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

We provide new concepts for understanding transport phenomena in flows of granular materials by using a non-Fickian macroscopic model of axial diffusion of a granular material in a finite cylindrical tumbler. The model accounts for diffusion induced by particle collisions only in a thin surface flowing layer due to localization of shear within the cross-section of the drum. All model parameters are related to measurable quantities in a granular flow. It is shown that the proposed model is a member of the general class of linear constitutive relations with memory. An exact solution for the spreading of a finite-width pulse initial condition under the proposed non-Fickian model is derived and compared to the solution of a Fickian model (i.e., the classicaldiffusion equation).

Automated summary

This study provides new concepts for understanding the transport phenomena in granular material flows by introducing a non-Fickian macroscopic model of axial diffusion in a cylindrical tumbler. The model considers diffusion induced by particle collisions only in a thin surface flowing layer due to shear localization. All model parameters are linked to measurable quantities in the granular flow. The proposed model is shown to be a specific case of linear constitutive relations with memory. An exact solution for the spreading of a finite-width pulse initial condition under the non-Fickian model is derived and compared to the solution of the Fickian model.