Granular flow in a wedge-shaped hopper with smooth walls and radial gravity: Theory and simulations

Hoppers are widely used in industrial granular processes. Discrete element simulations of the flow in an idealized wedge-shaped hopper, with frictionless walls and radial gravity, are compared to predictions of an exact theory by Savage, based on purely frictional rheology, and an extension of the theory based on a frictional-collisional rheology ($\ensuremath{\mu}$-I). The agreement is excellent when the finite stress at the exit of the hopper is taken into account. The theory and simulations provide new physical insights into the converging flow, for varying flow rates, inter-particle friction, particle stiffness and particle diameter.