Mechanism of Size Segregation of Particles in Filling a Hopper

Abstract

Mechanism of size segregation of particles in filling a hopper was theoretically analyzed on the basis of a screening or percolation model. According to the model, when mixed particles of different size are fed in the center of the hopper and flow down on solids heap surface, smaller particles within the mixture pass through interspaces of larger particles during flow and then are packed in interspaces of stationary large particles of the heap surface. By the analysis and experiments, a V-shaped zone, where smaller particles are contained as a result of segregation, was found to expand with smaller fraction of large particles in the feed, longer distance of flow along the heap surface, and larger feed rate of particles.

Modelling size segregation of granular materials: the roles of segregation, advection and diffusion

“…As the heap rises, small particles drop out of the flowing layer sooner and remain in the upstream region of the heap, while large particles are advected to the downstream region of the heap. This results in a separation of large and small particles in the streamwise direction (Williams 1963(Williams , 1968Shinohara et al 1972;Drahun & Bridgwater 1983;Goyal & Tomassone 2006;Fan et al 2012), which is also similar to segregation patterns in avalanche flows (Pouliquen et al 1997;Gray & Ancey 2009). …”

“…The model includes the effects of three different mechanisms -advection due to mean flow, segregation due to percolation, and diffusion due to random particle collisions. Compared with previous predictive models (Shinohara et al 1972;Boutreux & de Gennes 1996), the model presented here is based on an understanding of the kinematics of bounded heap flow and has no arbitrarily adjustable fitting parameters. Instead, particle configu-rations are controlled by two dimensionless parameters: Λ = SL/δ 2 and P e = 2qδ/DL.…”

“…However, in heap flow, since the flowing layer is only a few particle diameters thick (< 10d l ) (Fan et al 2013), the effect of the normal stress on percolation velocity can be safely neglected. Several models (Shinohara et al 1972;Savage & Lun 1988;May et al 2010;Marks et al 2011) for the percolation velocity have been proposed, but none incorporated all of these parameters or were tested in different flow geometries. Of course, when a granular mixture consists of different species with comparable volume fractions, the percolation velocity also depends on the local volume concentration of each species, since the void sizes are associated with the local packing.…”

“…Shinohara et al (1972) proposed a screening layer model in which the flowing layer is divided into three sublayers -large particles, mixed particles, and small particles -from the free surface to the bottom of the flowing layer. Invoking mass conservation in each sublayer and accounting for particle migration between adjacent layers, they derived a model that qualitatively predicted the local particle concentration of each species with several arbitrarily adjustable fitting parameters (e.g.…”

“…The theoretical predictions match quantitatively with both experiments and simulations. Compared to the models by Shinohara et al (1972) and Boutreux et al (Boutreux & de Gennes 1996;Boutreux 1998), our model relies on parameters characterizing the kinematics of the flow instead of arbitrarily adjustable parameters. The model demonstrates that the particle configuration is determined by the interplay of advection, segregation, and diffusion, which can be characterized by two dimensionless parameters, P e and Λ, that depend only on physical on control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity), which have a clear physical meaning and are determined from DEM simulations.…”