Eliminating Segregation in Free-Surface Flows of Particles

By introducing periodic flow inversions, we show both experimentally and computationally that forcing with a value above a critical frequency can effectively eliminate both density and size segregation. The critical frequency is related to the inverse of the characteristic time of segregation and is shown to scale with the shear rate of the particle flow. This observation could lead to new designs for a vast array of particle processing applications and suggests a new way for researchers to think about segregation problems.

Figure 1

A schematic representation of the (a) zigzag chute thought experiment, along with the (b) model simulation and (c) experiment used to approximate it. (a) In a vertical gravity field, the chute changes direction periodically so that the material becomes roughly inverted. (b) In our simulations, we use a simple model of this whereby the system is periodic in the flow direction and the inclined gravitational field, ${\overrightarrow{g}}_f$, has an oscillatory $y$ component. (c) Experimentally, in order to achieve an asymptotic concentration distribution in a modest-size system we put particles in a square tube which is first rocked, then rotated in order to alter the sense of gravity [taking advantage of particles’ tendency to behave like a solid during the rotate step by angling the tube at $\theta \gg \alpha$ (repose angle) during the rotate step].

Figure 2

Results from our models of the zigzag chute. (Left) Plotting our experimental results as a function of tube aspect ratio versus density ratio, we obtain agreement with theory for three different density ratios. Here the line is a plot of Eq. (2) with $\beta =1.06$, the solid circles denote mixed systems, and the open circles denote segregated systems. (Right) Under a wide range of conditions, our computational results show high (low) values of IS when $f/f_{\mathrm{crit}}$ is less (greater) than 1. The closed circles denote simulations using a density ratio of 0.25, while the squares represent 0.5. Lines through the points show the standard deviation of the shear rate calculation.

Figure 3

Images (a)–(f) show particle positions from DEM simulations for an unbaffled tumbler (a)–(c) and a tumbler with a single axially-located baffle (d)–(f). The light colored particles are in the fixed bed portion of the flow (low velocity relative to the tumbler wall), while the darker gray particles are in the flowing layer. At the outset of the simulations, we “tag” a vertical line of particles within the flowing layer and denote their original orientation with a black arrow (see frames (a) and (d). In the other frames, the green arrows denote the future average position and orientation of the initially tagged particles as they move through the bed. The broken, red arrow in frame (f) represents a particle orientation that has “folded” upon itself (i.e., the orientation contains a loop from a partial layer pass). Note that the orientation of the arrow in the unbaffled case both leaves and enters the flowing layer almost perfectly tangent, while the orientation of the arrow in the baffled case is rotated roughly 90°. The plot on the right shows the distribution of rotations between particle layer passes for various tumbler configurations. The black symbols represent the unbaffled case and a case with (short) traditional baffles, both of which have very narrow distributions centered on 0.5 rotations. In contrast the axially located baffles (green and blue symbols) or long traditional baffles (red symbols) result in much broader distributions, suggesting that the orientation of particles in future layer passes should be almost uncorrelated with previous passes. Note that we define long traditional baffles as those that actually transversely cut a portion of the flowing layer, much like the axially oriented baffles.

Figure 4

Asymptotic mixing results in tumbler mixers for both size (left) and density (right) segregation. Unbaffled tumblers [(a) and (b), experiments; (c) and (d), simulations] result in strong radial segregation. In contrast, baffles that truncate the flowing layer [shown experimentally in (e) and (f), and computationally in (g) and (h)] dramatically reduce the degree of segregation. For comparison, computational results for a traditional baffle arrangement are shown in (i) and (j).

Figure 5

Quantitative mixing results in tumbler mixers for both density (top) and size (bottom) segregation. Experiments are shown as symbols and simulations as lines. Note that unbaffled mixers and mixers with short baffles behave very similarly, while axial baffles or very long traditional baffles results in significantly lower IS values (increase the degree of mixing).