We perform granular flow experiments using metal disks falling through a two-dimensional hopper. When the opening of the hopper d is small, jamming occurs due to formation of an arch at the hopper opening. We study the statistical properties of the horizontal component X and the vertical component Y of the arch vector that is defined as the displacement vector from the center of the first disk to the center of the last disk in the arch. As d increases, the distribution function of X changes from a steplike function to a smooth function while that of Y remains symmetrical and peaked at [formula presented] When the arch vectors are classified according to the number of disk n in the arch, the mean value [formula presented] is found to increase with d. In addition, the horizontal component [formula presented] and the absolute value of the vertical component [formula presented] in each class have mean values increasing with n. Regarding the arch as a trajectory of a restricted random walker, we derive an expression for the probability density function [formula presented] of forming an n-disk arch. The statistics [formula presented] and the fraction [formula presented] of n-disk arches) of the arches generated by [formula presented] agree with those found in the experiment.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - 29 Jul 2002|