Axial transport of granular solids in horizontal rotating cylinders. Part 1: Theory

Abstract

A model for the axial transport of solids in a horizontal rotating cylinder is obtained. The physical basis of the model is a modified version of the single particle trajectory model of Saeman, which includes random deviations from the most probable trajectory. According to the model, each particle executes a one-dimensional random walk, and the stochastic evolution equation for the probability density of the axial position of the particle with time is derived. The average axial velocity (v) and the axial dispersion coefficient (D_a) are obtained in the course of the derivation in terms of the system parameters, and an unknown parameter, δ , which represents the maximum deviation of the trajectory from the model of Saeman. The model predictions are compared with the experimental data of Hehl et al. Reasonable agreement is obtained between theory and experiments for v, and the parameter δ is back-calculated from experimental values of D_a. The results give a better understanding of the mechanisms of axial transport in rotary cylinders.