Charge transport equation for bidisperse collisional granular flows with non-equipartitioned fluctuating kinetic energy

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.

Kinetic theory of granular particles immersed in a molecular gas

“…Another challenging work could be the determination of the non-Newtonian rheological properties of a granular suspension under simple shear flow. This study would allow the extension of previous studies (Tsao & Koch 1995;Sangani et al 1996;Chamorro et al 2015;Saha & Alam 2017;Alam et al 2019;Takada et al 2020) to arbitrary values of the mass ratio m/m g . The accuracy of the results for the shear viscosity can be tested by means of DSMC simulations.…”

“…For instance, by performing local deviations of the velocity field from its value in the homogeneous state and analysing the relaxation process (Brey, Ruiz-Montero & Cubero 1999 b ; Brey & Cubero 2001). Another possible project could be to revisit the results obtained in this paper by considering the charge transport equation recently considered by Ceresiat, Kolehmainen & Ozel (2021). Work along these lines will be carried out in the future.…”

“…Beyond the Navier-Stokes domain, this type of suspension model has also been considered to compute the rheological properties in sheared gas-solid suspensions (see e.g. Tsao & Koch 1995;Sangani et al 1996;Parmentier & Simonin 2012;Heussinger 2013;Seto et al 2013;Kawasaki, Ikeda & Berthier 2014;Chamorro, Vega Reyes & Garzó 2015;Hayakawa, Takada & Garzó 2017;Saha & Alam 2017;Alam et al 2019;Hayakawa & Takada 2019;Saha & Alam 2020;Takada et al 2020).…”

Charge–velocity correlation transport equations in gas–solid flow with triboelectric effects

“…In recent years, some efforts have been directed towards developing predictive mathematical tools capable of modelling the effect of this force in gas-solid flows (Chowdhury et al 2021). Rokkam, Fox & Muhle (2010) and Rokkam et al (2013) were among the first to propose the use of an Eulerian approach for a fluidized bed with electrostatic forces.…”

“…Multiple strategies are possible to overcome this problem. One can neglect them altogether (Ceresiat, Kolehmainen & Ozel 2021). A first-order approximation can be made by making an analogy with the heat transfer coefficient (Kolehmainen et al 2018b).…”