Continuum theory of partially fluidized granular flows.

A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order-parameter equation which describes the transition between the flowing and static components of the granular system. We apply this theory to several important granular problems: avalanche flow in deep and shallow inclined layers, rotating drums, and shear granular flows between two plates. We carry out quantitative comparisons between the theory and experiment.