Local origins of volume fluctuations in granular materials

Recent experiments and simulations have observed that the fluctuations in the local volume fraction, $\phi$, decrease as the granular material approaches jamming. We investigate the role of boundary condition and inter-particle friction, $\mu$, on these fluctuations for a dense bidisperse granular monolayer driven at the perimeter. Using a radical Voronoi tessellation, we find a universal linear relationship between the mean variance of $\phi$ independent of boundary condition and $\mu$. We examine the universality and origins of this trend using the recent granocentric model modified to draw neighbors from an arbitrary distribution $P(s)$, the edge-to-edge distance between neighbors. The mean and variance of the observed particle separation $s$ are described by a single length scale controlled by mean $\phi$. We tested diverse functional forms of $P(s)$ and found that each produces the trend of decreasing fluctuations, but only the experimentally-observed $P(s)$ provides quantitative agreement with the measured $\phi$ fluctuations. In conclusion, we find $P(\phi)$ and $P(s)$ encode similar information about the distribution of free volume in a driven granular system under different boundary conditions and inter-particle friction.