerated regime A, a stationary regime B, characterized by a constant average velocity and a jumping regime C. This result was found to be independent of the composition of the rolling ball and the rough surface. It has been demonstrated that regime B is characterized by a viscous-like friction force that appears for specific parameter values. This friction force can be explained by a model whose central ingredient is the geometry of the surface. The trajectory of the ball in regime B can be pictured as a driven random walk motion where the fluctuations of the local velocities are due to collisions of the moving sphere and the surface grains. A detailed analysis of diffusive properties of the motion is discussed. (c) 1999 American Institute of Physics.

Dynamics of spherical particles on a surface: collision-induced sliding and other effects

We present a model for the motion of hard spherical particles on a two-dimensional surface. The model includes both the interaction between the particles via collisions and the interaction of the particles with the substrate. We analyze in detail the effects of sliding and rolling friction, which are usually overlooked. It is found that the properties of this particulate system are influenced significantly by the substrate-particle interactions. In particular, sliding of the particles relative to the substrate after a collision leads to considerable energy loss for common experimental conditions. The presented results provide a basis that can be used to realistically model the dynamical properties of the system, and provide further insight into density fluctuations and related phenomena of clustering and structure formation.

Geometrical model for a particle on a rough inclined surface

A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which the dynamics is described by a one-dimensional map. This map is studied in detail and it is shown to exhibit several dynamical regimes (steady state, chaotic behavior, and accelerated motion) as the model parameters vary. A phase diagram showing the corresponding domain of existence for these regimes is presented. The model is also found to be in good qualitative agreement with recent experiments on a ball moving on a rough inclined line.