Frictional–collisional equations of motion for participate flows and their application to chutes

Measurements of the relation between mass hold-up and flow rate have been made for glass beads in fully developed flow down an inclined chute, over the whole range of inclinations for which such flows are possible. Velocity profiles in the flowing material have also been measured. For a given inclination it is found that two different flow regimes may exist for each value of the flow rate in a certain interval. One is an ‘energetic’ flow, and is produced when the particles are dropped into the chute from a height, while the other is relatively quiescent and occurs when entry to the chute is regulated by a gate. At some values of the inclination jumps in the flow pattern occur between these branches, and it is even possible for both branches to coexist in the same chute, separated by a shock. A theoretical treatment of chute flow has been based on a rheological model of the material which takes into account both collisional and fractional mechanisms for generating stress. Its predictions include most aspects of the observed behaviour, but quantitative comparison of theory and experiment is difficult because of the uncertain values of some parameters appearing in the theory.