Continuum modelling of segregating tridisperse granular chute flow

Abstract

Segregation and mixing of size multidisperse granular materials remain challenging problems in many industrial applications. In this paper, we apply a continuum-based model that captures the effects of segregation, diffusion and advection for size tridisperse granular flow in quasi-two-dimensional chute flow. The model uses the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The predictions from the model are consistent with experimentally validated discrete element method (DEM) simulations over a wide range of flow conditions and particle sizes. The degree of segregation depends on the Péclet number, , defined as the ratio of the segregation rate to the diffusion rate, the relative segregation strength between particle species and, and a characteristic length , which is determined by the strength of segregation between smallest and largest particles. A parametric study of particle size, , and demonstrates how particle segregation patterns depend on the interplay of advection, segregation and diffusion. Finally, the segregation pattern is also affected by the velocity profile and the degree of basal slip at the chute surface. The model is applicable to different flow geometries, and should be easily adapted to segregation driven by other particle properties such as density and shape.

Modelling segregation of bidisperse granular mixtures varying simultaneously in size and density for free surface flows

“…2016; Deng et al. 2018). Furthermore, an advection–diffusion transport equation has been successfully used to model the segregation (Bridgwater et al.…”

“…However, for the quasi-2-D bounded heap and most other free surface flows, so that can be accurately approximated by (Deng et al. 2018). With these assumptions, (2.3) can be written as or, rearranging, as When the normal component of flux for species is measured from DEM simulation, it is the entire quantity within the brackets of (2.5) that is measured.…”

“…2016; Deng et al. 2018). For accurate model predictions, the boundary conditions for (4.7) need to match those in the DEM simulations.…”

Asymmetric concentration dependence of segregation fluxes in granular flows

“…We have successfully applied the model using a segregation velocity linear with concentration (Eq. 5) for a variety of situations including bi-and polydisperse size segregation in bounded heap flow [7,8,39], bidisperse segregation in tumbler flow [32], tri-disperse size segregation in chute flow [41], bidisperse density segregation in bounded heap flow [16], and even segregation of rod-like particles in bounded heap flow [40]. Here we compare the predictions of the model using a segregation velocity linearly dependent on c s (Eq.…”

Measuring segregation characteristics of industrially relevant granular mixtures: Part I – A continuum model approach

“…where k = 2.3 and L is the streamwise length of the flowing layer, L = W/ cos α. While the profiles in this particular geometry are well characterized by exponential profiles, there exist scenarios in which other velocity profiles are possible, including linear [11,40,41] and Bagnold [33]. The velocity profile used in the continuum model must approximate that in the geometry being studied, and can usually be determined in geometries with transparent sidewalls using high speed imaging and image differencing techniques (e.g., Particle Tracking Velocimetry [16] or Particle Image Velocimetry [14,17]).…”