Size segregation mechanism of binary particle mixture in forming a conical pile

The Grouping and Segregation Error in the Rice Experiment

The grouping and segregation error, one of the seven sampling errors defined by Pierre Gy, is related to the combined effects of gravity and characteristics of the target analyte such as particle size, density, shape, and moisture content of the particulate materials being sampled. Kinetic energy acting on particulate materials that are moved, flow, transported, or stockpiled causes the spatial distribution of fragments relative to one another to change. The grouping and segregation error is identified, quantified, and measured in relative sampling variance terms by comparing the sampling variability due to fractional shovelling (scooping) with that using a Jones riffle splitter. The relative sampling variance of low concentrations, approximately 0.01%, of steel balls, lead balls, and flakes of tungsten carbide in the host substrate indicates that, in this specific sampling space, the grouping and segregation error is primarily a function of particle density. Conclusions from the experiments are that components of the grouping and segregation error, namely the grouping factor and segregation factor, can be identified, measured, and mitigated. Whereas the grouping and segregation error has historically been considered to be less than the fundamental sampling error, these experiments suggest that it can be up to four times the fundamental sampling error depending on the density of the segregated materials.

Evidence of reverse and intermediate size segregation in dry granular flows down a rough incline

In a dry granular flow, size segregation had been shown to behave differently for a mixture containing a few large particles with a size ratio above 5 [N. Thomas, Phys. Rev. E 62, 961 (2000)1063-651X10.1103/PhysRevE.62.961]. For moderately large size ratios, large particles migrate to an intermediate depth in the bed: this is called "intermediate segregation." For the largest size ratios, large particles migrate down to the bottom of the flow: this is called "reverse segregation," in contrast with surface segregation. As the reversal and intermediate depth values depend on the fraction of particles, this numerical study mainly uses one single large tracer. Small fractions of large beads are also computed showing the link between single tracer behavior and collective segregation process. For each device (half-filled rotating tumbler and rough plane), two (2D) and three (3D) dimensional cases are distinguished. In the tumbler, the trajectories of a large tracer show that it reaches a constant depth during the flowing phase. For large size ratios, this depth is intermediate. A progressive sinking of the depth is obtained when the size ratio is increased. The largest size ratios correspond to tracers being at the bottom of the flowing layer. All 3D simulation results are in quantitative agreement with the experimental surface, intermediate, and reverse-segregation results. In the flow down a rough incline, a large tracer reaches an equilibrium depth during flow. For large size ratios, the depth is inside the bed, at an intermediate position, and for the largest size ratios, this depth is reverse, located near the bottom. Results are slightly different for a thin or a thick flow. For 3D thick flows, the reversal between surface and bottom positions occurs within a short range of size ratios: no tracer stabilizes near half-height and two reachable intermediate depth layers exist, below the surface and above the bottom reverse layer. For 3D thin flows, all intermediate depths are reachable by a tracer, depending on the size ratio. The numerical study of larger fractions of tracers (5% or 10%) shows the three segregation patterns (surface, intermediate, reverse) corresponding to the three types of equilibrium depth. The reversal is smoother than for a single tracer, and happens around the size ratio 4.5, in good agreement with experiments.

Modelling density segregation in flowing bidisperse granular materials

Preventing segregation in flowing granular mixtures is an ongoing challenge for industrial processes that involve the handling of bulk solids. A recent continuum-based modelling approach accurately predicts spatial concentration fields in a variety of flow geometries for mixtures varying in particle size. This approach captures the interplay between advection, diffusion and segregation using kinematic information obtained from experiments and/or discrete element method (DEM) simulations combined with an empirically determined relation for the segregation velocity. Here, we extend the model to include density-driven segregation, thereby validating the approach for the two important cases of practical interest. DEM simulations of density bidisperse flows of mono-sized particles in a quasi-two-dimensional-bounded heap were performed to determine the dependence of the density-driven segregation velocity on local shear rate and particle concentration. The model yields theoretical predictions of segregation patterns that quantitatively match the DEM simulations over a range of density ratios and flow rates. Matching experiments reproduce the segregation patterns and quantitative segregation profiles obtained in both the simulations and the model, thereby demonstrating that the modelling approach captures the essential physics of density-driven segregation in granular heap flow.

Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps

Quasi-two-dimensional bounded heap flow is a useful model for many granular flows in industry and nature. It belongs to a family of free surface flows—inclined chute flow, rotating tumbler flow and unbounded heap flow—but differs from the others in that uniform deposition of particles onto the static bed results in the uniform rise of the heap. The kinematics, however, are only partially understood. We performed discrete element method simulations to study granular flows in quasi-two-dimensional bounded heaps. The experimentally validated computational results show a universal functional form for the streamwise velocity profile for both monodisperse and bidisperse systems when velocities and coordinates are scaled by the local surface velocity and the local flowing layer thickness. This holds true regardless of streamwise location, feed rate, particle size distribution and, most surprisingly, the local particle concentration for bidisperse flows. The local surface velocity decreases linearly in the streamwise direction, while the flowing layer thickness remains nearly constant; both quantities depending only on local flow rate and local mean particle diameter. Additionally, the velocity profile normal to the overall flow, which is important in understanding segregation, can be predicted analytically from the streamwise velocity and matches the simulation results.

Stop and restart of granular clock in a vibrated compartmentalized bidisperse granular system

This paper studies a bidisperse granular mixture consisting of two species of stainless steel spheres in a vertically vibrated compartmentalized container. The experiments show that with proper vibration acceleration, the granular clock stops when horizontal segregation of the large spheres residing in the far end from the barrier wall occurs. When the segregation is broken, the granular clock restarts. We present the phase diagrams of vibration acceleration versus container width and small particle number, which exhibits three different regions, namely, clustering state, stop-restart of the granular clock, and the granular clock. A generalized flux model is proposed to reproduce the phenomenon of stop and restart of the granular clock.

Stratification, segregation, and mixing of granular materials in quasi-two-dimensional bounded heaps

Segregation and mixing of granular mixtures during heap formation has important consequences in industry and agriculture. This research investigates three different final particle configurations of bidisperse granular mixtures--stratified, segregated and mixed--during filling of quasi-two-dimensional silos. We consider a large number and wide range of control parameters, including particle size ratio, flow rate, system size, and heap rise velocity. The boundary between stratified and unstratified states is primarily controlled by the two-dimensional flow rate, with the critical flow rate for the transition depending weakly on particle size ratio and flowing layer length. In contrast, the transition from segregated to mixed states is controlled by the rise velocity of the heap, a control parameter not previously considered. The critical rise velocity for the transition depends strongly on the particle size ratio.