  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.
