Discrete-element method for particle capture by a body in an electrostatic field. (English) Zbl 1202.78033
Summary: A discrete-element method is developed for applications involving interaction of spherical particles with a body of arbitrary shape in an electrostatic field. The electric field is induced both by charged particles and by other ’macroscopic’ bodies (e.g. electrodes). The electric field due to macroscopic bodies is computed using a boundary-element method that accounts for the particle influence. An algorithm using approximate particle images is introduced to improve electric field resolution for particles lying close to the body surface. The long-range electric field induced by particles is computed using an optimized, adaptive multipole expansion method. The method is applied to the formation of chain-like particle aggregates, with long-range particle attraction governed by the electric field and particle adhesion by van der Waals forces. The method is illustrated by simulation of the capture of uncharged particles on a cylindrical electrode. A local panel subdivision method is developed to mitigate particle drift toward panel edges induced by panel discretization errors. The particle deposition pattern at different cylinder surface charge levels is studied, which shows that long straight particle chains are formed under strong electric fields. The predicted particle capture efficiency agrees well with the experimental data.
MSC:
| 78M25 | Numerical methods in optics (MSC2010) |
| 78A30 | Electro- and magnetostatics |
Keywords:
discrete-element method; dielectrophoretic force; boundary-element method; electrostatic fieldReferences:
| [1] | Oak, Particle capture on fibers in strong electric fields. I. Experiment studies of the effects of fiber charge, fiber configuration and dendrite structure, Journal of Colloid and Interface Science 106 pp 490– (1985) |
| [2] | Oak, Particle capture on fibers in strong electric fields. II. An experimental test of a theory for the capture of uncharged particles on charged fibers, Journal of Colloid and Interface Science 106 pp 502– (1985) |
| [3] | Huang, Experimental investigation on the particle capture by a single fiber using microscopic image technique, Powder Technology 163 pp 125– (2006) |
| [4] | Wang, Electrostatic forces in fibrous filters-a review, Powder Technology 118 pp 166– (2001) |
| [5] | Jaworek, Modern electrostatic devices and methods for exhaust gas cleaning: a brief review, Journal of Electrostatics 65 pp 133– (2007) |
| [6] | Mazumder, Research needs in electrostatics for lunar and Mars, Industry Applications Conference 1 pp 327– (2005) |
| [7] | Calle, Particle removal by electrostatic and dielectrophoretic forces for dust control during lunar exploration missions, Journal of Electrostatics 67 pp 89– (2009) |
| [8] | Desai, A MEMS electrostatic particle transportation system, Sensors and Actuators 73 pp 37– (1999) |
| [9] | Morgan, Separation of submicron bioparticles by dielectrophoresis, Biophysical Journal 77 pp 516– (1999) |
| [10] | Yu, A three-dimensional dielectrophoretic particle focusing channel for microcytometry applications, Journal of Microelectromechanical Systems 14 pp 480– (2005) |
| [11] | Markarian, Particle motions and segregation in dielectrophoretic microfluidics, Journal of Applied Physics 15 pp 4160– (2003) |
| [12] | Jayasinghe, Controlled deposition of nanoparticle clusters by electrohydrodynamic atomization, Nanotechnology 15 pp 1519– (2004) |
| [13] | Burghard, Bridging of lateral nanoelectrodes with a metal particle chain, Applied Physics A 67 pp 591– (1998) |
| [14] | Koizumi, Estimation of the agglomeration coefficient of bipolar-charged aerosol particles, Journal of Electrostatics 48 pp 93– (2000) |
| [15] | Gady, Identification of electrostatic and van der Waals interaction forces between a micrometer-size sphere and a flat substrate, Physical Review B 53 pp 8065– (1996) |
| [16] | Feng, Relative importance of electrostatic forces on powder particles, Powder Technology 135 pp 65– (2003) |
