Density difference-driven segregation in a dense granular flow

Abstract

AbstractWe consider the segregation of spheres of equal size and different density flowing over an inclined plane, theoretically and computationally by means of distinct element method (DEM) simulations. In the first part of the work, we study the settling of a single higher-density particle in the flow of otherwise identical particles. We show that the motion of the high-density tracer particle can be understood in terms of the buoyancy and drag forces acting on it. The buoyancy force is given by Archimedes principle, with an effective volume associated with the particle, which depends upon the local packing fraction, $\phi $. The buoyancy arises primarily from normal forces acting on the particle, and tangential forces have a negligible contribution. The drag force on a sphere of diameter $d$ sinking with a velocity $v$ in a granular medium of apparent viscosity $\eta $ is given by a modified Stokes law, ${F}_{d} = c\pi \eta dv$. The coefficient ($c$) is found to decrease with packing fraction. In the second part of the work, we consider the case of binary granular mixtures of particles of the same size but differing in density. A continuum model for segregation is presented, based on the single-particle results. The number fraction profile for the heavy particles at equilibrium is obtained in terms of the effective temperature, defined by a fluctuation–dissipation relation. The model predicts the equilibrium number fraction profiles at different inclination angles and for different mass ratios of the particles, which match the DEM results very well. Finally, a complete model for the theoretical prediction of the flow and number fraction profiles for a mixture of particles of different density is presented, which combines the segregation model with a model for the rheology of mixtures. The model predictions agree quite well with the simulation results.