Density difference-driven segregation in a dense granular flow

Abstract

We 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.

Debris flows: Experiments and modelling

“…Eq. (4) has been used to model segregation due to density differences between the particles [2,17] and it is closely related to models of sedimentation in suspensions [61,62]. The next section will examine how such a model can be derived.…”

“…This form automatically satisfies the constraints (12) and reduces to the bidisperse case in any two-component sub-mixture. Assuming that there are no pressure perturbations exerted by any constituent on itself, and that the pressure perturbation on constituent ν due to constituent μ is equal and opposite to the pressure perturbation on constituent μ by constituent ν, then B (νν) = 0, ∀ν, (17) and the summation condition ∀ν f ν = 1 is automatically satisfied. The matrix B formed by the coefficients B νμ has the interesting property that it is antisymmetric, i.e.…”

“…Significant extensions of the theory include the ability to model particle-size and density driven segregation [17,69,70,77,109] as well as polydisperse mixtures of grains [44,77]. These theories allow the particle-size distribution to be calculated as it evolves in both space and time, provided that the segregation and diffusion rates are known (S ls and D r in the bidisperse case) and the bulk flow u is prescribed.…”

Particle-size segregation in dense granular avalanches

“…Fan and Hill [15] have put forward an alternative hypothesis that, in dense systems, large particles are driven to regions of higher granular temperature by kinetic stress gradients, which results in them rising to 20 the surface of the avalanche in a rotating drum [16] or being driven to the sidewalls in a vertical chute flow [15]. The problem can also be viewed as one of lift and drag forces acting on a large particle in an effective fluid medium of fine particles [17][18][19].…”

A hierarchy of particle-size segregation models: From polydisperse mixtures to depth-averaged theories

“…They showed that typical Peclet numbers Pe = Sr/Dr are of the order to 10-20. This equation has also proved useful in understanding segregation due to density differences between the particles [37,38].…”