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Eulerian modelling of gas–solid flows with triboelectric charging

Published online by Cambridge University Press:  05 June 2018

Jari Kolehmainen Open the ORCID record for Jari Kolehmainen [Opens in a new window] ,
Ali Ozel  and
Sankaran Sundaresan
Jari Kolehmainen
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08542, USA
Ali Ozel*
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08542, USA School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
Sankaran Sundaresan
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08542, USA
*
†Email address for correspondence: [email protected]
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Abstract

Particles subjected to flow are known to acquire electrostatic charges through repeated contacts with each other and with other surfaces. These charges alter gas–particle flow behaviour at different scales. In this work, we present a continuum framework for analysing the interplay between tribocharging and the flow of a monodisperse assembly of particles characterized by a single effective work function. Specifically, we have derived the continuum, kinetic theory transport equations for gas–particle flow and local-averaged charge on particles directly from the Boltzmann equation. We also derive the auxiliary conditions to capture tribocharging at bounding conducting walls. The resulting two-fluid model with tribocharging and boundary conditions has then been validated against results from discrete element simulations that have been specially designed to probe specific terms in the models.

JFM classification

Multiphase and Particle-laden Flows: Fluidized beds Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 848 , 10 August 2018 , pp. 340 - 369
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Copyright
© 2018 Cambridge University Press 

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References

Al-Adel, M. F., Saville, D. A. & Sundaresan, S. 2002 The effect of static electrification on gas–solid flows in vertical risers. Ind. Engng Chem. Res. 41 (25), 6224–6234.CrossRefGoogle Scholar
Bendimerad, S., Tilmatine, A., Ziane, M. & Dascalescu, L. 2009 Plastic wastes recovery using free-fall triboelectric separator. Intl J. Environ. Stud. 66 (5), 529–538.CrossRefGoogle Scholar
Blissett, R. S. & Rowson, N. A. 2012 A review of the multi-component utilisation of coal fly ash. Fuel 97, 1–23.CrossRefGoogle Scholar
Boateng, A. & Barr, P. 1996 A thermal model for the rotary kiln including heat transfer within the bed. Intl J. Heat Mass Transfer 39 (10), 2131–2147.CrossRefGoogle Scholar
Boelle, A., Balzer, G. & Simonin, O. 1995 Second-order prediction of the particle-phase stress tensor of inelastic spheres in simple shear dense suspensions. ASME FED 228, 9–18.Google Scholar
Carter, D. & Hartzell, C. 2017 Extension of discrete tribocharging models to continuous size distributions. Phys. Rev. E 95 (1), 012901.Google ScholarPubMed
Cercignani, C. 1975 Theory and Application of the Boltzmann Equation. Scottish Academic Press.Google Scholar
Chen, J. & Honaker, R. 2015 Dry separation on coal–silica mixture using rotary triboelectrostatic separator. Fuel Process. Technol. 131, 317–324.CrossRefGoogle Scholar
Chowdhury, F., Sowinski, A., Ray, M., Passalacqua, A. & Mehrani, P. 2018 Charge generation and saturation on polymer particles due to single and repeated particle-metal contacts. J. Electrostat. 91, 9–15.CrossRefGoogle Scholar
