Gravity driven flux of particles through apertures

When an assembly of particles is placed over an aperture the drainage flux of particles through is observed to be constant. We present a physical framework for such gravity-driven flows based on free-fall kinematics and boundary-layer corrections. A wide range of experiments and DEM simulations of relative aperture sizes are used to characterize the effects of confinement through the ratio of aperture to grain size, $D/d$. For large $D/d$, the mean velocity and packing are shown to be described by simple universal forms. Consequently, a complete description is provided for spherical, relatively mono-dispersed particles, falling through circular apertures, identifying the effects on confinement on the relevant physical ingredients. An expression for flux, with one introduced parameter - defining the extent of boundary influence - is presented. This framework is extended to more complex aperture shapes, and some results on non-spherical grains are also discussed. Effects of interparticle adhesion on flux are also studied with additional experiments and simulations. Finally, the structure of gravity-driven discharge spanning from the dilute to the dense jets is also explained using free-fall kinematics and aperture geometry.