Asymmetric concentration dependence of segregation fluxes in granular flows

Abstract

We characterize the local concentration dependence of segregation velocity and segregation flux in both size and density bidisperse gravity-driven free-surface granular flows as a function of the particle size ratio and density ratio, respectively, using discrete element method (DEM) simulations. For a range of particle size ratios and inlet volume flow rates in size-bidisperse flows, the maximum segregation flux occurs at a small particle concentration less than 0.5, which decreases with increasing particle size ratio. The segregation flux increases up to a size ratio of 2.4 but plateaus from there to a size ratio of 3. In density bidisperse flows, the segregation flux is greatest at a heavy particle concentration less than 0.5 which decreases with increasing particle density ratio. The segregation flux increases with increasing density ratio for the extent of density ratios studied, up to 10. We further demonstrate that the simulation results for size driven segregation are in accord with the predictions of the kinetic sieving segregation model of Savage and Lun [1]. arXiv:1806.07993v1 [physics.flu-dyn]

Remarkable simplicity in the prediction of nonspherical particle segregation

“…(1)] was developed and is accurate for mixtures with similar concentrations of the two species [7,8]. For mixtures with widely varying species concentrations, the segregation velocity is more accurately described by a model that is second order in concentration [9,10]. The segregation length scale for species i, S i , is an empirical parameter that characterizes the propensity for a bidisperse mixture of spherical particles to segregate that depends on the ratio of diameters of the constituent species, R D = d i /d j , and the diameter of the small species,…”

“…The coordinate system rises with the surface at a steady rise velocity, v r = q/W , so in its frame of reference the flow and segregation are steady. To quantify the segregation, particle data are spatially and temporally averaged in quadrilateral bins oriented parallel to and rising with the free surface (l max /2 in the depthwise, 2l max in the streamwise direction, and T in the spanwise direction) to find the bulk and species velocity, u and u i , respectively, the segregation velocity, w p,i = w − w i , and species concentration c i throughout the flowing layer, as in previous studies [8,10,30,31]. Particles overlapping multiple bins have their weighted partial volume applied to each overlapped bin.…”

“…Segregation of cylindrical particles. Figure 1(b) shows an example of the segregation velocity w p,i scaled byγ and a particle-based length scale that will be explained shortly, d s,eq , as in previous studies [8,10], versus concentration for a bidisperse mixture of rods and disks. The data are sampled throughout the entire flowing layer, resulting in a wide range of values for w p,i ,γ , and c i .…”

“…The challenge now is to determine an appropriate length scale to normalize S i and then to determine the dependence of S i on particle shape and size. Previous studies for mixtures of spheres have shown that S i , which has units of length, when normalized by the small particle diameter d s , can be represented solely as a function of a relevant ratio of a particle property, such as the diameter or density ratio [8,10,31] [for example, Eq. (2)].…”

Modeling segregation of polydisperse granular materials in developing and transient free‐surface flows

“…The key to accurately describing bidisperse segregation is the semi‐empirical relation for the component of the segregation velocity normal to the free surface, w p , i , which is based on a linearization of Savage and Lun's kinetic sieve model for size bidisperse mixtures composed of particles with diameters α i and α j . The segregation velocity of species i depends on the local shear rate, , and the concentration of the other species, c j , as where S ( α i , α j ) is an empirically determined segregation length scale dependent on size ratio and particle diameters as well as gravity and local pressure .…”