Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: (i) the Stokes time, accounting for the inertia of the particles, (ii) the mean collision time among the grains, (iii) the typical time scale of the flow, and (iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times, a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or may not appear.