| [17] | Marshall, Discrete-element modeling of particulate aerosol flows, Journal of Computational Physics 228 pp 1541– (2009) · Zbl 1410.76331 |
| [18] | Marshall, Particle aggregation and capture by walls in a particulate aerosol channel flow, Journal of Aerosol Science 38 pp 333– (2007) |
| [19] | Li, Discrete element simulation of micro-particle deposition on a cylindrical fiber in an array, Journal of Aerosol Science 38 pp 1031– (2007) |
| [20] | Dominik, Resistance to rolling in the adhesive contact of two elastic spheres, Philosophical Magazine A 92 pp 783– (1995) |
| [21] | Cordelair, Discrete element modeling of solid formation during electrophoretic deposition, Journal of Materials Science 39 pp 1017– (2004) |
| [22] | Severens, Discrete element method simulations of toner behavior in the development nip of the océ direct imaging print process, Granular Matter 8 pp 137– (2006) |
| [23] | Lu, Mixing in vibrated granular beds with the effect of electrostatic force, Powder Technology 160 pp 170– (2005) |
| [24] | Sun, A model for calculating electrostatic interactions between colloidal particles of arbitrary surface topology, Journal of Colloid and Interface Science 234 pp 90– (2001) |
| [25] | Adamiak, Interaction of two dielectric or conducting droplets aligned in the uniform electric field, Journal of Electrostatics 51 pp 578– (2001) |
| [26] | Vlad, Numerical computation of conducting particle trajectories in plate-type electrostatic separators, IEEE Transactions on Industry Applications 39 pp 66– (2003) |
| [27] | Scharstein, Capacitance of a tube, Journal of Electrostatic 65 pp 21– (2007) |
| [28] | Takahashi, Voltage required to detach an adhered particle by coulomb interaction for micromanipulation, Journal of Applied Physics 90 pp 432– (2001) |
| [29] | Barnes, A hierarchical O(N log N) force-calculation algorithm, Nature 324 pp 446– (1986) |
| [30] | Singh, Load balancing and data locality in adaptive hierarchical N-body methods: Barnes-Hut, fast multipole, and radiosity, Journal of Parallel and Distributed Computing 27 pp 118– (1995) · Zbl 0852.70009 |
| [31] | Hoffmann, DEM simulations of toner particles with an O(N log N) hierarchical tree code algorithm, Granular Matter 8 pp 151– (2006) · Zbl 1200.74141 |
| [32] | Marshall, Inviscid Incompressible Flow pp 238– (2001) |
| [33] | Jackson, Classical Electrodynamics pp 108– (1962) |
| [34] | Hess, Calculation of potential flow about arbitrary bodies, Progress in Aerospace Sciences 8 pp 1– (1967) · Zbl 0204.25602 |
| [35] | Jones, Electromechanics of Particles (1995) |
| [36] | Greengard, A fast algorithm for particle simulations, Journal of Computational Physics 73 pp 325– (1987) · Zbl 0629.65005 |
| [37] | Salmon, Skeletons from the treecode closet, Journal of Computational Physics 111 pp 136– (1994) · Zbl 0796.70002 |
| [38] | Clarke, Construction and validation of a discrete vortex method for the two-dimensional incompressible Navier-Stokes equations, Computers and Fluids 23 (6) pp 751– (1994) · Zbl 0813.76065 |
| [39] | Zhao, Spin coating of a colloidal suspension, Physics of Fluids 20 (2008) · Zbl 1182.76873 |
| [40] | Di Felice, The voidage function for fluid-particle interaction systems, International Journal of Multiphase Flow 20 pp 153– (1994) · Zbl 1134.76530 |
| [41] | Saffman, The lift on a small sphere in a slow shear flow, Journal of Fluid Mechanics 22 pp 385– (1965) · Zbl 0218.76043 |
| [42] | Saffman, Corrigendum to ’the lift force on a small sphere in a slow shear flow’, Journal of Fluid Mechanics 31 pp 624– (1968) · doi:10.1017/S0022112068999990 |
| [43] | Crowe, Multiphase Flows with Droplets and Particles (1998) |
| [44] | Johnson, Surface energy and the contact of elastic solids, Proceedings of the Royal Society of London, Series A 324 pp 301– (1971) |
| [45] | Tsuji, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technology 71 pp 239– (1992) |
| [46] | Lai, Unstructured grid arbitrarily shaped element method for fluid flow simulation, AIAA Journal 38 pp 2246– (2000) |
| [47] | Schlichting, Boundary-layer Theory (1979) |
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