Particle dynamics simulations of triboelectric charging in granular insulator systems

Particle dynamics simulations are carried out to study triboelectric charging in granular systems composed of a single insulating material. The simulations implement a model in which electrons trapped in localized high energy states can be transferred during collisions to low energy states in the other particle. It is shown that this effect alone can generate electrostatic charging in the system, and cause net electron transfer from larger particles to smaller particles. The magnitude of charging is small for systems of a single particle size but becomes much greater for a system with polydispersal particle sizes, due to the net electron transfer from larger to smaller particles. The negative charge of smaller particles, and positive charge of larger particles has been observed in field studies and laboratory experiments of granular systems.     

工业中粉体颗粒的荷电机理及数值模拟方法

工业过程中粉体颗粒不可避免地会相互摩擦碰撞而荷电. 荷电颗粒的存在可能会危害正常的工业生产过程, 也可能对工业过程起促进作用. 因此, 荷电粉体颗粒及其特性受到了广泛的关注, 但目前对粉体颗粒的荷电机理依然缺乏透彻的了解, 尤其是在气固两相流动中的粉体颗粒荷电现象. 事实上, 工业中存在的粉体颗粒的运动都受到流体的影响, 是典型的气固两相流系统, 流体对粉体颗粒的作用使粉体颗粒接触的荷电现象变得更为复杂, 因此从两相流动的观点来研究粉体颗粒荷电的物理本质就显得越来越重要. 本文介绍了工业过程中的几种不同类型的粉体颗粒荷电行为, 回顾了颗粒的荷电机理与描述颗粒荷电的数学模型. 对于工业过程中颗粒的荷电现象及颗粒在多相流体中的动力学行为, 介绍了研究颗粒受流体影响时荷电特性的数值模拟方法. 本文旨在对粉体颗粒的荷电机理、应用以及研究方法进行梳理与探讨, 为正确认识工业过程中粉体颗粒的荷电现象并加以控制利用提供理论借鉴.     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.     

Effect of particle size distribution on the polarity of triboelectric charging in granular insulator systems

Triboelectric charging occurs in granular insulating systems even when all particles are composed of identical material. A simple model is used here to address triboelectric charging in such systems. The basis of the model is the existence of electrons trapped in high-energy states, which can be released during collisions with another particle and transferred to the other particle. This model shows that triboelectric charging in insulator systems composed of particles of identical material can be attributed to a distribution of particle sizes, such that smaller particles tend to charge negatively and larger particles tend to charge positively. This polarity of charging has been observed in field studies of sand storms, dust devils and volcanic plumes, and most laboratory experiments on triboelectric charging in granular systems.     

Charge to radius dependency for conductive particles charged by induction

Particle charge is a critical parameter that needs to be determined in order to accurately predict behavior of a charged particle exposed to electrical forces. The effectiveness of various electrostatic applications depends directly on this charge or, more specifically, the charge to mass ratio. Previous studies report conflicting data for the size dependency of charge. In this paper, the relation between the value of charge on a conductive particle and the particle radius in the process of induction charging is investigated. The results of numerical simulations of a liquid atomization process are presented and a novel approach to the analytical solution of the problem is introduced. It is found that the exponent in the particle charge to radius dependency is equal to two when the particle is in the direct contact with the bulk material. The radius exponent decreases rapidly as the atomizing ligament length is increased. For ligament lengths many times greater than the particle radius, the radius exponent approaches one. Agreement between numerical and analytical results is found to be very good. The results of this study clarify some of the conflicting data in the previously published literature and suggest that the particle charge is practically linearly dependent on radius for atomized liquid particles and proportional to particle surface area for solid particles. In addition it is shown that the charge to mass ratio for liquid particles can be maximized by ensuring the ligament length during atomization is maximum.     

