Kinetic theory closures for electrostatic charge separation and transport accounting for finite contact time

Closure models based on the kinetic theory of granular flows (KTGF) have been recently developed to describe charge separation and transport in granular flows induced by binary collisions between particles, or a particle and a metallic wall. However, the KTGF relies on the assumption of instantaneous collisions, while charge separation models use the Hertzian theory to determine the contact area, assuming deformation and finite contact time. The latter implies lower collision frequency and, consequently, a lower rate of collisional charge transfer. We derive a set of kinetic theory closures for charge separation and transport accounting for finite contact time and show the impact on the prediction of the amount of charge transferred in the case of particle-particle and particle-wall collisions.