Complex segregation patterns in confined nonuniform granular shearing flows

TL;DR

This work addresses size-driven segregation in dense, nonuniform granular flows under confinement by combining annular shear-cell experiments with DEM simulations of bidisperse, inelastic spheres. It shows that, beyond classic buoyancy-like segregation, inverse and horizontal segregation emerge due to flow kinematics and boundary geometry; the rate and extent of segregation depend on the size ratio $d_L/d_S$ and the mass fraction $M_L/M_S$. The study highlights the coexistence of mixing and segregation at steady state, governed by diffusion, pressure, and confinement, and reveals interior flow details through interior measurements accessible in simulations. The findings advance understanding of how confinement and nonuniform shear influence segregation, with implications for industrial processing where complete demixing is rarely achieved.

Abstract

When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell experiments complemented with discrete numerical simulations of bidisperse, inelastic, and frictional spheres under gravity. We explored the role of shear localization, granular temperature, boundaries, and mixture properties in the evolution of the segregation rate and the maximum degree of segregation achieved by a bidisperse granular system in the steady state. A faster segregation process and a more developed degree of segregation is observed for bidisperse mixtures with a larger size ratio and a higher proportion of large particles. Normally, in the presence of gravity, size segregation induces large particles to rise and small particles to sink. However, two additional complex segregation patterns were found: inverse segregation and horizontal segregation. The first might be related to the kinematics of the flow, while the second is a geometrical effect. This additional segregation mechanism, in addition to diffusion fluxes and high confining pressure, hampers complete segregation in the steady state, where some degree of mixing always persists.

Figures (12)

• Figure 1: Sketch of the experimental annular shear cell. Top view shows a bottom plate that rotates at an angular velocity $\Omega$. Cross section shows the granular material bounded by an outer ($R_\mathrm{out}$) and an inner ($R_\mathrm{in}$) sidewall, and confined by a top loading plate free to move up and down. $H$ is the depth of the flow. Granular flow is filmed from outer and inner sidewall using a mirror.
• Figure 2: Snapshot of the initial state of the simulated shear cell. Granular flow is bounded by two flat frictional lateral walls, separated at a distance of $W$, and confined by a top wall free to move up and down. $H$ is the depth of the flow. The bottom wall moves at a linear velocity $U$ in $x$ direction. The cell is initially filled following an inverse segregation pattern (large particles at the bottom). Colors correspond with particle size including 10% polydispersity.
• Figure 3: Evolution of the local concentration of large particles $C_L/(C_L+C_S)$ as a function of the dimensionless shear deformation $\Delta x/d$ in the outer sidewall of annular shear cell experiments. Small particles are represented in dark red, while large particles in midnight blue [(a)--(c)] and yellow [(d)--(f)]. Light colors represent a mixed state. Upper row [(a)--(c)] correspond to a particle size ratio of $d_L/d_S=1.5$, while bottom row [(d)--(f)] correspond to $d_L/d_S=2$. Columns from left to right correspond to mass fractions of $M_L/M_S=$ 1/3, 1, and 3, respectively.
• Figure 4: Evolution of the local concentration of large particles $C_L/(C_L+C_S)$ as a function of the dimensionless shear deformation $\Delta x/d$ in the inner sidewall of annular shear cell experiments. Small particles are represented in dark red, while large particles in midnight blue [(a)--(c)] and yellow [(d)--(f)]. Light colors represent a mixed state. Upper row [(a)--(c)] correspond to a particle size ratio of $d_L/d_S=1.5$, while bottom row [(d)--(f)] correspond to $d_L/d_S=2$. Columns from left to right correspond to mass fractions of $M_L/M_S=$ 1/3, 1, and 3, respectively.
• Figure 5: Depth profiles of the mass concentration of large particles $C_L/(C_L+C_S)$ in the steady state ($\Delta x\approx100\times10^3d$) in annular shear cell experiments. Continuous lines with filled markers correspond to data from the outer sidewall, while dashed lines with void markers correspond to data from the inner sidewalls.