Suppression and Emergence of Granular Segregation under Cyclic Shear

While convective flows are implicated in many granular segregation processes, the associated particle-scale rearrangements are not well understood. A three-dimensional bidisperse mixture segregates under steady shear, but the cyclically driven system either remains mixed or segregates slowly. Individual grain motion shows no signs of particle-scale segregation dynamics that precede bulk segregation. Instead, we find that the transition from nonsegregating to segregating flow is accompanied by significantly less reversible particle trajectories and the emergence of a convective flow field.

Figure 1

(a) The split-bottom shear cell and a sample horizontal cross section (an aligned second laser sheet and a high sensitive camera that captures images from the top down are not pictured). (b) Sample trajectories of a small (light green to dark blue) and large (light yellow to dark red) grain under steady shear. The black circle represents the shearing disk.

Figure 2

Cross sections of the granular pile at 3.8 cm above the shearing disk, or about 2 large grain diameters from the free surface, (a) in the initial mixed state and (b) after 29.3 revolutions of the shearing disk. Large red and small blue circles represent large and small grains, respectively.

Figure 3

(a) Volume fractions of large and small grains under all shearing procedures considered: steady (red $+$’s and blue $\times$’s), ${\theta }_r=10°$ (filled orange and empty cyan circles), and ${\theta }_r=40°$ (filled gold and empty green squares) in the top 60% of the pile, directly above the shearing disk. Inset: Same as (a), but showing only steady shear and including total volume fraction (black asterisks). (b) The average rate of change of $\varphi$ of large and small grains for $|\Delta \theta |\ge 1000°$.

Figure 4

(a) Fraction of broken grain contacts and (b) MSDs over a single cycle versus that particular cycle number.

Figure 5

Time- and $\theta$-averaged flows of large (dark red arrows) and small (light cyan arrows) grain flows plotted together for all shearing procedures considered: (a) steady, (b) ${\theta }_r=10°$, and (c) ${\theta }_r=40°$. Vectors are scaled such that the grid spacing corresponds to $5.6\times {10}^{-3}\mathrm{mm}/\mathrm{degree}$ shear. (d) Average magnitude of secondary flow vectors within the shear zone outer boundary [black curves in (a)–(c)].

Figure 6

For ${\theta }_r=10°$, reversible secondary flows can be seen when averaging over (a) positive and (b) negative strain. For ${\theta }_r=40°$, such a strong distinction cannot be made between (c) positive and (d) negative strain. Flow vectors are shown on the same scale as in Fig. 5.