Avalanche mixing of granular solids in a rotating 2D drum: diffusion and fractionality

TL;DR

This paper analyzes avalanche mixing in a rotating 2D drum, revealing how the mixing process behaves like diffusion with a variable coefficient depending on the stability angle difference, and identifies conditions where mixing time diverges.

Contribution

It provides an analytical solution for avalanche mixing dynamics in a 2D drum considering finite stability angle differences, highlighting fractional diffusion behavior.

Findings

Mixing resembles linear diffusion with a variable coefficient.

Mixing time diverges when the stability angle difference is an integer multiple of π.

The study predicts how mixing time depends on the angle difference.

Abstract

The dynamics of the avalanche mixing in a slowly rotated 2D upright drum is studied in the situation where the difference $\delta$ between the angle of marginal stability and the angle of repose of the granular material is finite. An analytical solution of the problem is found for a half filled drum, that is the most interesting case. The mixing is described by a simple linear difference equation. We show that the mixing looks like linear diffusion of fractions under consideration with the diffusion coefficient vanishing when $\delta$ is an integer part of $\pi$. The characteristic mixing time tends to infinity in these points. A full dependence of the mixing time on $\delta$ is calculated and predictions for an experiment are made.