Local Packing Fraction Statistics in a Two-Dimensional Granular Media

We experimentally investigate local packing fraction statistics of a two-dimensional bidisperse granular material supported by a horizontal air table and rearranged under impulses from the boundary. Our apparatus permits investigation of dense liquids close to the jamming transition under either constant pressure (CP) or constant volume (CV) boundary conditions and three different coefficients of friction. We calculate the probability distribution of the local packing fraction $\phi$ using both radical Voronoi tessellations ($\phi_{V}$) and the Central Limit Theorem ($\phi_{CLT}$). The two distributions have the same mean: $\langle \phi_{V}\rangle=\langle \phi_{CLT} \rangle$. For both methods, we observe that the variance strictly decreases as the mean increases; the functional dependence reveals information about the system. The variance of $\phi_{V}$ is larger under CP than CV, as expected since the cell volumes adjust to fluctuations in global volume. Interestingly, this feature is missing from $\phi_{CLT}$. Instead, the variance of $\phi_{CLT}$ is sensitive to the internal friction of the system.