Collision-induced friction in the motion of a single particle on a bumpy inclined line

By means of molecular-dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in two dimensions: a single ball confined to moving along an inclined line consisting of balls. The global characteristics of the motion depend strongly on the size of the moving ball relative to the size of the balls on the line, as well as the distribution of the balls on the line. We find that in the steady state the friction force acting on the ball is independent of material properties such as the Coulomb friction coefficient and the coefficient of restitution. Contrary to previous notions about the details of the motion, we find that it is very regular and consists of many small bounces on each ball on the line. As a result of this regularity, introducing a random spacing between the balls on the line has mainly the same influence as a regular spacing of adequate length. The insensitivity of the steady-state velocity to material properties and to the detailed arrangement of the balls on the line allows for an analytical estimation of the mean velocity that fits the simulation results very well. We find that results from the two-dimensional case can probably not be transferred to the three-dimensional case of a ball moving on a rough inclined plane as easily as has been suggested previously.