Granular Flow Modeling In Tumbling Mills

A continuum based granular flow model of charge motion that combines the inherent frictional nature of particles with its distinctly fluid-like structure is presented. Starting with Newton?s 2nd Law on a volume element of charge, we derive the velocity field in the bed free-surface and the rising en-masse region. Invoking flux conservation within the two regimes of interest then yields a (simple) differential equation for the free-surface of the charge body. Combining the velocity field gradients with a suitable constitutive choice for the shear stress completes the picture with a description of the in-situ rate of shear power dissipation in a tumbling mill ? a mechanistically correct account of power draw in a tumbling mill. Positron Emission Particle Tracking (PEPT) was used to measure the in-situ flow fields of the charge within opaque systems like tumbling mills. The accurate velocity and mass distribution derived from PEPT form the basis for direct verification of the resulting granular flow models. In this regard a wide range of milling conditions is investigated and presented in this paper.