Investigating a granular length scale using the central limit theorem

This work proposes a method for determining the length scale for interaction among particles in a granular system. A two-dimensional bidisperse bed of grains is driven by pulses of air and images are taken. The location of each grain is found in every image as well as the volume of space occupied by each grain. The probability distributions of volumes of clusters of neighboring grains are examined. It is found that the cluster distributions do not scale in a way that is consistent with the Central Limit Theorem, indicating that the individual grain volumes are not independent. However, when looking at clusters of grains separated by some distance, the scaling predicted by the Central Limit Theorem is recovered. This use of the Central Limit Theorem thus yields the length scale of correlated grains.