  We propose an Eulerian formulation for the triboelectric charging of powder
flows. Recently, continuum descriptions of the charging of monodisperse and
bidisperse powder appeared. Now, we propose the first Eulerian formulation for
this type of flows that can fully account for polydisperse particle size
distributions. To this end, the joint particle size, velocity, and charge
distribution function is solved through the direct quadrature method of
moments. The newly established approach includes the uptake of electrostatic
charge by the particles when contacting a solid wall and the exchange of charge
in-between particles during collisions. The electrostatic field induced by the
charge of the particles and the drag forces of the surrounding gas affect the
particle dynamics. Test cases of two-dimensional steady channel flows
demonstrate the charging of the flow from the walls towards the center and in
downstream direction. Further, the method predicts the effect of variations of
the particle size and initial velocity distribution and the charge diffusion
coefficient. The ability to handle polydispersity is a step towards the
simulation of the electric charge build-up of real powder flows in full-scale
technical applications.
