| As close packed grains slide relative to one another during slow deformation the stresses are due to the resulting normal and tangential frictional forces at contact. When the grain density is low and the deformation rate high, then momentum is transferred primarily during grain-grain collisions. Traditionally, particulate flow models have been developed for either the high density, slow deformation or for the low density, rapid deformation limits, while most flows of practical interest occur under conditions in which both collisions and friction contribute significantly to the flow behavior. In this research a continuum model is developed that combines both frictional and collisional constitutive expressions, and therefore is applicable over the entire range of shear rates and particle densities. The proposed governing equations include mass, momentum, and pseudo-thermal energy balances, as well as boundary conditions applicable at solid and free-surfaces. Grain-boundary slip and inelastic grain-boundary collisions were included.; Solutions to the governing equations have been computed for two steady plane shear flows: horizontal plane shearing between two parallel plates, and gravity-driven inclined plane flow. Solutions for the horizontal shearing were compared with reported measurements from annular shear cell tests. The inclined flow solutions, on the other hand, were compared with measurements from an inclined chute flow loop constructed for this research. Experiments were performed with 0.1cm diameter glass beads in both rough and smooth chutes. The data includes velocity profiles, bulk densities, flow depths, and mass flow rates as functions of inclination angle and entrance conditions. The comparisons between predicted and measured results indicated that the model more reasonably predicted the observed data than did models including only purely frictional or collisional stress contributions. Both experimental and predicted inclined chute results showed that flow behavior depends on entrance conditions and that different flow states were observed for the same mass flow rate. The chute predictions were very sensitive to parameter changes, and hence, a wide range of behaviors was predicted. For some parameter values multiple flow solutions were predicted, while for others no steady flow solutions were obtained. |
