Different shear regimes in the dense granular flow in a vertical channel

Abstract

The steady dense granular flow in a vertical channel bounded by flat frictional walls in one horizontal direction and with periodic boundary conditions in the other horizontal and vertical directions is studied using the discrete element method. The shape of the scaled velocity profile is characterized quantitatively by a universal exponential function, and the ratio of the maximum and slip velocities is independent of the average volume fraction $\bar {\phi }$ and the channel width $W$ . For sufficiently wide channels, the maximum and slip velocities increase proportional to $\sqrt {W}$ , and the thickness of the shearing zones increases proportional to $W$ . There are four zones in the flow, each with distinct dynamical properties. There is no shear in the plug zone at the centre, but there is particle agitation, and the volume fraction $\phi$ is lower than the random close packing volume fraction $\phi _{rcp}$ . In the adjoining dense shearing zone, $\phi$ is greater than the volume fraction for arrested dynamics $\phi _{ad} = 0.587$ , and the granular temperature and shear rate depend on the particle stiffness. Adjacent to the dense shearing zone is the loose shearing zone where $\phi < \phi _{ad}$ . Here, the properties do not depend on the particle stiffness, and the constitutive relations are well described by hard-particle models. The rheology in the loose shearing zone is similar to the dense flow down an inclined plane. There is high shear and a sharp decrease in $\phi$ in the wall shearing zone of thickness about two particle diameters, where the particle angular velocity is different from the material rotation rate due to the presence of the wall.