A particle-in-cell simulation of dust charging and shielding in lowpressure glow discharges

The transport of particles (“dust”) in low pressure electrical glow discharges is being studied in regard to its role in contaminating silicon wafers during plasma etching and deposition. Particles (10 s nm-μm) negatively charge in glow discharges and, to first order, appear to be massively large negative ions around which sheaths develop. The forces on particles in plasmas include electrostatic (drift of charged particles in electric fields) and viscous ion drag. The latter force is momentum transfer from ions to particles by either collisions or orbital motion. This force critically depends on the charge on the particle and the shape of the sheath surrounding the particle. In this work, we report on a pseudoparticle-in-cell (PIC) simulation of the transport of electrons and ions in the vicinity of dust particles in low pressure glow discharges. The simulation produces the electrical charge on the dust particle, the sheath structure around the dust particle and the orbital dynamics of the ions. A companion molecular dynamics simulation uses these parameters to produce ion-dust and electron-dust particle cross sections for momentum transfer and collection. Results will be discussed for charge, sheath thickness, cross sections and viscous ion drag forces on dust particles as a function of radius and plasma parameters     

Detection of elementary charges on colloidal particles

We have succeeded in determining the charge of individual colloidal particles with resolution higher than the elementary charge. The number of elementary charges on a particle is obtained from the analysis of optical tracking data of weakly charged silica spheres in an electric field in a nonpolar medium. The analysis also yields an accurate value of the particle size. Measurement of the charge as a function of time reveals events in which the particle loses or gains an elementary charge due to ionization or recombination processes at the surface.     

Interactions of charged dust particles in clouds of charges

Two charged dust particles inside a cloud of charges are considered as Debye atoms forming a Debye molecule. Cassini coordinates are used for the numerical solution of the Poisson-Boltzmann equation for the charged cloud. The electric force acting on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the average distance between dust particles should be approximately equal to two Debye radii. Second, attraction takes place when similar charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of total charge of the same polarity, repulsion between the particles takes place at all distances. We apply our results to the experiments with thermoemission plasma and to the experiments with nuclear-pumped plasma.     

Electrostatic behavior of different fines added to a Faraday cup fluidized bed

Experiments were performed in a Faraday cup fluidization column to determine the changes in the electrostatic charges on various fine particles after their addition to gas–solid fluidized beds to better understand their role in influencing electrostatic charge generation/dissipation. The charges transported by different fines (Larostat 519 antistatic agent, glass beads (GB), silver-coated GB, catalyst and silica particles) were determined after their injection into an initially charged bed of much larger mono-sized particles (GB or polyethylene) for a range of relative humidities. Entrained fines carry significant charges out of the column, therefore leaving a net charge behind, with the polarity and quantity of charge depending on the size, physical properties and chemical structure of the particles, and on the moisture content of the fluidizing gas.     

The role of fluid turbulence on contact electrification of suspended particles

A probabilistic version of a well-known phenomenological model for contact electrification is used to examine the effect of fluid turbulence on charge development for suspended particles as a function of the particle Stokes number. The distribution of particle collisions and particle charge appear to approach asymptotic states for high values of the Kolmogorov-scale Stokes numbers, exhibiting approximately normal distributions. The influence on particle contact electrification of differences in initial charge carrier density and in particle size are examined.     

Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

Nonequilibrium accumulation of surface species and triboelectric charging in single component particulate systems

Triboelectric charging occurs in granular systems composed of chemically identical particles even though there is no apparent driving force for charge transfer. We show that such charging can result from nonequilibrium dynamics in which collision-induced electron transfer generates electron accumulation on a particle-size-dependent subset of the system. This idea rationalizes experimental results that suggest that smaller particles charge negatively while the large ones charge positively. This effect occurs generally when there are high energy electrons on a surface that cannot equilibrate to lower energy states on the same surface, but can transfer to lower energy states on other particles during collisions.     

Estimation of particle size distributions obtained by gas phase processes

Nanoparticles intended for high value added applications often require special size distributions. Based on model calculations, this article compares the particle size distributions obtained with conventional and plasma processes. The model is based on an estimation of the probability for collisions; either for neutral or equally charged particles, whereas the growth of the particles is calculated using a model derived from Markov chains. The results of these calculations confirm the empirical knowledge that, under the special conditions of particles carrying electric charges of equal sign, plasma processes deliver products with the narrowest particle size distribution. Synthesis of extremely small particles with conventional processes leads to a significant residue of unreacted precursor. This finding is important in cases of expensive educts. The results of these model calculations are in perfect agreement with experimental findings.     

