Correlation between Particle Motion and Voronoi-Cell-Shape Fluctuations during the Compaction of Granular Matter

We track particle motions in a granular material subjected to compaction using a laser scattering-based imaging method where compaction is achieved through thermal cycling. Particle displacements in this jammed fluid correlate strongly with rearrangements of the Voronoi cells defining the local environment about the particles, similar to previous observations of Rahman on cooled liquids. Our observations provide further evidence of commonalities between particle dynamics in granular matter close to jamming and supercooled liquids.

Figure 1

Experimental setup: Glass beads immersed in index-matching oil in a cylinder are subjected to thermal cycling via a water bath. The fluorescently dyed fluid is imaged via a laser sheet that is moved across the sample. One of 600 cross-sectional images shown.

Figure 2

Packing fraction vs cycle number for various temperature differentials. $\tau =5.2\pm 0.4\mathrm{\text{cycles}}$ for $\Delta T=25°\mathrm{C}$, $\tau =4.9\pm 0.3\mathrm{\text{cycles}}$ for $\Delta T=40°\mathrm{C}$, and $\tau =3.8\pm 0.3\mathrm{\text{cycles}}$ for $\Delta T=60°\mathrm{C}$.

Figure 3

Histogram of Voronoi-cell volumes. Inset: Pair correlation function $g(r)$ averaged over 10 thermal cycles.

Figure 4

Definition of particle displacement vector $v$ and $u$ vector for a cross section of the 3D Voronoi-cell volume.

Figure 5

(a) Preferred direction probability distribution functions (PDFs) for a system with $\Delta T=40°\mathrm{C}$ for each thermal cycle. (b) Preferred direction PDFs for a system with $\Delta T=25°\mathrm{C}$ for each thermal cycle. (c) Preferred direction PDFs for a system at constant temperature. (d) 3D reconstruction of a system from the perspective of a given particle facing five vertices of its Voronoi cell. Notice that the vertex is located in the void between particles.