Kinetic Theory Approach for Modeling Granular Segregation

Momentum conservation equations for individual constituents have been used to derive expressions for the percolation velocities of bidisperse segregating species in a granular flow. Many gravity-driven segregation models assume that the inter-species drag takes the form of Darcy's law, which gives a linear relation between the drag forces and the percolation velocities. However, a simple linear drag law is not sufficient to describe the segregation behavior. To address this, we propose a relation based on the kinetic theory of granular flow that includes terms to account for the effects of the particle surface friction, the coefficient of restitution, and the local inertial number. The percolation velocity derived from the momentum balance equation with this drag model agrees well with DEM simulations of uniform shear flows of density bidisperse particles, accurately predicting the difference between upward species velocity and downward species velocity through the depth of the flowing layer for different density ratios and relative constituent concentrations.