(Left) Simulation of a granular outflow from rectangular hopper. You can see the funnel and wall layer. (Right) Outflow of frictionless particles from rectangular hopper. Color denotes a local free volume. Seen an increase in free volume in the regions of shear flow due to the effect of dilatancy.
Rectangular outflow: frictional VS frictionless walls
Simulation of a granular outflow from rectangular hopper. Front and back walls is frictional (right two) and frictionless (left two). You can see different flows pattern.
Simulation of a granular outflow from a cylindrical hopper with flat bottom. On the right hand side, particles are colored by local volume of solid. You can see the rarefaction in the shear flow region at bottom of the cylinder due to dilatancy.
(Left) Simulation of a granular outflow from a cylindrical hopper with conical bottom. (Right) How granular materials jam in a hopper. The simulation is inspired by experimental work of J.Tang and R.P. Behringer http://youtu.be/lWSJwZhqoQw