Disentangling the Free-Fall Arch Paradox in Silo Discharge

Abstract

Several theoretical predictions of the mass flow rate of granular media discharged from a silo are based on the spontaneous development of a free-fall arch region, the existence of which is still controversial. In this Letter, we study experimentally and numerically the particle flow through an orifice placed at the bottom of 2D and 3D silos. The implementation of a coarse-grained technique allows a thorough description of all the kinetic and micromechanical properties of the particle flow in the outlet proximities. Though the free-fall arch does not exist as traditionally understood - a region above which particles have negligible velocity and below which particles fall solely under gravity action - we discover that the kinetic pressure displays a well-defined transition in a position that scales with the outlet size. This universal scaling explains why the free-fall arch picture has served as an approximation to describe the flow rate in the discharge of silos.