Controlling Cohesive Particle Mixing and Segregation

We observe experimentally that particle systems that would otherwise mix can be made to segregate and vice versa simply by adding moisture. Using a newly developed theoretical approach, we generate phase diagrams that exhibit both mixed and segregated phases and show how the location of phase boundaries may be manipulated via modifying the mechanical and surface properties of the particles. These results have implications for industrial mixing/separation processes as well as novel particle production methods (e.g., engineered agglomerates with precisely prescribed compositions).

Figure 1

Phase diagram of cohesive mixing/segregation in a binary system. Comparing the three ${\mathrm{B}\mathrm{o}}_{g_{i-j}}$ (1-1, 2-2, 1-2) for varying size ratios and wetting angles (for identical densities) yields a phase diagram of the asymptotic segregation behavior of wet granular materials. Contrary to previous findings, we predict that there are particulate systems whereby segregation may be enhanced by cohesion. The solid lines represent the phase boundary between regions where interstitial moisture mitigates segregation ($M$ phase, dark) and where it enhances segregation ($E$ phase, light). The labeled points correspond to experiments in Figs. 2, 3.

Figure 2

Instant mixing/segregation: just add water. (a) Particles of two differing sizes, but otherwise identical mechanical and surface properties (Fig. 1, point 2b) will segregate strongly when tumbled dry. (b) The same particles can be made to mix through the introduction of a small amount of interstitial moisture. (c) Particles with differing surface properties (red: hydrophilic and green: hydrophobic) but otherwise identical in all other respects [Fig. 1, point(s) 2d; note that the “larger” particle is undefined in this case] will mix perfectly when tumbled dry; however, (d) when interstitial water is added, they will instead segregate.

Figure 3

Varying size ratio and wetting angle. The left and right columns correspond to size ratios of 0.53 and 0.75, respectively. From top to bottom the images represent results when dry: (a),(b); wet with the larger particle (red/orange) being more hydrophobic: (c),(d); wet with both particles hydrophilic: (e),(f); and wet with the smaller particle (red/orange) being more hydrophobic: (g),(h). Results are in agreement with the predictions from theory (Fig. 1). Note that when the smaller particle (red/orange) is more hydrophobic—(g) and (h)—the two size ratios respond differently, as expected.

Figure 4

Varying density ratio. By changing the density ratio the relative size of the $M$ and $E$ phases changes; the $M$ phase grows when the smaller particle is less dense and shrinks when it is more dense. (a) A phase diagram for density ratio of 0.56 (the smaller particle is more dense). The phase boundary is shown as a solid line, while the phase boundary for the inverse case (density ratio of 1.78) is shown as a dashed line, i.e., the lighter gray region becomes part of the $E$ phase. When particles of size ratio 0.9 and wetting angle ratio 0.56 (in the $E$ phase, point c) are tumbled: (b) dry, they will segregate radially only slightly; (c) add water and they segregate more profoundly.