A Vibrated Compacting Granular System: A DEM Light Scattering Comparison

Abstract

We perform Discrete Element Method (DEM) simulations of granular particles (polystyrene spheres) vibrated inside a cubic container. The study investigates the evolution of the packing fraction with and without rotational friction at different shaking amplitudes. The mean-squared displacement (MSD) is used to analyze the particles' diffusive, subdiffusive, and superdiffusive behavior. By monitoring both the dynamics and density evolution, one can observe the system's glassification. The comparison with experiments shows that the MSDs from the simulations are significantly higher than the MSDs measured by Diffusing Wave Spectroscopy (DWS) \cite{kunzner2025dynamics}. Following our finding that the rotational MSD is of the same order of magnitude as the MSD measured in DWS experiments, we propose that the experimental signal is not dominated by translational motion but rather by rotational particle dynamics. This provides access to a relevant particle property that has previously been difficult to measure directly. Finally, we conclude that the system reaches a dynamically constrained state well before random close packing, with particle displacements already below the Lindemann length.

Figures (6)

• Figure 1: Schematic representation of the simulation setup after sedimentation. The gravitational force $F_g$ acts downward, while the container walls oscillate vertically with amplitude $A$ and angular frequency $\omega$.
• Figure 2: Density evolution of the system for $A=3 \times 10^{-5}$ (blue), $A=2\times 10^{-5}$ (green), and $A=1\times 10^{-5}$ (orange). All lines correspond to the average over at least 7 configurations. The light areas correspond to the uncertainty. In the inset, the black data points correspond to the experimental data from kunzner2025dynamics.
• Figure 3: MSDs of the particles during the shaking process. Bright lines correspond to earlier times, while dark ones correspond to late times. We show the MSDs for different shaking amplitudes $A=3 \times 10^{-5}$ (blue), $A=2\times 10^{-5}$ (green), and $A=1\times 10^{-5}$ (orange). As indicated in the legend, the gray lines for orientation correspond to $t$, and $t^2$, respectively.
• Figure 4: Comparison of translational MSD and rotational MSD for the case of $x_\mu=0.1$ and $\Gamma=1.21$, i.e., tangential forces play a role here. The dashed line is the case $x_\mu=0$ for a comparison. Solid lines correspond to the case of $x_\mu=0.1$. The dotted lines correspond to simulations with $x_\mu=0.1$, but a higher packing fraction ($\phi = 0.604$). For this, we took a configuration from the case $x_\mu$, as discussed in the text, and later switched on the effect of friction. The inset shows the evolution of the density profile, with scatter points at the times where (r)MSDs are measured. The horizontal line corresponds to $\phi = 0.604$.
• Figure 5: Density-dependent parameter deduced from MSD at 0.1 s for agitation amplitudes between $\Gamma = 1.4$ and $\Gamma = 0.4$ without rotational friction (circles) and with rotational friction (diamonds) (a) MSDs and (b) power-law exponents. The dashed line indicates the Lindemann length.