Surface flows of granular mixtures .1. General principles and minimal model

We discuss theoretically the filling of a (two-dimensional) silo when a mixture of particles is poured at the center. Our basic tool is a coupled set of equations (for the local density of rolling species, and for the profile) proposed by Bouchaud et al. We extend this to a pair of species, including various processes: amplification, capture, and exchange of rolling grains. Using the simplest form of the resulting equations, we obtain predictions for the steady state profile and for the concentration distribution. At the bottom side of the slope, we generally expect to have complete purification. Near this point, the concentrations should show unusual power laws.