Numerical Modeling of Conductive Particle Trajectories in Roll-Type Corona-Electrostatic Separators

Several attempts have already been made to simulate particle trajectories in roll-type electrostatic separators. However, the predictive value of the results is limited by an excessive number of simplifying assumptions regarding the electric field distribution, as well as particle charging and discharging mechanisms. The present work is aimed at improving the existing models by taking into account: (1) the non-uniformity of the electric field in the active zone of the separator and (2) the effect of spark discharges occurring between the electrodes. Based on previous observations, the conductive particles were assumed to lift-off when no longer exposed to corona discharge. The numerical simulations were performed for particles of various sizes. The electric field was computed in each point of the trajectory using a finite element program. It was found that: (1) some of the smaller particles impact the static electrode and are deviated to the middling compartment of the collector and (2) field annealing which accompanies spark discharges significantly affects the trajectories of conductive particles. The results of this study could guide the design of new electrostatic separation applications.     

Mathematical modeling of powder paint particle trajectories inelectrostatic painting

The trajectories of charged powder particles in an electrostatic powder coating system were modeled considering electrical and fluid forces. The mathematical model employed an iterative technique wherein the charge simulation method was used to compute the electric field strength and the method of characteristics was used to compute the charge density in the gun-to-target region. The fluid flow between the electrostatic gun and the target was modeled using interpolated experimental data assuming stagnation point flow. Particle trajectories were simulated for size range 10-40 μm and charge-to-mass ratios of -0.1 to -1 μC/g. The simulation results showed good agreement with experimental data (charge and mass measurements) at several collection points on the painting target and provided valuable information concerning particle deposition     

A finite-element analysis of the electrostatic force on a uniformlycharged dielectric sphere resting on a dielectric-coated electrode in adetaching electric field

In the electrophotographic process, charged toner particles are transferred from one surface to another with an electric field. To enable electric field transfer of toner, the externally applied field strength must be greater than a threshold value, so that the Coulomb force can overcome the toner adhesion force at the supporting surface. In this paper, the threshold field strength to detach a charged dielectric particle is determined efficiently by using the Galerkin finite-element method to simultaneously solve the Laplace equation for the field distribution and an overall constraint equation for the force balance. This computational method also enables calculation of the electrostatic adhesion force and is applicable to various particle-electrode configurations. For illustrative purposes, however, we consider the axisymmetric problem of electric field detachment of a dielectric sphere with uniform surface charge resting on a planar dielectric-coated electrode. The analysis is particularly focused on the dependence of the electrostatic force upon the dielectric overcoating thickness and spacing between parallel plate electrodes. The electrostatic force on a uniformly charged particle in contact with a surface is found to be influenced significantly by the thickness of dielectric overcoating and the spacing between electrodes when either becomes less than five times the particle radius     

Analysis of the behavior of ions produced by pulsed coronadischarge

The motion of an ion cloud which is produced by a corona discharge with the high-voltage pulse of a short duration and is introduced into parallel plate electrodes was calculated numerically. The ion cloud initially placed at the tip of a needle electrode was simulated by a number of ring charges and the trajectories of individual ring charges were calculated by using electric field strength obtained with a charge simulation method. Not only movement of the ion cloud but also the waveform of the induced current flowing through a ring electrode located at the center of the parallel plate electrode were simulated and analyzed. The ion cloud with an initial diameter of 0.5 mm expands to 5 mm by electrostatic repulsion within 10 μs after the beginning of drift. During drifting toward the counter electrode, the ion cloud extends wider to a diameter of around 20-25 mm. The size and velocity of ion clouds agree with those estimated by experiments and the waveform of induced current obtained by experiments was reproduced by this simulation     

Charging of insulating spheres on the surface of an electrodeaffected by monopolar ions

The charge acquired by an insulating sphere in a uniform monoionized electric field has been accurately evaluated by Pauthenier. In certain electrostatic applications, such as the electroseparation of mixed granular solids, the particles to be charged are on the surface of an electrode. Under these circumstances, Pauthenier's formula is no longer valid, because the field is nonuniform. This paper addresses this problem from both a computational and an experimental point of view. A numerical method of field analysis was employed for the evaluation of the charge acquired by spheres of various dielectric constants, on the surface of a plate electrode. The numerically computed values of the saturation charge in this situation were always greater than those given by Pauthenier's formula. The experiments were carried out on laboratory equipment provided with various types of corona electrodes. An electrometer was used to measure the charge acquired by calibrated spheres of polyamide (3 mm diameter) when subjected to the positive or negative corona discharge generated between these electrodes and a metallic rotating roll electrode (150 mm diameter) connected to the ground. The experimental data were in good agreement with the theoretical predictions; the saturation charge increases linearly with the applied voltage, up to a threshold at which the self discharge of the particle occurs. The efficiency of ionic charging was shown to depend on the type of corona electrode that is employed     

