(87d) Kinetic Theory Closures with Finite Contact Time for Electrostatic Charge Generation and Transport

Electrostatic charging is a critical phenomenon in systems that manufacture insulating particles because particle collisions with walls or among themselves lead to significant charge accumulation and electric potential difference between the particles and the ground, affecting both the functionality of the production systems and the safety of their operations.

Charge transport models have been developed over the past few years [1–5] to describe the evolution of electrostatic charge in such systems. Our previous work [1,2] focused on Eulerian-Eulerian multi-fluid models with kinetic theory closures for the particulate phase due to their wide adoption to simulate devices of practical interest. Such models have demonstrated charge separation and particle buildup at reactor walls. However, they do not account for finite collision times, between particles. Including such effects modifies the collision frequency, affecting the dissipation of granular energy and, consequently, the fluid dynamic properties of the disperse phase and the rate of charge separation due to particle-particle and particle-wall collisions. Considering finite contact time in the Eulerian model closures for electrostatic charging also addresses an inconstancy present in previously formulated models, where Hertzian collisions with finite contact time are considered in the charge separation model [6], while kinetic theory closures for the hydrodynamic properties of the disperse phase are determined with standard kinetic theory closures [7], assuming instantaneous collisions (t_c=0).

We consider the work of Berzi and Jenkins [8] and leverage their findings to formulate closures for electrostatic charging accounting for finite contact time, whose effect on the prediction of electrostatic charging is then evaluated by comparing the predictions obtained with the new closures to those provided by previously derived closures considering instantaneous collisions.

References

[1] M. Ray, F. Chowdhury, A. Sowinski, P. Mehrani, A. Passalacqua, An Euler-Euler model for mono-dispersed gas-particle flows incorporating electrostatic charging due to particle-wall and particle-particle collisions, Chem. Eng. Sci. 197 (2019) 327–344. https://doi.org/10.1016/j.ces.2018.12.028.

[2] M. Ray, F. Chowdhury, A. Sowinski, P. Mehrani, A. Passalacqua, Eulerian modeling of charge transport in bi-disperse particulate flows due to triboelectrification, Phys. Fluids 32 (2020) 023302. https://doi.org/10.1063/1.5140473.

[3] J. Kolehmainen, A. Ozel, S. Sundaresan, Eulerian modelling of gas–solid flows with triboelectric charging, J. Fluid Mech. 848 (2018) 340–369. https://doi.org/10.1017/jfm.2018.361.

[4] J. Kolehmainen, A. Ozel, C.M. Boyce, S. Sundaresan, A hybrid approach to computing electrostatic forces in fluidized beds of charged particles, AIChE J. 62 (2016) 2282–2295. https://doi.org/10.1002/aic.15279.

[5] L. Ceresiat, J. Kolehmainen, A. Ozel, Charge Transport Equation for Bidisperse Rapid Granular Flows with Nonequipartitioned Fluctuating Kinetic Energy, ArXiv200904503 Phys. (2020). http://arxiv.org/abs/2009.04503 (accessed April 24, 2021).

[6] J.C. Laurentie, P. Traoré, L. Dascalescu, Discrete element modeling of triboelectric charging of insulating materials in vibrated granular beds, J. Electrost. 71 (2013) 951–957. https://doi.org/10.1016/j.elstat.2013.08.001.

[7] J.T. Jenkins, S.B. Savage, A theory of the rapid flow of identical, smooth, nearly elastic spherical particles, J. Fluid Mech. (1983) 187–202.

[8] D. Berzi, J.T. Jenkins, Steady shearing flows of deformable, inelastic spheres, Soft Matter 11 (2015) 4799–4808. https://doi.org/10.1039/C5SM00337G.