Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler

Abstract

We formulate and solve a non-Fickian macroscopic model of axial diffusion of a granular material in a finite cylindrical tumbler. The model accounts for localization of shear and, thus, diffusion induced by particle collisions in a thin surface flowing layer in the cross-section of the drum. All model parameters are related to measurable quantities in a granular flow. The proposed non-Fickian model could address certain ``anomalous'' features previously identified in experiments on axial diffusion and segregation of granular materials. It is shown that the proposed model is a member of the general class of linear constitutive relations with memory. The theoretical predictions suggest new ideas to interpret the results of experimental measurements.Comment: 7 pages, 2 figures, Springer journal class; submitted to Granular Matter: Special Issue In Memoriam of Robert P. Behringer; v2: minor revision