Modeling of electrostatic-based pesticide spray systems

A microscopic model for the electrostatic spraying system is presented to investigate the effect of the voltage applied to the induction nozzle on the droplet's charge, mobility, and charge-to-mass ratio. The variation of these parameters along the jet was also included. The model also lays particular emphasis on the effect of the applied voltage on the spray current and the charge density at the nozzle. A macroscopic model for the electrostatic spraying system is also presented. The objective of the model was to study the spatial distribution of the droplet charge density, transit time, and trajectory in the region between the nozzle and the target in terms of the flow velocity of the spray and the space-charge-produced electric field. On the macroscopic scale, both the droplet charge density and the spray current increase with the voltage applied to the charging electrode. With the decrease of the spray flow velocity, the space-charge-produced electric field becomes dominant and tends to: contract the droplet trajectories toward the axis of the spray system, and hence enhance the droplet deposition efficiency; and decrease the charge density at the target with the possibility of minimizing back-ionization. On the microscopic scale, induction charging eliminates the ion current from the current to the target and the associated back-ionization. The calculated droplet charge and charge-to-mass ratio which increase with the voltage applied to the charging electrode, agreed with the values reported previously     

Particle Charging in Combined Corona-Electrostatic Fields

The association of several ionizing and nonionizing electrodes generates combined corona-electrostatic fields, characterized by space charge zones of well-defined extensions. In a previous paper, the authors presented an effective numerical method for the computation of such fields. The aim of this present work is to show how these results can be employed for estimating the charge acquired by insulating and conducting particles when passing through the space charge zones generated by various corona-electrostatic electrode geometries. The study is done under several assumptions that authorize the use of Pauthenier's formula. Diffusion charging can be neglected, the applied electric field is quasi-uniform in the vicinity of particles, and particle speed is low compared with that of air ions. The charging model takes into account the computed spatial distribution of the electric field and charge density. The computations were performed for various values of the geometrical parameters of the electrode system and of the particle transit time through the corona discharge zone. The results can be used for the design of the electrode system of any electrostatic process employing corona discharge fields.      

High-voltage electrode position: a key factor of electrostatic separation efficiency

Industry application of electrostatic separation technologies still faces a major difficulty: good results can be obtained only by adequate control of a multitude of operating parameters. The aim of the present paper is to analyze a key factor of electrostatic separation efficiency: the position of the high-voltage electrodes. Experiments were performed with two types of granular materials: chopped electric wire wastes and foundry sands. The electrostatic separator employed for the tests was provided with a wire-type corona electrode, associated - in some experiments - with a tubular-type electrostatic electrode, at various angular and radial positions, with respect to a rotating roll electrode connected to the ground. The experimental data are discussed in relation to the results of the numerical analysis of the electric field, carried out with a charge simulation program. They show that the outcome of the separation process (i.e., the weight percentage of the conductor and nonconductor fractions, as well as the purity of the recovered materials) depends on the configuration of the electrode system. The position of the electrodes affects both the particles charging conditions on the surface of the roll electrode, and the trajectories of the charged particles in the high-intensity electric field of the separator. Some recommendations could be formulated for the industrial application of the electrostatic separation technology.     

Corona inception in typical electrode configurations forelectrostatic processes applications

The corona inception electric field at the surface of a wire electrode is usually evaluated by an empirical formula established by Peek. That formula was found to be valid in several simple electrode configurations (wire cylinder, wire plate), which are typical to electrostatic precipitators. The aim of this paper is to extend the study to other situations encountered in electrostatic applications. The experimental setup specifically modeled the several electrode arrangements which are commonly used with roll-type electrostatic separators. It consisted of wire-type corona electrodes, connected to a regulated DC high-voltage supply, and a rotating roll electrode, connected to the ground. The effect of associating the corona wire to one or several tubular electrodes of various shapes and sizes was investigated. The experimentally determined corona inception voltage was used as input data of a boundary-element-method program for the electric field computation. The computed values of the electric field were compared with those given by Peek's formula for wire electrodes of the same radius. The derived conclusions can be of help in the custom design of the corona electrode arrangements for various electrostatic applications     

Computational and Experimental Study of Ionic Space Charge Generated by Combined Corona–Electrostatic Electrode Systems

Numerical computation of the electric field intensity and space charge density in electrode systems consisting of ionizing and nonionizing elements, connected at the same direct current (dc) high-voltage supply and facing a grounded plate, is a difficult problem, which is of interest to several electrostatic processes applications. The aim of the present paper is to demonstrate the effectiveness of an original method of field computation in the analysis of the factors that influence the distribution of the ionic space charge in such combined corona–electrostatic electrode systems. The computations and the experiments were carried out for an ionizing wire of diameter 0.3 mm, located at different distances$h$(10–30 mm) from a tubular support of diameter 25 mm. Several interelectrode distances (20–45 mm) were simulated. The extension of the zone at the surface of the grounded electrode, which is affected by the space charge, diminishes when reducing the intervals between these elements of the electrode system, and, at similar applied voltage, the density of the corresponding corona current increases. The experimental data were in good agreement with the computed results, validating the accuracy of the numerical method of space-charge calculation in this special electrode configuration.     

