No abstract

Starting from the Boltzmann–Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances for each solid phase. To close locally averaged transport equations, a Maxwellian distribution is presumed for both particle velocity and charge. The hydrodynamic equations for bidisperse solid mixtures are first revisited and the resulting model consisting of the transport equations of mass, momentum, total kinetic energy, which is the sum of the granular temperature and the trace of fluctuating kinetic tensor, and charge is then presented. The charge transfer between phases and the charge build-up within a phase are modelled with local charge and effective work function differences between phases and the local electric field. The revisited hydrodynamic equations and the derived charge transport equation with constitutive relations are assessed through hard-sphere simulations of three-dimensional spatially homogeneous, quasi-one-dimensional spatially inhomogeneous bidisperse granular gases and a three-dimensional segregating bidisperse granular flow with conducting walls.

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.