Experimental Study of Ordering of Hard Cubes by Shearing

We experimentally analyze the compaction dynamics of an ensemble of cubic particles submitted to a novel type of excitation. Instead of the standard tapping procedure used in granular materials we apply alternative twists to the cylindrical container. Under this agitation, the development of shear forces among the different layers of cubes leads to particle alignment. As a result, the packing fraction grows monotonically with the number of twists. If the intensity of the excitations is sufficiently large, an ordered final state is reached where the volume fraction is the densest possible compatible with the boundary condition. This ordered final state resembles the tetratic or cubatic phases observed in colloids.

Figure 1

Experimental cell and sketch of the twist excitation. The pictures show the initial (left) and final (right) states for a ensemble of 25 000 cubes submitted to $N=3\times {10}^5$ twists of intensity $\mathrm{\Gamma }=1.01$.

Figure 2

(a) Lateral view of the cell after different numbers of twists $N$. The green dotted lines indicate the mean height used to calculate the packing fraction $\varphi$. In the inset, the green shadows correspond to the area used to calculate the lateral volume fraction $\phi$, and the arrows define the dice orientation with respect to the horizontal ${\mathbf{u}}_i$. (b) Packing fraction $\varphi$ versus $N$ in logarithmic scale for various $\mathrm{\Gamma }$ as indicated in the legend. (c) Evolution of the lateral volume fraction $\phi$ as a function of $N$ for the same values of $\mathrm{\Gamma }$.

Figure 3

Free surface after $N=1\times {10}^5$ twists for (a) $\mathrm{\Gamma }=0.31$ and (b) $\mathrm{\Gamma }=1.01$. The central region has been amplified to remark the difference between both final states. More detailed images can be found in Ref. [23].

Figure 4

Dice orientations distribution $pdf(\theta )$ vs $N$ for (a) $\mathrm{\Gamma }=0.31$, and (b) $\mathrm{\Gamma }=1.01$. The bottom, middle, and top curves correspond, respectively, to the distributions obtained for the bottom, middle, and top regions of the cell. (c) Cubatic index $S_4$ vs $N$ for three values of $\mathrm{\Gamma }$ as indicated in the legend. (d) Cubatic index $S_4$ versus lateral volume fraction $\phi$ for several values of $\mathrm{\Gamma }$ as indicated in the legend.

Figure 5

(a) Orientational spatial correlation function $G_4(r)$ for low and high values of $\mathrm{\Gamma }$ after different numbers of twists $N$ as indicated in the legend. $r$ is the distance normalized by the cube’s side length. (b) Sketch of the cube’s ordering phase diagram. The black squares correspond to states where, after $N=3\times {10}^4$ twists, the lateral volume fraction is maximum; the open diamonds indicate states where different cluster orientations coexist. The dotted line is a guide for the eyes.