Competition between geometrically induced and density-driven segregation mechanisms in vibrofluidized granular systems

The behaviors of granular systems are sensitive to a wide variety of particle properties, including size, density, elasticity, and shape. Differences in any of these properties between particles in a granular mixture may lead to segregation, or “demixing,” a process of great industrial relevance. Despite the known influence of particle geometry in granular systems, a considerable fraction of research into these systems concerns only uniformly spherical particles. We address, for the case of vertically vibrated granular systems, the important question of whether the introduction of differing particle geometries entirely invalidates our existing knowledge based on purely spherical granulates, or whether current models may simply be adapted to account for the effects of particle shape. We demonstrate that while shape effects can indeed influence the dynamical and segregative behaviors of a granular system, the segregative mechanisms associated with particle geometry are decidedly secondary to those related to particle density. The relevant control parameters determining the extent of geometrically induced segregation are established. Finally, a manner in which shape effects may be accounted for in simulations utilizing purely spherical particles is proposed.

Figure 1

Top: Scale diagrams showing the dimensions of the three differing particle geometries used in experiment: spherical (left), disklike (horizontal center), and cuboidal (right). For each particle type, plan (top) and side (bottom) views are shown (due to the symmetry of the particles used, the end view is, clearly, redundant). Bottom: Photographic images of the particles represented above. Closeup images of the particles' surfaces acquired using scanning electron microscopy may additionally be seen in Fig. 2.

Figure 2

Scanning electron microscope (SEM) images showing the surface topography of (a) spherical, (b) cuboidal, and (c) disklike steel particles.

Figure 3

Schematic diagram (not to scale) of the experimental system from which data are obtained. For simplicity, only a monodisperse bed of spherical particles is represented.

Figure 4

Two-dimensional velocity vector fields for (a) a system of steel squares and spheres driven with a frequency $f=40$ Hz and amplitude $A=1.67$ mm, showing the randomized flow field typical of all systems explored, and (b) a similar system of horizontal extent $L_{x,y}=100$ mm whose sidewalls are composed of (highly dissipative) lead.

Figure 5

One-dimensional vertical packing profiles for various bidisperse-by-shape systems: (a) spheres (solid line) and cuboids (dashed line) driven with a frequency and amplitude of 40 Hz and 1.67 mm, respectively; (b) cuboids (solid line) and disklike particles (dashed line) driven with the same $f$ and $A$; (c) spheres (solid line) and cuboids (dashed line) driven with $f=100$ Hz and $A=0.67$ mm; (d) spheres (solid line) and cuboids (dashed line) driven with $f=80$ Hz and $A=0.42$ mm, producing an equal $\Gamma$ value to case (a), but with a reduced $V$. In all cases, $N=1800$ and $L_{x,y}=80$ mm. Although, for clarity, error bars are not included in the images presented, it is worth noting that the calculated $\eta$ values for any given region of space carry errors of less than $5\%$, with the exception of the most dilute regions $\left(\eta <0.01\right)$, where the low particle density will clearly result in greater statistical noise. Results are shown for both experiment [orange (light gray)] and simulation (black). Details regarding the manner in which the simulations shown approximate the effects of the particles' nonspherical geometries may be found in Sec. 4c.

Figure 6

Packing profiles [blue (dark gray)] from Figs. 5 and 5 replotted alongside their respective vertical temperature distributions [orange (light gray)]. In all instances, data corresponding to the lighter species are represented by a dotted line, and the heavier species are shown by a solid line.

Figure 7

Experimental data showing the variation of segregation intensity, $I_s$, with differing driving parameters. Data are shown for systems comprising cuboidal and spherical particles (circles) as well as for systems composed of disks and spheres (triangles). In each case, the blue dashed lines denote data sets in which $V$ is varied at a fixed acceleration $\Gamma =12$ and the red dotted lines represent cases in which $V$ is held constant at $V=0.19$ while $\Gamma$ is adjusted. For all data shown, $N=2400$ and $L_{x,y}=60$.

Figure 8

Vertical packing profiles for systems comprising particles of equal volume, but differing in both geometry and material density. Data are shown for (a) steel and nylon spheres $\left(I_s=0.42\right)$, (b) steel cuboids and nylon spheres $\left(I_s=0.67\right)$, (c) steel cuboids and glass spheres $\left(I_s=0.41\right)$, and (d) steel cuboids and nylon disklike particles $\left(I_s=0.86\right)$. Systems (a)–(c) are driven at a frequency of 65 Hz and an amplitude of 1.03 mm, and they consist of $N=1800$ particles. System (d) is driven at $f=40$ Hz, $A=3.57$ mm. For each image, the heavier component is represented by a solid line, and the lighter component is represented by a dashed line; orange (light gray) lines denote experimental data, while simulated results are shown in black.