Contact Dynamics in a Gently Vibrated Granular Pile

We use multispeckle diffusive wave spectroscopy to probe the micron-scale dynamics of a water-saturated granular pile submitted to discrete gentle taps. The typical time scale between plastic events is found to increase dramatically with the number of applied taps. Furthermore, this microscopic dynamics weakly depends on the solid fraction of the sample. This process is largely analogous to the aging phenomenon observed in thermal glassy systems. We propose a heuristic model where this slowing-down mechanism is associated with a slow evolution of the distribution of the contact forces between particles. This model accounts for the main features of the observed dynamics.

Figure 1

Evolution of the packing fraction for four experimental runs. Each run consists of a first step in which high amplitude taps allow rapid compaction of the sample, followed by a sequence of gentle vibrations, during which the internal dynamics is probed. The arrows indicate the change in tapping intensity, which occurs after (+) 0, (×) 50, (□) 150, (▵) 8000 high impulsion pulses. There is a systematic error of 2% on the measurements of the packing fraction.

Figure 2

Three different correlation functions obtained after three different times $t_w$. Solid lines correspond to experimental values and dashed lines to the stretched exponential fit.

Figure 3

Evolution of the dynamical time $\tau$ with the number of low magnitude taps $t_w$ for different packing fractions ${\phi }_s$.

Figure 4

Results of the numerical model for ${\sigma }_0=1$ and $\overline{\delta \sigma }={\sigma }_0/20$: (a) distributions of normal forces for $t_w=1$, 10, 100, 1000, and 10 000 (from left to right); (b) distributions of tangential forces for ${\sigma }_n={\sigma }_0$ at the same times $t_w$ (from bottom to top).