Mixing and segregation rates in sheared granular materials

The vertical size segregation of granular materials, a process commonly associated with the Brazil-nut effect, has generally been thought to proceed faster the greater the size difference of the particles. We experimentally investigate sheared dense bidisperse granular materials as a function of the size ratio of the two species and find that the mixing rate at low confining pressure behaves as expected from percolation-based arguments. However, we also observe an anomalous effect for the resegregation rates, wherein the segregation rate is a nonmonotonic function of the particle size ratio with a maximum for intermediate particle size ratio. Combined with the fact that increasing the confining pressure significantly suppresses both mixing and segregation rates of particles of sufficiently dissimilar size, we propose that the anomalous behavior may be attributed to a species-dependent distribution of forces within the system.

Figure 1

(Color online) (a) Schematic of experimental apparatus (not to scale) showing initial configuration of particles within the annulus. Sample images taken at window for $d_S=4\text{mm}$ (dark particles) and $d_L=6\text{mm}$ (light particles): (b) initial configuration, (c) mixed state, and (d) final resegregated state.

Figure 2

(Color online) Sample cell height data for $r=2/6$ and $\tilde{P}=0.36$. An averaging window of 0.5 s was used to smooth the raw signal. (a) Cell height $H\left(t\right)$ with values $H_{\text{min}}$, $H_{\text{f}}$, and $t_0$ marked. (b) Magnified portion of $H\left(t\right)-H_{\text{min}}$ showing fit to determine mixing time scale ${\tau }_m$. (c) Magnified portion of $H_{\text{f}}-H\left(t\right)$ showing fit to determine segregation time scale ${\tau }_s$.

Figure 3

(Color online) (a) Mixing time scale ${\tau }_m$ (○, left axis) and segregation time scale ${\tau }_s$ (▲, right axis) as function of particle size ratio $r$. (b) Mixing rate ${\Omega }_m$ (○, left axis) and segregation rate ${\Omega }_s$ (▲, right axis) as function of particle size ratio $r$. The error bars represent the standard error among at least five independent measurements. All data are collected at $\tilde{P}=0.36$.

Figure 4

(Color online) (a) Mixing rate ${\Omega }_m$ as a function of scaled pressure for $r=2/6$ (▽) and $r=5/6$ (◻). (b) Segregation rate ${\Omega }_s$ as a function of scaled pressure for $r=2/6$ (▼) and $r=5/6$ (◼). The error bars represent the standard error among at least three independent measurements. The dashed line is $\tilde{P}=0.36$, which coincides with data from Fig. 3.