Motion of grains down a bumpy surface.

Abstract

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.