Avalanche mixing of granular solids

Mixing of two fractions of a granular material in a slowly rotating two-dimensional drum is considered. The rotation is around the axis of the upright drum. The drum is filled partially, and mixing occurs only at the free surface of the material. We propose a simple theory of the mixing process which describes a real experiment surprisingly well. The dependence of the mixing time on the drum filling is calculated. The mixing time is infinite in the case of the half-filled drum. We describe the singular behaviour of mixing near this critical point.