Ding, J. & Gidaspow, D. 1990 A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36 (4), 523–538.CrossRefGoogle Scholar
Duff, N. & Lacks, D. J. 2008 Particle dynamics simulations of triboelectric charging in granular insulator systems. J. Electrostat. 66 (1–2), 51–57.CrossRefGoogle Scholar
Fan, F., Tian, Z. & Wang, Z. L. 2012 Flexible triboelectric generator. Nano Energy 1 (2), 328–334.CrossRefGoogle Scholar
Février, P., Simonin, O. & Squires, K. D. 2005 Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech. 533, 1–46.CrossRefGoogle Scholar
Fotovat, F., Alsmari, T. A., Grace, J. R. & Bi, X. T. 2016 The relationship between fluidized bed electrostatics and entrainment. Powder Technol. 316, 157–165.CrossRefGoogle Scholar
Fotovat, F., Bi, X. T. & Grace, J. 2017 Electrostatics in gas–solid fluidized beds: a review. Chem. Engng Sci. 173, 303–334.CrossRefGoogle Scholar
Fox, R. O. 2014 On multiphase turbulence models for collisional fluid particle flows. J. Fluid Mech. 742, 368–424.CrossRefGoogle Scholar
Garzó, V., Tenneti, S., Subramaniam, S. & Hrenya, C. M. 2012 Enskog kinetic theory for monodisperse gas–solid flows. J. Fluid Mech. 712, 129–168.CrossRefGoogle Scholar
Gatignol, R. 1983 The Faxen formulas for a rigid particle in an unsteady non-uniform Stokes-flow. J. Méc. Théor. Appl. 2 (2), 143–160.Google Scholar
Gobin, A., Neau, H., Simonin, O., Llinas, J., Reiling, V. & Sélo, J. 2003 Fluid dynamic numerical simulation of a gas phase polymerization reactor. Intl J. Numer. Meth. Fluids 43 (10–11), 1199–1220.CrossRefGoogle Scholar
Grosshans, H. & Papalexandris, M. V. 2016 Large Eddy simulation of triboelectric charging in pneumatic powder transport. Powder Technol. 301, 1008–1015.CrossRefGoogle Scholar
Grosshans, H. & Papalexandris, M. V. 2017 Direct numerical simulation of triboelectric charging in particle-laden turbulent channel flows. J. Fluid Mech. 818, 465–491.CrossRefGoogle Scholar
Gu, Z., Wei, W., Su, J. & Yu, C. W. 2013 The role of water content in triboelectric charging of wind-blown sand. Sci. Rep. 3 (1), 1337.CrossRefGoogle ScholarPubMed
Harper, W. R.1967 Contact and frictional electrification. PhD thesis, Oxford.Google Scholar
Hassani, M. A., Zarghami, R., Norouzi, H. R. & Mostoufi, N. 2013 Numerical investigation of effect of electrostatic forces on the hydrodynamics of gas–solid fluidized beds. Powder Technol. 246, 16–25.CrossRefGoogle Scholar
Hendrickson, G. 2006 Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting. Chem. Engng Sci. 61 (4), 1041–1064.CrossRefGoogle Scholar
Hogue, M. D., Calle, C. I., Weitzman, P. S. & Curry, D. R. 2008 Calculating the trajectories of triboelectrically charged particles using discrete element modeling (DEM). J. Electrostat. 66 (1–2), 32–38.CrossRefGoogle Scholar
Hsiau, S. S. & Hunt, M. L. 1993 Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows. Trans. ASME J. Heat Transfer 115, 541–548.CrossRefGoogle Scholar
Hunt, M. 1997 Discrete element simulations for granular material flows: effective thermal conductivity and self-diffusivity. Intl J. Heat Mass Transfer 40 (13), 3059–3068.CrossRefGoogle Scholar
Jalalinejad, F., Bi, X. T. & Grace, J. R. 2015 Effect of electrostatics on interaction of bubble pairs in a fluidized bed. Adv. Powder Technol. 26 (1), 329–334.CrossRefGoogle Scholar
Jalalinejad, F., Bi, X. T. & Grace, J. R. 2016 Comparison of theory with experiment for single bubbles in charged fluidized particles. Powder Technol. 290, 27–32.CrossRefGoogle Scholar
