Modeling Segregation in Modulated Granular Flow

Abstract

We consider unsteady segregating granular flows, focusing on stratification in bidisperse bounded heap flow. Experiments indicate that periodically changing the feed rate of particles falling onto the upstream portion of the heap results in a stratified segregation much like that which occurs at low feed rates, but with more regular stratified layers of large and small particles and a higher overall feed flow rate. Experiments clarify how a front of large particle at a high feed rate deposits a layer of large particles that is subsequently covered over by a layer of small particles during a low feed rate, thus generating layers of large and small particles. The stratification can be modelled using a version of an advection-segregationdiffusion equation with a segregation velocity. Simply repeatedly switching the model from a low volume flow rate to a high volume flow rate instantaneously along the entire length of the flowing layer results in stratification patterns that are similar to those observed in experiments. Using a modulated feed rate offers the potential to intentionally create extended layers of bidisperse granular materials to enhance the effective degree of mixing of the deposited materials at heap length scales.

Particle Segregation in Dense Granular Flows

“…(h) Segregated and (i ) stratified heaps (Gray & Hutter 1997). ( j) Rotated experiment and (k) simulation of modulated inflow on a heap (Lueptow et al 2017). (l ) Christmas tree pattern in a silo.…”

“…The resulting stratification patterns (Williams 1968, Gray & Hutter 1997, Makse et al 1997, Gray & Ancey 2009 have interleaved layers of large and small particles (Figure 11i ) and are directly analogous to the Catherine wheel pattern in a rotating drum. Although industry would prefer their grains to be evenly mixed throughout, a stratified heap is preferable to a completely segregated one, and researchers are now investigating modulated inflows (Lueptow et al 2017) to purposely stratify the deposit (Figure 11j,k). Rotational feeders, helical chargers, and other inserts are also commonly used in industry to minimize the formation of avalanches at the free surface of the deposits, where the initial segregation occurs.…”

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

“…Particles are fed into the system at one end at a two-dimensional volumetric feed rate, q 0 = Q/T , where Q is the bulk volumetric feed rate and T is the gap width between the sidewalls. In this study, all initial conditions are fully mixed, but the continuum model techniques have been shown to apply to bounded heap flow with initially segregated [5] or time-periodic [39] inlet conditions. After entering the system, particles flow down the heap away from the feed zone and deposit with angle α static relative to the horizontal.…”