New understanding of the regimes and controlling mechanisms in a falling curtain of particles

Abstract

A stream of free-falling particles from a rectangular hopper, hereafter called a ‘curtain’, was characterised systematically using a well-resolved, non-intrusive optical shadowgraphic method, to reveal both an additional axial region and an additional dilute region distributed laterally on either side of the curtain, relative to those identified previously. The effects of particle size and hopper outlet thickness on the evolution of the particle curtain were separately isolated, whilst measuring particle mass flow rate. The curtains were characterised into four distinct axial regions, namely a near-field expansion region near to the hopper exit, a neck zone where the curtain contracts, a region of intermediate-field expansion and a far field with particles reaching terminal velocity. The initial expansion half-angle, $2.3^{\circ } \le \alpha \le 4.8^{\circ }$ , was found to be insensitive to particle size, but to increase with hopper outlet thickness. The ‘trough’ in the neck zone was deduced to be caused by a pressure gradient driven by particle acceleration. The curtain expansion rate at the intermediate field was found to increase with a decrease in particle size and hopper outlet thickness. The outermost dilute-particle region was deduced to be caused by collisions, induced by gradients in the velocity profile near to the hopper exit. New dimensionless analysis reveals that the dynamics of curtains can be characterised broadly into two regimes, one in which the aerodynamics is dominant and the other where it is weak. Curtain transmittance was found to scale with the Froude number, highlighting the importance of particle momentum.