A granular mixture of different size particles flowing over an inclined surface is known to segregate with large particles concentrating near the free surface. In order to understand and predict size segregation of granular mixtures, we first propose a novel method to measure the upward force acting on a single, unconstrained, large particle in a granular medium of small particles flowing over inclined plane using discrete element method (DEM) simulation. Frictional, slightly inelastic, soft deformable spherical particles flowing over an inclined bumpy surface are simulated with few large particles. Four (nine) equidistant intruder particles of large size are sandwiched between two cubic lattice configuration of nontouching small particles at the beginning of the simulations. The particles are allowed to settle under the influence of gravity and the flow is continued until steady state. A harmonic spring force is used to ensure that the intruder particles remain nearly at the same height. In addition, a small repulsive force is used between the intruder particles to prevent them from coming close to each other during the evolution of the flow. Once the flow reaches steady state, the harmonic attraction force and the repulsive force between the intruder particles are switched off. The mass of each intruder particles is set as desired and the simulation is continued. Depending on their mass, the intruder particles may either rise or sink in the flowing layer. The average velocity of the intruder along the vertical direction is obtained as the slope of the average trajectory of many particles by means of a linear fit. Mass of the intruder shows a linear variation with the local viscosity, intruder velocity and diameter, indicating a Stokes' like drag acting on the rising/settling particles. By calculating the mass of the intruder that remains neutrally buoyant in the flowing layer, we measure the net upward force that leads to segregation of large particles near free surface in shear flows. Using this measure of the net force acting on the large size intruder particle, we next formulate a theory to predict the segregation due to size difference. While the predictions agree very well with simulation results across most part of the layer, it fails to capture the behaviour near the free surface where the concentration of large particles is much higher.
We next take into account the fact that the net upward force on a single large particle should reduce as the concentration of the large particle increases and must approach to zero in the limiting case of large particles concentration approaching unity. The measured net upward force on a single large intruder, when corrected for the large particle concentration dependence, yields a segregation flux with cubic dependence on the large particle concentration and linear dependence on shear rate. In addition, a dependence on the inclination angle is also predicted by the theory which is not captured in the empirical segregation flux-based approaches. Accurate predictions of the concentration and the velocity field are done using this approach for steady, fully developed chute flow of binary mixtures for a wide range of compositions and inclinations for two different size ratios. The theoretical formulation suggests a simple, yet quantitative, way of predicting size segregation in size bidisperse mixtures and paves way for predicting segregation of mixtures differing in both size and density.
References:
Anurag Tripathi, Alok Kumar, Mohit Nema and D. V. Khakhar, "A theory for size segregation in flowing granular mixtures based on computation of forces on a single large particle", Phys. Rev. E., 103 (3), L031301 (2021)
