Avalanche Mixing of Granular Solids

TL;DR

This paper presents a simple geometrical theory for granular mixing in a rotating drum, accurately predicting mixing times and revealing singular behavior near critical filling levels.

Contribution

It introduces a geometrical approach to model granular mixing, avoiding complex criticality concepts, and predicts the dependence of mixing time on drum filling.

Findings

Mixing time depends on drum filling level.

Mixing time becomes infinite at half-filling.

The model accurately describes experimental results.

Abstract

Mixing of two fractions of a granular material in a slowly rotating two-dimensional drum is considered. The rotation is around the axis of the upright drum. The drum is filled partially, and mixing occurs only at a free surface of the material. We propose a simple theory of the mixing process which describes a real experiment surprisingly well. A geometrical approach without appealing to ideas of self-organized criticality is used. The dependence of the mixing time on the drum filling is calculated. The mixing time is infinite in the case of the half-filled drum. We describe singular behaviour of the mixing near this critical point.