MOTION OF A SINGLE BEAD ON A BEAD ROW - THEORETICAL INVESTIGATIONS

The motion of a single bead on an inclined ''line'' made up of juxtapo sed identical beads is analytically investigated. Initially, an entire ly analytical method is presented in some detail: the problem is tract able with the usual analytical tools as long as any slip motion is ign ored. Under these conditions, we show i) the existence of a steady reg ime within a certain range of line slopes and ii) that the mean veloci ty of the mobile bead may be calculated by induction. When compared to all the series of experiments (after the adjustment of the collisiona l parameter), this approach reflects well all the features displayed b y experiments. The influence of slip is then numerically investigated, but, unfortunately, the unicity of solution to motion equations canno t be proved. Despite this uncertainty, energy considerations show that the main dissipation process is due to collisions. The analytical mod el is then compared to three alternative types of approach, namely a p henomenological approach, an heuristical model, and one based on molec ular-dynamics model. The comparison throws light on the role of (solid ) friction and collisions in granular materials: here, it is found tha t the macroscopic coefficient of friction (bulk resistance) is mainly due to geometrical characteristics and collisional effects.