Unipolar charging of cylindrical insulating particles nearelectrode surfaces

Numerous papers have discussed the ionic charging of insulating spheres in uniform electric fields. However, in certain electrostatic technologies, such as separation and flocking, the particles are often cylindrical in shape, and they get charged on the surface of an electrode or in its proximity, so that existing formulas cannot be used. This paper addresses this problem from both a computational and an experimental point of view. The charge acquired by cylindrical particles of various dielectric constants was evaluated with an original computer program, based on the boundary-element method of field analysis. The computed results show that the position of the particle with respect to the electrodes changes the value of the saturation charge. The experimental setup simulated the charging conditions in a roll-type electrostatic separator. The unipolar space charge was generated by a needle-type electrode. An electrometer was used to measure the charge acquired by millimeter-size calibrated cylinders of polyethylene and polyvinyl chloride on a rotating roll electrode. The experimental results, which were in good agreement with the theoretical predictions, put forward a particle self-discharge effect, at field intensities beyond a well-defined threshold. This kind of information may guide the design of the electrostatic technologies based on the corona charging of granular matter     

Charges and forces on conductive particles in roll-typecorona-electrostatic separators

Mathematical modelling is a powerful tool in the optimization of electroseparation technologies and equipment. This paper proposes the use of a numerical method of field analysis to evaluate more accurately the charges and forces on millimeter-size conductive particles of virtually any shape in contact with an electrode. A program based on the boundary-element method was tested for this purpose, and provided the input data to an algorithm for the computation of particle trajectories. The results were in good agreement with the observations made on a laboratory electroseparator. The effect of space charge on the behavior of conductive particles was studied with a three-electrode system (a grounded grid, between a corona electrode and a metallic plate, energized by two high-voltage supplies of opposite polarities). The accuracy of numerical simulations of electroseparation processes is expected to increase when a mathematical model of particle motion in DC corona fields will be incorporated in the existing computer programs     

直流电压下SF_6气体中电极覆膜对金属微粒启举的影响机理

为研究直流电场下SF_6气体中低压电极覆膜对金属微粒启举的影响机理,搭建了实验平台并使用高速摄像机记录运动轨迹。实验结果表明,随着SF_6气体压力的增大,微粒启举场强升高,且启举后到达高压电极的时间缩短。基于图像处理获得了微粒的瞬时位移,结合运动力学方程和最小二乘法提出了启举时电荷量的计算方法,微粒电荷量的计算分析表明启举时的电荷量减小。建立了覆膜后金属微粒周围电场分布的理论模型,电场分析表明金属微粒与薄膜间的电场明显增大及表面电荷密度分布的改变,使得金属微粒受到向下的极化作用力。研究认为:电荷量减小和极化作用力向下综合导致金属微粒的启举场强提高;覆膜后局部放电是金属微粒的带电机理;SF_6气体压力增大使得金属微粒发生局部放电的起始场强升高,导致极化作用力增大,需要更高场强发生启举。     

Optimization of corona electrode position in roll-type electrostatic separators

The position of the corona electrode(s) is known to be a key factor of electrostatic separation efficiency, as it influences both the charging conditions of the granular materials on the surface of the roll electrode connected to the ground, and the magnitude of the electric forces exerted on the particles. Response surface methodology was employed for the design of the experiments performed on a laboratory roll-type corona-electrostatic separators, with samples of chopped electric wire wastes typically processed by such techniques. The results of the electrostatic separation tests are discussed in relation to the data obtained from two other experiments, in which corona current and particle charge measurements were performed for various positions of the standard wire-type electrode. The conclusions of this study enabled the formulation of several recommendations for the improvement of the outcome of industrial separation processes (i.e., maximize the weight percentage as well as the purity of the recovered materials).     

