We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with fluctuating contact networks but not thermal collisions, as in normal fluids.PACS numbers: PACS number(s): 45.70.Mg, Granular flow is an attractively simple and yet surprisingly complex subject [1]. Fast, dilute flows are known to obey classical hydrodynamics (with inelastic collisions), but slow, dense flows pose a considerable challenge to theorists, due to many-body interactions and non-thermal fluctuations. Beyond their fundamental scientific interest, such flows have important engineering applications [2], e.g. to new pebble-bed nuclear reactors [3], whose efficiency and safety depend on the degree of mixing in very slow granular drainage (< 1 pebble/min).Although dense granular drainage is very familiar (e.g. sand in an hourglass), it is far from fully understood. Over the past forty years, a number of theoretical approaches have been proposed for steady state flow [4,5,6,7,8]. Continuum approaches are based on the critical-state theory of soil mechanics and yield only mean velocity fields [7,8]. On the other hand, the diffusive void model [4, 5] takes a particle approach, in which 'voids' injected at the orifice cause drainage by diffusing upward and exchanging position with particles along the way. Averaging over the void trajectories yields the same continuum velocity field for particles as the 'kinematic model ' [6, 8], which provides a reasonable fit to experimental data with only one fitting parameter (the diffusion length, b) [5,6,9,10], although the void model on a regular lattice (as in Ref. [11]) underpredicts its value [12]. Remarkably, these models depend only on geometry and not on momentum, energy, etc.In spite of the success of the kinematic model, however, its only microscopic basis, the void model, greatly overpredicts diffusion. To see this, consider the Péclet number, Pe x = v z d/D x , the dimensionless ratio of advection in uniform downward flow of speed, v z , to diffusion with a horizontal diffusivity, D x , at the scale of a particle diameter, d. In the void model, when a particle falls a distance ∆h, Pe x = (∆h/∆t)d/( ∆x 2 /2∆t) = ∆h 2d/ ∆x 2 , is of order one for any conceivable packing since ∆h ≈ ∆x ≈ d, and therefore it diffuses horizontally by roughly √ ∆h. This prediction is contradicted by ev- eryday experience and our experiments below, which exhibit far less mixing. ...