Forces on a segregating particle

Size segregation in flowing granular materials is not well understood at the particle level. In this study, we perform a series of 3D Discrete Element Method (DEM) simulations to measure the segregation force on a single spherical test particle tethered to a spring in the vertical direction in a shearing bed of particles with gravity acting perpendicular to the shear. The test particle is the same size or larger than the bed particles. At equilibrium, the downward spring force and test particle weight are offset by the upward buoyancy-like force and a size ratio dependent force. We find that the buoyancy-like force depends on the bed particle density and the Voronoi volume occupied by the test particle. By changing the density of the test particle with the particle size ratio such that the buoyancy force matches the test particle weight, we show that the upward size segregation force is a quadratic function of the particle size ratio. Based on this, we report an expression for the net force on a single particle as the sum of a size ratio dependent force, a buoyancy-like force, and the weight of the particle.