110th Anniversary: Effect of System Size on Boundary-Driven Contact Charging in Particulate Flows

We study wall-induced triboelectrification of particles by analyzing a continuum model for charge transport. We first consider an idealized case of homogeneous distribution of granular materials in a periodic channel and show that the domain-average charge per particle is inversely proportional to the channel size. We then perform three-dimensional simulations of fluidized beds in quasi-periodic channels and cylinders by coupling the charge transport equation with a two-fluid model for flow. In both cases, the domain-average charge per particle varies inversely with a characteristic size, namely, the channel width and the tube diameter, respectively, just as in the idealized case. The effect of tribocharging at the wall on the flow becomes rather weak even for channel widths and tube diameters of only 100 particle diameters. This implies that the effect of tribocharging at the walls in most flow problems will be limited only to a small boundary layer near the walls.