离子风对静电除尘器中颗粒物脱除的影响机制研究

静电除尘器中电晕放电产生的离子风是影响颗粒迁移和沉积的重要因素,通过建立多过程耦合的静电除尘器数值模型,研究了不同极配型式静电除尘器的电场分布特性及离子风对空间流场和颗粒物脱除的影响规律。结果表明,针刺电极电场强度和离子电荷密度的最高值均略高于芒刺电极,但是芒刺电极的静电场分布更加均匀。在外加电压为60k V时,针刺电极和芒刺电极的离子风最高流速分别可达7.91m/s和4.62m/s,离子风会促进荷电颗粒向收尘极板运动,同时也会形成近壁高速区造成堆积颗粒的不均匀分布并导致二次扬尘。由此,针对不同形式静电除尘器提出了合理调整放电电极结构方法,进行离子风调控以强化颗粒物脱除。     

Analysis of Electrostatic Adhesion and Detachment of a Nonuniformly Charged Particle on a Conducting Plane

This paper presents the analysis of electrostatic adhesion and detachment of a charged, dielectric particle resting on a conducting plane. We have studied the effects of particle dielectric constant and the nonuniform charge distribution on the force acting on the particle. Charge on the particle surface is assumed to be smoothly varied and (a) concentrated at the bottom pole or (b) concentrated at the top and bottom poles. The analysis utilizes the method of multipole images to obtain accurate values of the electric field, and determines the electrostatic force from the stress on particle surface. Compared with the force on a uniformly charged particle having the same total charge amount, the analytical results show that the force is significantly enhanced by both kinds of nonuniform charge distribution treated in this work, and is particularly strong when charge is highly concentrated at the bottom pole. It is found that electric field in a limited range must be applied in order to detach the particle from the conducting plane. The electric field necessary for detachment depends strongly on the dielectric constant and the distribution of charge on the particle. The detachment becomes difficult for a particle with charged distributed at the bottom pole, and may be hardly possible if the dielectric constant is too high.     

Resolution and signal processing technique of surface charge density measurement with electrostatic probe

When an electrostatic probe is used to measure the surface charge on an insulating plate of constant thickness, the measuring system is regarded a shift-invariant system and the relation between the surface charge density and the probe output can be treated in the spatial frequency domain. The distribution of the surface charge density on an insulating plate just after occurrence of a surface discharge is measured by a Pockels probe, which is regarded as a kind of electrostatic probe without the guard electrode, and restored by Wiener inverse filter. The performance of a Pockels probe and a conventional electrostatic probe are compared quantitatively in terms of the spatial resolution. In the case that the measured object is 3 mm thickness PMMA plate and is charged up to 10 nC/cm/sup 2/ in atmospheric air, it is estimated that the spatial resolution of the Pockels probe with 0.2 mm gap is 1.5 mm and that of the conventional electrostatic probe with the grounded guard electrode with 3 mm gap is 2.2 mm.     

The effect of electric field strength on the induction charge of freely levitating particles

Many industrial processes such as electrostatic separation, fluidization, and coating rely upon induction charging of fine particles. This paper considers the effects of electric field strength on the magnitude of the induction charge on freely levitating particles. The charging time and charge on a freely levitating particle depend on a number of properties, mainly the electric field strength, particle size, density, and resistivity. A charging model showing the dependence upon the electric field strength is presented and analyzed, along with a model of the levitation process. A high-speed digital imaging system was used to measure individual particle motion during levitation. Using these data along with the developed models, it was possible to determine the charge on the particle. Semiconductive particles with a mass mean diameter (MMD) of 156 /spl mu/m were used in these experiments and tested at electric fields of 6.8, 8.5, 15, and 21 kV/cm, respectively. In addition, some experiments using particles 97-/spl mu/m and 412-/spl mu/m MMD at an electric field of 15 kV/cm were carried out to confirm the results obtained for the 156-/spl mu/m particles. It was found that the particle charge was dependent upon both the charging time and electric field strength. In particular, for high electric fields the particle did not achieve its saturation charge before liftoff occurred. This shows that higher electric field strength is not necessarily the optimum condition for levitation of semiconductive particles.     

Dynamic motion of a conductive particle in viscous fluid under DCelectric field

When plastic waste is liquefied for recycling, the impurities present could influence the quality of the reprocessed products. In order to explore the possible method for removing solid impurities using electrostatic forces, the motion of spherical conductive particles under a uniform electric field has been carefully investigated. In this paper, a solid impurity and liquefied plastics are simulated by a conductive spherical particle and viscous insulating liquid, silicone oil, respectively. Experimental results indicate that the particle undergoes repeated motion between the parallel electrodes. The motion of the particle can be divided into four modes: settling on the lower electrode, moving upward, settling on the upper electrode, and moving downward. The higher the applied voltage, the faster the average particle velocity and the shorter the resting time of the particle. The particle accelerates after leaving the electrode and decelerates before reaching the other electrode. This deceleration could be explained by the viscous effect of the liquid layer between the particle and the electrode. The settling mode could be explained by the fact that there is a liquid flow induced by the particle motion and it pushes the particle against the electrode until the flow decreases. It is, therefore, suggested that the hydrodynamic effect is dominant in our case, as well as the electrostatic force