Diffusion, mixing, and segregation in confined granular flows

Abstract

Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate that the collisional diffusion is essentially independent of overburden pressure. Because the rate of segregation diminishes with overburden pressure, the tendency for particles to segregate weakens relative to the remixing of particles due to collisional diffusion as the overburden pressure increases. Using a continuum approach that includes a pressure-dependent segregation velocity and a pressure-independent diffusion coefficient, the interplay between diffusion and segregation is accurately predicted for both size and density bidisperse mixtures over a wide range of flow conditions when compared to simulation results. Additional simulations with initially segregated conditions demonstrate that applying a high enough overburden pressure can suppress segregation to the point that collisional diffusion mixes the segregated particles.

Bridging the gap between particle-scale forces and continuum modelling of size segregation: application to bedload transport

“…A classical continuum approach to model size segregation is the advection–diffusion model (Dolgunin & Ukolov 1995; Gray & Thornton 2005; Fry et al. 2019; Umbanhowar et al. 2019).…”

“…The Péclet number reads and is therefore constant with , so that the diffusion coefficient has to have the same dependency on the inertial number as the segregation coefficient where is taken as and should be pressure independent (Fry et al. 2019).

Figure 2.Profiles and configuration from the DEM simulations.

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“…2015; Fry et al. 2019). It has been suggested that it should depend on the volume fraction (Cai et al.…”

“…2019; Fry et al. 2019; Umbanhowar, Lueptow & Ottino 2019) where denotes for time, the vertical axis, and are the small and large particle concentrations and sum to unity (with ), is the advection velocity of segregation and is the diffusion coefficient. This equation is characterised by the segregation flux , and the advective velocity , which encompass the physical dependencies of the size segregation discussed previously.…”

Diffusion of ellipsoidal granular particles in shear flow

“…This diffusion process is commonly encountered in geophysical flows, as well as industrial processes handling bulk solids such as plastic pellets, food, pharmaceuticals and ores. The self‐diffusion of monodisperse spheres has been studied for several decades from theoretical, 2‐7 experimental 8‐10 and computational 4,5,11,12 points of view. For monodisperse spheres in the dilute regime, where particles interact mainly through binary collisions, kinetic theories 2,13 and particle simulations 2 indicate that , where d is the particle diameter and T is the granular temperature 14 calculated from particle velocity fluctuations.…”