Levitation and dynamics of a collection of dust particles in afully ionized plasma sheath

Examines the dynamics of a collection of charged dust particles in the plasma sheath above a large body in a fully ionized space plasma when the radius of the large body is much larger than the sheath thickness. The dust particles are charged by the plasma, and the forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. These forces will often act in opposite directions and may balance, making dust suspension and collection possible. The dust particles are supplied by injection or by electrostatic levitation. The ability of the sheath to collect dust particles, will be optimal for a certain combination of gravitation and plasma and dust particle parameters. In a dense dust sheath, the charges on the dust particles contribute significantly to the total space charge, and collective effects become important. These effects will reduce the magnitude of the sheath electric field strength and the charge on the dust particles. As dust particles are collected, the dust sheath is stretched and the largest dust particles may drop out, because the sheath is no longer able to suspend them. In a tenuous dust sheath, the inner layer, from the surface and about one Debye length thick, will be unstable for dust particle motion, and dust will not collect there. In a dense dust sheath, collective effects will decrease the thickness of this inner dust-free layer, making dust collection closer to the surface possible. By linearization of the force and current equations, the necessary and sufficient conditions for a stable dust sheath are found. The authors consider conditions which resemble those of planetary system bodies, but the results may also be of relevance to some laboratory plasmas     

Three-dimensional numerical studies on the effect of the particle charge to mass ratio distribution in the electrostatic coating process

Charge to mass ratio is a crucial parameter that governs the behavior of particle trajectories in a charged cloud of particles. The complex nature of the charging process limits our ability to accurately determine the charging level when particles of varying size are present. Using a numerical approach, it is possible, however, to take into account predefined values for this parameter. In this paper, the average charge to mass ratio and the distribution of the charge to mass ratio in the coating of a flat target were systematically varied to demonstrate their effect on the motion of the charged particles. The results show that the transfer efficiency increases as the average charge to mass ratio increases. It was found that the transfer efficiency is a weak function of the average particle size in the range tested and that it increases as the width of the size distribution increases.     

Dust in Plasma I. Particle Size and Ion‐Neutral Collision Effects

A fully kinetic self‐consistent model of an absorbing particle immersed in stationary isotropic weakly collisional plasma has been developed. The combined effects of particle size and ion‐neutral charge exchange collisions have been investigated for intermediate regimes, where no analytic theories are available. It is shown that collisional effects related to the ion orbital destruction (presence of extrema in ion flux collected on the particle surface and in particle potential and charge) are important for small particles, while they are totally absent for large particles. The potential distribution around the particle is quite well represented by a Yukawa form, but with an effective screening length that shows different dependences from the gas pressure for small and large particle size. Analytical fitting formulas of particle charge and potential and screening length depending on the particle radius parameter and on the Knudsen number have been obtained (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas

The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg-de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron-ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.     

Nanostructured Deposition of Nanoparticles from the Gas Phase

For many applications, nanoparticles from the gas phase are of interest due to their physical properties. Especially for electronic or optoelectronic applications, the transfer from their random distribution in the gas phase onto flat substrate surfaces has to be controlled because the particles are needed in exactly defined areas on the substrate. We demonstrate a parallel process for the transfer of charge patterns on oxidized silicon surfaces followed by the deposition of monodisperse singly charged nanoparticles, which allows the creation of particle arrangements reaching from 100 nm resolution up to structures in the upper micrometer range. The charge patterns are transferred using a polydimethylsiloxane (PDMS) stamp, which is covered with a metal layer. By applying different voltages to the stamp, negative or positive charges can be transferred. Thus, nanoparticles of different polarities can be guided to certain places.     

Interaction of ions and electrons with nanoparticles in hydrocarbon combustion plasmas

The interaction of electrons and ions with a polydisperse ensemble of soot nanoparticles during the combustion of hydrocarbon fuels is studied. The dynamics of the particle charging is analyzed. It is shown that, in the initial stage, all the soot particles are charged negatively, the largest particles (100–150 nm) carrying up to 40–50 elementary charges. As time elapses, the negative charge is neutralized and the charge distribution becomes more symmetric. Finally, because of the interaction between ions (electrons) and soot particles, the total concentration of the positive ions becomes higher than that of the negative ones.