Reverse segregation and self-organization in inclined chute flows of bidisperse granular mixtures

TL;DR

Bidisperse inclined chute flows with large diameter disparity ($\alpha$ up to $8$) and varying coarse-mass fraction ($f_c$) show a robust transition from usual to reverse segregation and a self-organized layering of coarse-rich and fine-rich planes along the gradient, with layer spacing scaling as $(1+\alpha)d$. Using discrete element method (DEM) simulations via the GRANULAR package in LAMMPS, the study maps local concentrations, packing densities, and flow fields across $(\alpha,f_c)$, identifying an $\alpha$-dependent threshold $f_c^*$ that governs the segregation state. Layered regions exhibit stair-stepped velocity profiles, with low shear inside coarse-rich layers and higher shear in fine-rich layers, and fines appear to lubricate flow by reducing coarse–coarse contacts, especially at large $\alpha$ and intermediate $f_c$. These findings inform continuum models for large size ratios and suggest practical routes to tailor mixing or demixing in industrial granular systems.

Abstract

In the usual segregation scenario for stable inclined chute flows of bidisperse mixtures of fine and coarse spherical particles, coarse particles rise toward the free surface, forming a coarse-rich region atop the flowing pile. Beyond a threshold coarse-to-fine diameter ratio of approximately 4, conversely, the weight of the coarse particles exceeds the segregation driving forces, causing individual coarse particles to sink within the pile and producing a reversed segregation state. However, an understanding of the collective evolution of the pile structure is still lacking when the particle diameter ratio exceeds 4 {\textit{and}} the coarse particle mass fraction is appreciable. To explore this broadly bidisperse limit, we perform discrete element method simulations considering mean particle diameter ratios of up to 8 and coarse particle mass fractions spanning 0.1 to 0.9. The steady-state flow profiles reveal several intriguing behaviors that depend on the diameter ratio and mass fraction. These include a previously identified transition from usual to reverse segregation and a newfound tendency to self-organize into alternating coarse- and fine-rich particle layers stacked along the shear gradient direction, with layer thickness dictated by the coarse particle diameter. A fuller understanding of segregation at this scale could pave the way for enhanced mixing or demixing techniques at the commercial scale.

Figures (15)

• Figure 1: Snapshot of the initial configuration for $\alpha = 6$ and $f_c = 0.5$. Mobile coarse and fine particles are shown in blue and red, respectively. The frozen base also consists of fine (light gray) and coarse particles (dark gray).
• Figure 2: Flowing configurations obtained at $t = 2\cdot 10^4\tau_0$ for a) $f_c = 0.5$ and b) $f_c = 0.3$ for the indicated $\alpha$. The respective flow and span base dimensions are $50d$ by $50d$ for $\alpha = 2$ and 4 and $100d$ by $50d$ for $\alpha = 6$ and 8. The images were rendered in OVITO ovito.
• Figure 3: Evolution of the segregation index with time for four values of $\alpha$ and the nine values of $f_c$ indicated in the legend of the $\alpha = 4$ panel. Data are normalized to unity at $t = 0$. Markers are shown at fixed intervals to differentiate the curves. The inset of the $\alpha = 2$ panel shows the segregation index obtained at $t = 2\cdot 10^4\tau_0$ for each $\alpha$ and $f_c$ combination.
• Figure 4: Steady state coarse particle concentrations for each $\alpha$ and the selected values of $f_c$ indicated in the legend of the $\alpha = 2$ panel. Markers are shown at fixed intervals to differentiate the curves.
• Figure 5: a) Top-down views of horizontal slices of depth $3d$ taken at $z/H\approx 0.5$ for the $f_c = 0.5$ snapshots depicted in Fig. \ref{['fig:fig2']}a). b) Three dimensional coarse-coarse radial distribution functions computed for the same flows as in a). Markers are shown at fixed intervals to differentiate the curves.