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 a 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 singular behaviour of the mixing near this critical point. A beautiful experiment on so called avalanche mixing of granular solids in a slowly rotated two-dimensional drum was presented in the paper of Metcalfe et al [1]. The patterns observed were so striking that one of the figures made the cover of the March (1995) issue of Nature. In the present communication, we shall propose a simple theory which provides a surprisingly good description of this experiment. We shall demonstrate that kinetics of avalanche mixing can be understood using a geometrical approach without appealing to ideas of self-organized criticality [2]. (One should note that the flow of granular solids in rotated drums is usually used to study self-organized ∗e-mail: [email protected]