Charge Transport Equation for Bidisperse Rapid Granular Flows with Nonequipartitioned Fluctuating Kinetic Energy

Starting from the Boltzmann-Enskog kinetic equations, the charge transport equation for bidisperse rapid 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, an isotropic 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 are 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 validated through hard-sphere simulations of three-dimensional spatially homogeneous and quasi-one-dimensional spatially inhomogeneous bidisperse granular gases.