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

Abstract

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference $δ$ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time $τ$ 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 $δ$ is an integer part of $π$. Introduction of fluctuations of $δ$ supresses the singularities of $τ(δ)$ and smoothes the dependence $τ(δ)$.