Euler-Euler Model for Charge Transport in Fluidized Beds of Polyethylene Particles

Ray, M., Iowa State University
Passalacqua, A., Iowa State University
Chowdhury, F., University of Ottawa
Sowinski, A., University of Ottawa
Mehrani, P., University of Ottawa


Triboelectric charging encountered in polyethylene production is of deep concern which requires pre-assessment. In this article, a Eulerian model which treats both the solid and gas phases as continuous phases is discussed, which can be used to reasonably predict charge distribution in fluidized beds. The kinetic theory of granular flows has been used to formulate charge diffusion expressions for the monodisperse as well bi-disperse models. The discrete charging model of (Matsusaka, Ghadiri, and Masuda 2000) has been used as the discrete charging model in evaluating the collision integrals. Self-diffusion which assumes non-zero correlation between variance of charge and granular temperature has also been included. For model validation, simulation results were compared to experimental observation in a lab-scale fluidized bed of polyethylene particles. The former predicts that particles less than 450 μm may stick to the wall, while an average layer of 600 μm was seen in the experiments. The model was subsequently modified to simulate bi-disperse particulate flows, based on the work of Jenkins and Mancini (1987). Example results of the same will be presented as well.


A particularly interesting example of triboelectrification is represented by charging of polyethylene particles during production in fluidized bed reactors, where electrostatic charging leads to reactor wall sheeting which can clog the reactor inlet and disrupt the manufacturing process. Electrostatic phenomena can lead to safety issues when high electric potentials develop, which sometimes causes sparks and fire. Numerical modelling to simulate the contribution of charge towards the behavior of fluidized systems has been attempted by few previous authors. Of particular note is the work of Rokkam et al. (2013), who used particles of constant charge magnitudes which varied as a function of particle size, predicting charge-driven preferential segregation in a fluidized bed. Their work was based on the particle charge magnitudes observed by Sowinski (2012), (Andrew Sowinski, Mayne, and Mehrani 2012), who had carried out detailed experiments to test the effect of particle size, fluidizing velocity and wall material on bed electrification. Rokkam’s work, dealt with charge transport through only advection, and neglected diffusion and charge generation. (Kolehmainen, Ozel, and Sundaresan 2018) formulated an Euler-Euler model which includes charge generation from the wall, and modeled the charge diffusion coefficient by analogy to the term found for heat transfer by (Hsiau and Hunt 1993). Particle charge and velocity were assumed to be uncorrelated.

In the present work we account for particle charging in the case of monodisperse particles and derive a charge generation and a charge diffusion model, consistent with the kinetic theory model used to describe the granular flow (Jenkins and Savage 1983), where it is assumed that particle velocity and particle charge are correlated. This leads to the formulation of a charge diffusion coefficient and of a charge source term for the charge transport equation. A wall boundary condition to model particle charging due to collisions of particles with a wall was derived considering wall charging model of Matsusaka et al. (2000) and Matsusaka and Masuda (2003). This led to the formulation of an Eulerian charge model consistent with the boundary conditions for slip velocity and pseudo-thermal granular energy of Johnson and Jackson (1987).


The model developed in this work was applied to a two-dimensional computational domain, representing the laboratory-scale fluidized bed employed by Sowinski (2012)where the effect of different particle sizes was investigated. Three different particle sizes of approximate diameters 362, 462 and 550 μm were used in the simulations. Constant fluidization velocity magnitudes 50% higher than the minimum fluidization velocities were assigned. The simulation was run until steady state values of total bed charge and total electric potential were obtained. Like the experiments, adhesion of particles to the fluid bed wall due to charging was predicted for smaller sized particles (< 450 μm) in preference to larger-sized ones. The average bed charge was shown to increase by over 250% in each case with a sharp boundary layer of about 500 μm thickness forming at the wall. The electric potential developed was also found to be below the Paschen curve for air, thereby eliminating the possibility of electric breakdown. The net bed charge was shown to be negative for all particle sizes tested.


Hsiau, S. S., and M. L. Hunt. 1993. “Kinetic Theory Analysis of Flow-Induced Particle Diffusion and Thermal Conduction in Granular Material Flows.” Journal of Heat Transfer 115 (3): 541–48.

Jenkins, J. T., and S. B. Savage. 1983. “A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Spherical Particles.” Journal of Fluid Mechanics 130 (May): 187.

Johnson, P. C., and R. Jackson. 1987. “Frictional–collisional Constitutive Relations for Granular Materials, with Application to Plane Shearing.” Journal of Fluid Mechanics 176 (March): 67–93.

Kolehmainen, Jari, Ali Ozel, and Sankaran Sundaresan. 2018. “Eulerian Modelling of Gas–solid Flows with Triboelectric Charging.” Journal of Fluid Mechanics 848 (August): 340–69.

Matsusaka, Shuji, Mojtaba Ghadiri, and Hiroaki Masuda. 2000. “Electrification of an Elastic Sphere by Repeated Impacts on a Metal Plate.” Journal of Physics D: Applied Physics 33: 2311–19.

Matsusaka, Shuji, and Hiroaki Masuda. 2003. “Electrostatics of Particles.” Advanced Powder Technology 14 (2): 143–66.

Rokkam, R.G., A. Sowinski, R.O. Fox, P. Mehrani, and M.E. Muhle. 2013. “Computational and Experimental Study of Electrostatics in Gas–solid Polymerization Fluidized Beds.” Chemical Engineering Science 92 (April): 146–56.

Sowinski, A. 2012. “The Study of Reactor Wall Fouling in Gas-Solid Fluidized Beds Caused by Electrostatic Charge Generation.” Thesis dissertation, University of Ottawa.

Sowinski, Andrew, Antonio Mayne, and Poupak Mehrani. 2012. “Effect of Fluidizing Particle Size on Electrostatic Charge Generation and Reactor Wall Fouling in Gas–solid Fluidized Beds.” Chemical Engineering Science 71 (March): 552–63.