A simple bimodal model for the evolution of non-spherical particles undergoing nucleation,coagulation and coalescence

A simple and efficient particle dynamics model is developed accounting for simultaneous nucleation, coagulation, and coalescence or sintering of non-spherical particles. In this model two discrete monodisperse modes are used to represent the non-spherical particle size distributions approximately: a size-fixed nucleation mode and a moving accumulation mode. The size-fixed nucleation mode accounts for the introduction of newly generated particles and the moving accumulation mode characterizes the particle growth by coagulation and coalescence. The simulation results for titania particle formation and growth using the proposed bimodal model are compared with those using the previous monodisperse non-spherical particle dynamics model and non-spherical polydisperse sectional model. The present bimodal model results in a very good agreement with the polydiserse sectional model even when particle nucleation coexists with coagulation process while the monodisperse model shows significant differences. It successfully predicts the morphological change of the non-spherical particles by coalescence. The present model is also shown to be capable of predicting the polydispersity of non-spherical particle distribution. The present non-spherical bimodal model requires the same level of the computation time that the simple monodisperse model does.     

Influence of flame-generated ions on the simultaneous charging and coagulation of nanoparticles during combustion

Flames generate a large amount of chemically and thermally ionized species, which are involved in the growth dynamics of particles formed in flames. However, existing models predicting particle formation and growth do not consider particle charging, which may lead to bias in the calculated size distribution of particles. In this study, Fuchs' charging theory was coupled with a monodisperse particle growth model to study the simultaneous charging and coagulation of nanoparticles during combustion. In order to quantify the charging characteristics of nanoparticles, a high-resolution DMA was used to measure the mobilities of ions generated from a premixed flat flame operated at various conditions. The effect of temperature on ion–particle and particle–particle combination coefficients was further examined. The proposed model showed that the influence of charging on particle growth dynamics was more prominent when the ion concentration was comparable to or higher than the particle concentrations, a condition that may be encountered in flame synthesis and solid fuel-burning. Simulated results also showed that unipolar ion environments strongly suppressed the coagulation of particles. In the end, a simplified analysis of the relative importance of particle charging and coagulation was proposed by comparing the characteristic time scales of these two mechanisms.

© 2017 American Association for Aerosol Research     

Bipolar charging and neutralization of nanometer-sized aerosol particles

An experimental study of charging and neutralization of 2.5–10 nm aerosol particles by bipolar air ions has been carried out. The time required to attain the charge equilibrium state, both for charging of initially uncharged particles and for neutralization of charged particles, has been previously determined using different-sized diffusive type chargers. To avoid sizing errors caused by space charge field and Brownian diffusion effects, a tandem DMA (differential mobility analyzer) system has been used. The first DMA classifies a certain fraction of particles, and the second one allows precise determination of their size. The experimental charging probabilities at equilibrium are in relatively good agreement with calculations based on Fuchs' theory, except in the particle size range below 3 nm where large deviations have been observed.     

The effect of ion and particle losses in a diffusion charger on reaching a stationary charge distribution

Bipolar charging of nanometer-sized aerosol particles in a tube containing a radioactive source has been investigated theoretically. A model has been developed which accounts for diffusion losses of particles and ions to the tube wall, as well as for the spatial dependency of the ion-pair generation rate. The ion generation rate profile along the tube axial direction as a function of the source size and of the tube length and radius has been evaluated and, subsequently, used to examine the aerosol charging process. Comparative calculations were also performed for uniform ion generation and negligible diffusion losses. In a real charger, where diffusion losses are unavoidable, particles cannot attain a steady charge distribution. On the contrary, provided the nt product (ion mean concentration × mean aerosol residence time) is large enough, the number concentration of charged particles of a given size reaches a maximum at a certain axial location and thereafter decreases. The extrinsic charging efficiency (fraction of originally neutral particles which carry a net charge at the ionizer outlet) depends in a complex manner on a number of parameters: particle size and polarity, tube length and radius, nt product, and relative aerosol-to-ion concentration.     

A discrete-sectional model for particle growth in aerosol reactor: Application to titania particles

A one-dimensional discrete-sectional model has been developed to simulate particle growth in aerosol reactors. Two sets of differential equations for volume and surface area, respectively, were solved simultaneously to determine the size distributions of agglomerates and primary particles. The surface area equations were derived in such a way that the coagulation integrals calculated for the volume equations could be used for the surface area equations as well, which is new in this model. The model was applied to a production of TiO₂ particles by oxidation of titanium tetrachloride. Model predictions were compared with experimental data and those of a two-dimensional sectional model. Good agreement was shown in calculated particle size distributions between the present model and the two-dimensional model, which is more rigorous but demands a large amount of computer time and memory. Compared to experimental data, the primary particle size calculated by the model was more sensitive to the variation of reactor temperature.     

