Gravity-Driven Flux of Particles through Apertures

The gravity-driven discharge of granular material through an aperture is a fundamental problem in granular physics and is classically described by empirical laws with different fitting parameters. In this Letter, we disentangle the mass flux into distinct velocity and packing contributions by combining three-dimensional experiments and simulations. We define a dimensionless flux ratio that captures confinement-driven deviations from a free-fall limit, which is recovered when the aperture is large compared to the grain size. For spherical cohesionless grains, the deviations from the free-fall limit are captured by a single exponential correction factor over a characteristic length scale of ∼10-15 grain diameters. This is shown to be the scale over which the packing structure is modified due to the boundary. Building on the sqrt[gD] exit-velocity scaling, we propose a kinematic framework that explains the universality of granular discharge beyond empirical descriptions.