It has been known for centuries that during a mechanical contacts materials may develop static charges. This phenomenon is observed when one rubs a balloon against wool cloth, and observes the balloon sticking to the cloth and is known as tribocharging. It has also been known for decades that granular material in transport lines and fluidized beds tend to create charges \cite{lacks_contact_2011}. This charging may cause spark generation leading even to powder explosions \cite{jones_king_1991}. Triboelectric charging is generally been considered unwanted phenomenon, such as particle wall fouling in polyethylene reactors \cite{hendrickson_electrostatics_2006}, but is also crucial in certain applications such as photocopying and laser printing where toner particles are charged via triboelectric charging.
Triboelectric charging is still very poorly understood phenomenon and multiple different mechanism have been proposed for this in past decades \cite{lacks_contact_2011}. The most widely cited mechanism for the tribocharging is electron transfer \cite{harper_1967}, where the charge transfer is believed to happen due to electrons transfering from material surface to another material surface. While this mechanism is found to be in good agreement with experiments for metals, there is some debate weather it is applicable to insulators \cite{mccarty_electrostatic_2008}.
In electron transfer model materials tendency to pick up charges is described by a work function value. For metals this work function value is defined as the energy needed to remove one electron form the metal surface \cite{harper_1967}. For insulators this work function value correlates poorly with the tribocharging behavior, and instead effective work function value is often used to describe the charging behavior of insulators in numerical simulations \cite{laurentie_numerical_2010}. Unfortunately, there is no direct way to measure the effective work function value due to its vague definition.
Moreover, it is well-known that the triboelectric charging of insulators depends on the ambient humidity \cite{gouveia_electrostatic_2009} and on the particle size \cite{sowinski_investigation_2010,forward_charge_2009,zhao_bipolar_2003}. It is not straght forward to determine these effects and the effective work function would need to modelled for these parameters. There has also been more direct simulation approaches to take the insulator charge size dependency into account by modelling the electrons on the particle surface \cite{duff_particle_2008} or by introducing high and low energy electrons \cite{kok_electrification_2009}. While these models can capture the size dependency to some extent, it is hard to incorporate charge transfer of different materials into these models. Furthermore, modelling the electrons in the particle surface is computationally very demanding and not suitable for fluidized bed simulations with more than thousand particles.
It was proposed in \cite{laurentie_discrete_2013} that the effective work function value could be determined from macroscopic charging behavior. Laurentie et. al. charged the particles by a vibrated bed, and determined run series of simulations with various effective work function values to match the simulations and experiments. The determined work function value was validated by similar experiments, and the results showed very good agreement. For these reasons, this study will also base the triboelectric charging behavior to effective work functions as they seem a promising tool for simulating triboelectric charging.
There has been multiple studies concentrating in electrostatic effects on fludized beds. Earlier computational studies were based on Eulerian-Eulerian simulations that model the solid and gas phase as continuum \cite{rokkam_computational_2010,jalalinejad_effect_2012}. These studies assumed constant charge on particles, and solved the electric field by solving a Poisson equation for electric potential. If the permittivity of the varying solid content is taken into account the large scale electric field can be solved accurately \cite{rokkam_computational_2010}. These studies found that the electrostatics altered the bubbling behavior of fluidized beds by squeezing bubbles at the center of the bed \cite{rokkam_computational_2010,jalalinejad_electro-hydrodynamics_2013,jalalinejad_effect_2015}.
The shortcoming of the Eulerian-Eulerian approach is that it require additional modeling for particle drag and particle stresses since the local electrostatic effects may alter these parameters. These local effects have not been addressed in any of these simulations. Furthermore, it is not easy to simulate non uniform charge distributions with Eulerian-Eulerian simulations. To overcome this recent article \cite{hassani_numerical_2013} simulated bubbling fluidized bed by employing four-way-coupled CFD-DEM simulations that model particles individually, and use Eulerian modeling for the solid phase. The study used also predefined charges on particles and considered both monodisperse (same charge on all the particles) and bidisperse case where particles had different prefixed charges.
In the article \cite{hassani_numerical_2013} concluded that the bubble size decreased with introduction of charge on particles in mono charged case that is in-line with the Eulerian studies of Jalalinejad \cite{jalalinejad_effect_2012,jalalinejad_electro-hydrodynamics_2013,jalalinejad_effect_2015}. In the bidisperse case, the oppositely charged particles formed chains inside the bubbling bed, and interestingly caused the bubbles that were similar to the neutrally charged case.
The aim of this study is to inspect the interplay between the triboelectric charging and electrostatic effects. The triboelectric model chosen was similar to \cite{laurentie_discrete_2013} while the electrostatic force was modelled in a similar way to \cite{hassani_numerical_2013}. The fluidization regime was chosen slightly above the bubbling regime as its more relevant for polyethylene reactors.