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

TL;DR

This paper derives a charge transport equation for bidisperse granular flows considering nonequipartitioned kinetic energies, using kinetic theory and Maxwellian assumptions, and validates the model with simulations of granular gases and flows.

Contribution

It introduces a novel charge transport model for bidisperse granular flows with nonequipartitioned energies, extending previous hydrodynamic equations and incorporating contact electrification effects.

Findings

Model accurately predicts charge distribution in bidisperse granular flows.

Simulation results validate the derived charge transport equation.

The model captures segregation and charge build-up phenomena.

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-onedimensional spatially inhomogeneous bidisperse granular gases and a three-dimensional segregating bidisperse granular flow with conducting walls.