Eulerian modelling of gas–solid flows with triboelectric charging

Abstract

Particles subjected to flow are known to acquire electrostatic charges through repeated contacts with each other and with other surfaces. These charges alter gas-particle flow behavior at different scales. In this work, we present a continuum framework for analyzing the interplay between tribocharging and flow of monodisperse assembly of particles characterized by a single effective work function. Specifically, we have derived the continuum, kinetic theory transport equations for gas-particle flow and local-averaged charge on particles directly from the Boltzmann equation. We also derive the auxiliary conditions to capture tribocharging at bounding conducting walls. The resulting two-fluid model with tribocharging and boundary condition has then been validated against results from discrete element simulations that have been specially designed to probe specific terms in the models.

Modelling of the mean electric charge transport equation in a mono-dispersed gas–particle flow

“…It is also worth noting that this equation is very similar to the one proposed by Kolehmainen et al (2018). However, our model shows an additional contribution of the two last term on the right-hand side.…”

“…In order to close the collision integrals in the mean charge equation, we need to give an expression for the joint charge–velocity two particle number density function . Assuming uncorrelated colliding particle velocities and charges in the frame of the Enskog theory of a dense gas (Chapman & Cowling 1970), Kolehmainen et al (2018) and Ray et al (2019) proposed the following model: where is the radial distribution function and is given by uncorrelated charge and velocity Maxwellian distributions …”

“…However, our model shows an additional contribution of the two last term on the right-hand side. These terms come from the charge–velocity correlation, which is neglected in the Kolehmainen et al (2018) approach (corresponding to ).…”

“…In a previous study conducted by Kolehmainen et al (2018), they suggested that the collisional dispersion coefficient is known to underestimate the dispersion process; and they added a kinetic dispersion coefficient by analogy with particle temperature dispersion in granular flows (Hsiau & Hunt 1993).…”

Triboelectric charging of polyethylene powders: Comparison of same-material and different-material contributions to the charge build-up

“…However, the P\ \P collisions in the model effectively only transfer the (unipolar) charge caused by P\ \W collisions from the wall particles towards the particulate bulk. In other words, it appears that the same-material P\ \P collisions themselves don't produce a bipolar charge, similar to the models in [23,24]. Such description may be representative for the ideal case of systems of spherical particles of uniform size and exactly same material and surface properties (which is in the real case not achievable), but otherwise is in a contradiction with extensive experimental data regarding P\ \P same-material charging.…”