Anomalous diffusion in silo drainage

TL;DR

This study investigates anomalous diffusion phenomena during silo discharge using molecular dynamics simulations, revealing non-Gaussian statistics, superdiffusive behavior, and transitions between ballistic and diffusive regimes, modeled via non-extensive thermodynamics.

Contribution

It introduces a nonlinear diffusion model based on non-extensive thermodynamics to describe grain movement and anomalous diffusion in silo drainage.

Findings

Non-Gaussian PDFs at discharge start

Superdiffusive behavior observed

Transition between ballistic and diffusive regimes for large orifices

Abstract

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well defined relationship ($\gamma = 2/(3-q)$) between the anomalous diffusion exponent $\gamma$ and the entropic parameter $q$ introduced by the non-extensive formalism to fit the PDF of the fluctuations.