Modeling segregation of bidisperse granular materials using physical control parameters in the quasi‐2D bounded heap

Abstract

in Wiley Online Library (wileyonlinelibrary.com)Quantitatively predicting segregation of size-disperse granular materials is of potential value in many industrial applications. We consider granular segregation of size-bidisperse particles in quasi-2D bounded heaps, a canonical granular flow, using an advection-diffusion transport equation with an additional term to account for particle segregation. The equation is characterized by two dimensionless parameters that are functions of control parameters (flow rate, system size, and particle sizes) and kinematic parameters (flowing layer depth, diffusion coefficient, and percolation length scale). As the kinematic parameters are usually difficult to measure in practice, their dependence on the control parameters is determined directly from discrete element method simulations. Using these relationships, it is possible to determine which values of the control parameters result in a mixed or segregated heap. The approach used here is broadly applicable to a wide range of other flow geometries and particle systems. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 1524AIChE J, 61: -1534AIChE J, 61: , 2015 While k can be chosen such that the surface velocity approaches a smaller fraction of the surface velocity, DEM simulations indicate that the concentration changes minimally in the normal direction below this cut-off.

Granular flow in a wedge‐shaped heap: Velocity field, kinematic scalings, and segregation

“…Beginning at the free surface ( z / δ = 0), the profile decreases steeply from a maximum velocity, then gradually transitions to quasi‐static creeping flow below z / δ = −0.7. Like the quasi‐2D bounded heap, an exponential fit provides a reasonable approximation to the velocity profile, shown by the solid curve in Figure 6b. Similar results occur for the other conditions tested as listed in Table .…”

“…An asymmetry in the profiles with respect to the centerline is evident in Figure 5a, with slightly greater velocities to the left of the centerline, and is consistent with that mentioned with respect to z/δ = −0.7. Like the quasi-2D bounded heap, 12,20,26,27 an exponential fit provides a reasonable approximation to the velocity profile, shown by the solid curve in Figure 6b. Similar results occur for the other conditions tested as listed in Table 1.…”

“…For the simulations in this paper, k n /m eff = 9.919 × 10 8 s −2 and γ n = 2.231 × 10 3 s −1 , which corresponds to a binary collision time t c = 1 × 10 −4 s and normal restitution coefficient ϵ n = 0.8, shown to be valid for modeling glass spheres in dense flows. 12,20,26 A simulation timestep δt = 2:5 × 10 −6 s = tc 40 was chosen to ensure numerical stability. 38 Static friction is modeled using a linear elastic spring, whose elongation is initiated at the point of contact between the colliding spheres.…”

Asymmetric concentration dependence of segregation fluxes in granular flows

“…Discrete element method (DEM) simulations of granular flows have reached the point where their results are nearly equivalent to those measured in corresponding experiment [3,7,16], but with the significant benefit that all the properties of the simulated flow are easily measured. Accordingly, we use DEM simulation to study segregation in the context of a gravity-driven free surface flow of granular material in a one-sided quasi-2D bounded heap with a sloped lower boundary (to reduce the number of simulated particles), see Fig.…”

“…The simplest explanation for segregation relies on the idea, for size-disperse mixtures, that small particles fall through voids generated between large particles and accumulate in the lower regions of the flowing layer, while large particles are forced upward by concentrated regions of small particles. Quantitative models of segregation have been developed and have now reached a state where accurate prediction is possible for a range of material properties and flow geometries [7,8,32,[35][36][37][38][39][40][41].…”