Jenkins, J. T. & Mancini, F. 1989 Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys. Fluids A 1 (12), 2050–2057.CrossRefGoogle Scholar
Jenkins, J. T. & Richman, M. W. 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28 (12), 3485–3494.CrossRefGoogle Scholar
Jenkins, J. T. & Richman, M. W. 1986 Grad 13-moment system for a dense gas of inelastic spheres. In The Breadth and Depth of Continuum Mechanics, pp. 647–669. Springer.CrossRefGoogle Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.CrossRefGoogle Scholar
Jones, T. B. & King, J. L. 1991 Powder Handling and Electrostatics. Lewis Publishers Inc.Google Scholar
Karnik, A. & Shrimpton, J. 2012 Mitigation of preferential concentration of small inertial particles in stationary isotropic turbulence using electrical and gravitational body forces. Phys. Fluids 24 (7), 073301.CrossRefGoogle Scholar
Kim, J., Chae, S. S., Han, S. W., Lee, K. H., Ki, T. H., Oh, J. Y., Lee, J. H., Kim, W. S., Jang, W. S. & Baik, H. K. 2016 Triboelectric generator based on a moving charged bead. J. Phys. D: Appl. Phys. 49 (47), 47LT02.CrossRefGoogle Scholar
Koch, D. L. & Sangani, A. S. 1999 Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid Mech. 400, 229–263.CrossRefGoogle Scholar
Kok, J. F. & Lacks, D. J. 2009 Electrification of granular systems of identical insulators. Phys. Rev. E 79 (5), 051304.Google ScholarPubMed
Kolehmainen, J., Ozel, A., Boyce, C. M. & Sundaresan, S. 2016 A hybrid approach to computing electrostatic forces in fluidized beds of charged particles. AIChE J. 62 (7), 2282–2295.CrossRefGoogle Scholar
Kolehmainen, J., Ozel, A., Boyce, C. M. & Sundaresan, S. 2017a Triboelectric charging of monodisperse particles in fluidized beds. AIChE J. 63 (6), 1872–1891.CrossRefGoogle Scholar
Kolehmainen, J., Sippola, P., Raitanen, O., Ozel, A., Boyce, C. M., Saarenrinne, P. & Sundaresan, S. 2017b Effect of humidity on triboelectric charging in a vertically vibrated granular bed: experiments and modeling. Chem. Engng Sci. 173, 363–373.CrossRefGoogle Scholar
Korevaar, M. W., Padding, J. T., Van Der Hoef, M. A. & Kuipers, J. A. M. 2014 Integrated DEM-CFD modeling of the contact charging of pneumatically conveyed powders. Powder Technol. 258, 144–156.CrossRefGoogle Scholar
Lacks, D. J. & Mohan, S. R. 2011 Contact electrification of insulating materials. J. Phys. D: Appl. Phys. 44 (45), 453001.CrossRefGoogle Scholar
LaMarche, K. R., Muzzio, F. J., Shinbrot, T. & Glasser, B. J. 2010 Granular flow and dielectrophoresis: the effect of electrostatic forces on adhesion and flow of dielectric granular materials. Powder Technol. 199 (2), 180–188.CrossRefGoogle Scholar
Laurentie, J. C., Traoré, P. & Dascalescu, L. 2013 Discrete element modeling of triboelectric charging of insulating materials in vibrated granular beds. J. Electrostat. 71 (6), 951–957.CrossRefGoogle Scholar
Laurentie, J. C., Traoré, P., Dragan, C. & Dascalescu, L. 2010 Numerical modeling of triboelectric charging of granular materials in vibrated beds. In Proceedings of Industry Applications Society Annual Meeting (IAS), pp. 1–6.Google Scholar
Lee, V., Waitukaitis, S. R., Miskin, M. Z. & Jaeger, H. M. 2015 Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 11, 733–737.CrossRefGoogle Scholar
Lowell, J. & Rose-Innes, A. C. 1980 Contact electrification. Adv. Phys. 29 (6), 947–1023.CrossRefGoogle Scholar
Lun, C. K. K. & Savage, S. B. 1987 A simple kinetic theory for granular flow of rough, inelastic, spherical particles. Trans. ASME J. Appl. Mech. 54 (1), 47–53.CrossRefGoogle Scholar
