  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 $\tau(\delta)$.
