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.
Highlights
Granular materials acquire electrostatic charges after coming into frictional contact with themselves or with other materials
Each solid phase has separate mean velocity, total fluctuating kinetic energy, which is the sum of the granular temperature and the trace of fluctuating kinetic tensor, charge variance and mean charge
The constitutive relations of collisional flux and source terms for momentum, granular temperature and charge balance equations, which account for the rate of change of the quantities between phases and within a phase, are presented
Summary
Granular materials acquire electrostatic charges after coming into frictional contact with themselves or with other materials. To achieve simulations of gas–solid flows with charged particles in larger systems, the kinetic-theory-based Eulerian–Eulerian models ( called two-fluid models) with tribocharging have been recently developed for monodisperse particles (Kolehmainen, Ozel & Sundaresan 2018b; Ray et al 2019) Kolehmainen et al (2018b) validated the constitutive equations for mean charge transfer through hard-sphere simulation results whereas Ray et al (2019) validated the developed models through gas–solid fluidized bed experimental data (Sowinski, Mayne & Mehrani 2012). The developed model predictions are assessed through a set of hard-sphere simulations of bidisperse granular flows with various particle sizes, particle mass ratios and mixture solid volume fractions in a range from 0.2 to 0.4.
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