Avalanche mixing of granular solids in a rotating 2D drum: diffusion and fractionality
Abstract
The dynamics of the avalanche mixing in a slowly rotated 2D upright drum is studied in the situation where the difference
δ
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
δ
is an integer part of
π
. The characteristic mixing time tends to infinity in these points. A full dependence of the mixing time on
δ
is calculated and predictions for an experiment are made.