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223–256.CrossRefGoogle Scholar
Matsusaka, S., Maruyama, H., Matsuyama, T. & Ghadiri, M. 2010 Triboelectric charging of powders: a review. Chem. Engng Sci. 65 (22), 5781–5807.CrossRefGoogle Scholar
Matsuyama, T. & Yamamoto, H. 1995 Characterizing the electrostatic charging of polymer particles by impact charging experiments. Adv. Powder Technol. 6 (3), 211–220.CrossRefGoogle Scholar
Maxey, M. R. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883.CrossRefGoogle Scholar
McCarty, L. S. & Whitesides, G. M. 2008 Electrostatic charging due to separation of ions at interfaces: contact electrification of ionic electrets. Angew. Chem. Intl Ed. Engl. 47 (12), 2188–2207.CrossRefGoogle ScholarPubMed
McCarty, L. S., Winkleman, A. & Whitesides, G. M. 2007 Ionic electrets: electrostatic charging of surfaces by transferring mobile ions upon contact. J. Am. Chem. Soc. 129 (13), 4075–4088.CrossRefGoogle ScholarPubMed
Mehrotra, A., Muzzio, F. J. & Shinbrot, T. 2007 Spontaneous separation of charged grains. Phys. Rev. Lett. 99 (5), 058001.CrossRefGoogle ScholarPubMed
Mizutani, M., Yasuda, M. & Matsusaka, S. 2015 Advanced characterization of particles triboelectrically charged by a two-stage system with vibrations and external electric fields. Adv. Powder Technol. 26 (2), 454–461.CrossRefGoogle Scholar
Naik, S., Saurabh, S., Vipul, G., Bruno, H. C., Abramov, Y., Yu, W. & Chaudhuri, B. 2015 A combined experimental and numerical approach to explore tribocharging of pharmaceutical excipients in a hopper chute assembly. Intl J. Pharmaceutics 491, 58–68.CrossRefGoogle Scholar
Naik, S., Sarkar, S., Hancock, B., Rowland, M., Abramov, Y., Yu, W. & Chaudhuri, B. 2016 An experimental and numerical modeling study of tribocharging in pharmaceutical granular mixtures. Powder Technol. 297, 211–219.CrossRefGoogle Scholar
Pähtz, T., Herrmann, H. J. & Shinbrot, T. 2010 Why do particle clouds generate electric charges? Nat. Phys. 6 (5), 364–368.CrossRefGoogle Scholar
Park, A. & Fan, L. 2007 Electrostatic charging phenomenon in gas–liquid–solid flow systems. Chem. Engng Sci. 62 (12), 371–386.CrossRefGoogle Scholar
Pei, C., Wu, C.-Y., England, D., Byard, S., Berchtold, H. & Adams, M. 2013 Numerical analysis of contact electrification using DEM-CFD. Powder Technol. 248, 34–43.CrossRefGoogle Scholar
Rahman, M. A. & Saghir, M. Z. 2014 Thermodiffusion or soret effect: historical review. Intl J. Heat Mass Transfer 73, 693–705.CrossRefGoogle Scholar
Rokkam, R. G., Fox, R. & Muhle, M. E. 2010 CFD modeling of electrostatic forces in gas–solid fluidized beds. J. Comput. Multiphase Flows 2 (4), 189–205.CrossRefGoogle Scholar
Rokkam, R. G., Sowinski, A., Fox, R. O., Mehrani, P. & Muhle, M. E. 2013 Computational and experimental study of electrostatics in gas–solid polymerization fluidized beds. Chem. Engng Sci. 92, 146–156.CrossRefGoogle Scholar
Sakiz, M. & Simonin, O. 1999 Development and validation of continuum particle wall boundary conditions using Lagrangian simulation of a vertical gas–solid channel flow. In Proceedings of FEDSM, vol. 99.Google Scholar
Schella, A., Herminghaus, S. & Schröter, M. 2016 Influence of humidity on the tribo-electric charging and segregation in shaken granular media. Soft Matt. 13 (2), 394–401.CrossRefGoogle Scholar
Schiller, L. & Naumann, Z. 1935 A drag coefficient correlation. Vdi Zeitung 77 (318), 51.Google Scholar
