Charging kinetics of a vibrated bed of particles by numerical simulations and experiments

Abstract

Through particle dynamics simulations and experiments, we investigate the charging kinetics of a granular bed in a vibrating cell. The numerical method is based on a theoretical model combining an equation for charge transfer at the particle scale with a theoretical model of charge relaxation. Simultaneously, experiments are carried out to calibrate and validate the numerical model using a vibrated cell with glass beads. Specific charge per unit mass induced by vibrations initially increases before leveling off. Saturation specific charge and charging characteristic time decrease with increasing bed mass. Data collapse onto a master curve is observed when normalizing specific charges and times. At the particle scale, we find that charge saturation results from the balance between charge transfer and relaxation. Saturation specific charge correlates with the relative rate of collisions between particles and the vibrating plate. We introduce a simple expression for the average ballistic time based on single-particle dynamics and a restitution coefficient dependent on bed mass. The characteristic time is proportional to the ballistic time and decreases with increasing bed mass due to more inelastic collisions between particles.