Time of avalanche mixing of granular materials in a half filled rotated drum

TL;DR

This paper investigates how the difference between stability and repose angles affects mixing times in a rotating granular drum, revealing a diffusion-like process influenced by angle fluctuations.

Contribution

It introduces a linear difference equation model for avalanche mixing and shows how angle differences and fluctuations impact mixing time behavior.

Findings

Mixing time is restricted by the angle difference δ.

Mixing resembles linear diffusion with a vanishing coefficient at δ = integer multiples of π.

Fluctuations in δ smooth out singularities in mixing time dependence.

Abstract

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference $\delta$ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time $\tau$ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when $\delta$ is an integer part of $\pi$. Introduction of fluctuations of $\delta$ supresses the singularities of $\tau(\delta)$ and smoothes the dependence $\tau(\delta)$.