Siu, T., Cotton, J., Mattson, G. & Shinbrot, T. 2014 Self-sustaining charging of identical colliding particles. Phys. Rev. E 89 (5), 052208.Google ScholarPubMed
Siu, T., Pittman, W., Cotton, J. & Shinbrot, T. 2015 Nonlinear granular electrostatics. Granul. Matt. 17 (2), 165–175.CrossRefGoogle Scholar
Sowinski, A., Mayne, A. & Mehrani, P. 2012 Effect of fluidizing particle size on electrostatic charge generation and reactor wall fouling in gas–solid fluidized beds. Chem. Engng Sci. 71, 552–563.CrossRefGoogle Scholar
Takada, S., Saitoh, K. & Hayakawa, H. 2016 Kinetic theory for dilute cohesive granular gases with a square well potential. Phys. Rev. E 94 (1), 012906.Google ScholarPubMed
Tanoue, K., Tanaka, H., Kitano, H. & Masuda, H. 2001 Numerical simulation of tribo-electrification of particles in a gas–solids two-phase flow. Powder Technol. 118 (1), 121–129.CrossRefGoogle Scholar
Waitukaitis, S. R., Lee, V., Pierson, J. M., Forman, S. L. & Jaeger, H. M. 2014 Size-dependent same-material tribocharging in insulating grains. Phys. Rev. Lett. 112 (21), 218001.CrossRefGoogle Scholar
Wang, Z. L. 2017 Catch wave power in floating nets. Nature 542 (7640), 159.CrossRefGoogle ScholarPubMed
Wiles, J. A., Fialkowski, M., Radowski, M. R., Whitesides, G. M. & Grzybowski, B. A. 2004 Effects of surface modification and moisture on the rates of charge transfer between metals and organic materials. J. Phys. Chem. B 108 (52), 20296–20302.CrossRefGoogle Scholar
Yang, L. L., Padding, J. T. & Kuipers, J. A. M. 2016a Modification of kinetic theory of granular flow for frictional spheres, part I: two-fluid model derivation and numerical implementation. Chem. Engng Sci. 152, 767–782.CrossRefGoogle Scholar
Yang, L. L., Padding, J. T. & Kuipers, J. A. M. 2016b Modification of kinetic theory of granular flow for frictional spheres, part II: model validation. Chem. Engng Sci. 152, 783–794.CrossRefGoogle Scholar
Yang, Y., Ge, S., Zhou, Y., Sun, J., Huang, Z., Wang, J., Lungu, M., Liao, Z., Jiang, B. & Yang, Y. 2018 Effects of DC electric fields on meso-scale structures in electrostatic gas–solid fluidized beds. Chem. Engng J. 332, 293–302.CrossRefGoogle Scholar
Yang, Y., Zi, C., Huang, Z., Wang, J., Lungu, M., Liao, Z., Yang, Y. & Su, H. 2016c CFD-DEM investigation of particle elutriation with electrostatic effects in gas–solid fluidized beds. Powder Technol. 308, 422–433.CrossRefGoogle Scholar
Yoshimatsu, R., Araújo, N. A. M., Shinbrot, T. & Herrmann, H. J. 2016 Field driven charging dynamics of a fluidized granular bed. Soft Matt. 12 (29), 6261–6267.CrossRefGoogle ScholarPubMed
Yoshimatsu, R., Araújo, N. A. M., Shinbrot, T. & Herrmann, H. J.2017a Segregation of charged particles in shear induced diffusion. arXiv:1705.04113.CrossRefGoogle Scholar
Yoshimatsu, R., Araújo, N. A. M., Wurm, G., Herrmann, H. J. & Shinbrot, T. 2017b Self-charging of identical grains in the absence of an external field. Sci. Rep. 7, 39996.CrossRefGoogle ScholarPubMed
Zelmat, M. E., Rizouga, M., Tilmatine, A., Medles, K., Miloudi, M. & Dascalescu, L. 2013 Experimental comparative study of different tribocharging devices for triboelectric separation of insulating particles. IEEE Trans. Ind. Applics. 49 (3), 1113–1118.CrossRefGoogle Scholar
Zhou, Y. S., Wang, S., Yang, Y., Zhu, G., Niu, S., Lin, Z., Liu, Y. & Wang, Z. L. 2014 Manipulating nanoscale contact electrification by an applied electric field. Nano Lett. 14 (3), 1567–1572.CrossRefGoogle ScholarPubMed