Charging of aerosol particles by ionizing radiation in the presence of an electric field

An ionizing particle (alpha particle in the experiment) produces pairs of positive and negative ions along its trajectory until its kinetic energy is exhausted. The ion production field can be computed if the system geometry, disintegration rate and energy are known.Without an electric field, positive and negative ions are distributed isotropically around the trajectories of the ionizing particles. In this case aerosol particles are neutralized.When, however, a strong electric field is applied to the ion production field, it dominates ionic motion and creates regions where concentration ratios between positive and negative ions exist. In such a field, particles obtain charges depending on their size and dielectric constant, concentrations of positive and negative ions and electric field strength.Differential equations for impaction charging and diffusion charging were derived for this bipolar case. Solutions are for the most general cases when charging time is finite, and the initial charge is not zero.A simple electrostatic precipitator (ESP) was developed to test this equation for impaction charging. The test dust was lycopodium spores (d = 28 μm). The agreement with theory and experimental results was good. Differences at higher field strengths appear to be due to secondary ionization.     

Bipolar Charge Distributions of Aerosol Particles in High-Purity Argon and Nitrogen

The bipolar diffusion charging has been studied for monodisperse sodium chloride and silver particles of 5–100 nm in atmospheric air, argon and nitrogen. The particles were bipolarly charged in a neutralizer by ions, produced by beta-rays from a Kr 85 source. The differently charged particle fractions were separated in a differential mobility analyzer and measured with an aerosol electrometer. The experimentally determined results in atmospheeric air are comparable with earlier measured asymmetric bipolar charge distributions. They show good agreement with the theoretically determined results based on the extended Fuchs model with four-input ion parameters: mobilities and masses of positive and negative ions. The experimentally determined bipolar charge distributions in argon and nitrogen are more asymmetric than in atmospheric air. The theoretically determined distributions, based on the extended Fuchs model, can be fitted to the experimental data. Furthermore, the extended Fuchs model is strongly dependent upon variations of the four input ion parameters. No differences for the experimentally determined bipolar charge distribution could be found between different gas purities and different particle materials.     

Bipolar Diffusion Charging of Aggregates

In this paper, the effect of particle morphology on bipolar diffusion charging is studied. A modified tandem differential mobility analyzer (TDMA) method used to measure the charge distribution of submicron particles in the range of 70–300 nm is described in detail. The method requires an independent measurement of the neutral fraction, followed by the measurement of the size-dependent charge distribution, which requires the knowledge of the neutral fraction. The method was validated experimentally using dioctyl sebacate and ammonium sulfate spherical particles and compared with Fuchs’ theory. Diesel particles and silver aggregates were used to evaluate the impact of morphology on charging. The results show that aggregates have a slightly lower (about 7%) neutral fraction than spheres. These results are in agreement with the predictions of Lall and Friedlander's theory and previous studies. However, results from charge distribution indicate that more (about 46%) particles are negatively charged than predicted by Lall and Friedlander's theory, while 32% fewer particles are positively charged. This relatively large asymmetry between the negative and the positive charge fraction is not fully predicted by either Fuchs' or aggregate charging theories. Our results suggest that the current inversion method of scanning mobility particle sizer (SMPS) data, based on Fuchs’ or Lall and Friedlander's distribution, would underestimate the total number concentration by about 15% or 27% if applied to diesel aggregates.

Copyright 2012 American Association for Aerosol Research     

Comment on: Penetration of Ultrafine Particles and Ion Clusters Through Wire Screens by Ichitsubo et al.

The bipolar diffusion charging of aerosol particles in the transition and continuum regimes was studied theoretically and experimentally under the conditions of high particle / ion concentration ratios. The basic equations for the bipolar diffusion charging of monodisperse and polydisperse aerosols were numerically solved for geometric mean diameters of 0.01–1.0 μm, geometric standard deviations of 1–2, and for various concentrations of bipolar ions. From the calculation results presented in terms of dimensionless parameters, the ion number concentrations and charging times required to attain the equilibrium charge distributions were determined. In the experiment, the changes in the particle charge distribution and ion number concentration in the flow-type chamber were measured for various particle number concentrations, ion generation rates, and residence times. For bipolar ion generation rates > 3.5 × 10¹¹ m^?3 s^?1, the experimental results were found to agree with the theoretical predictions. For smaller ion generation rates, however, the particles were not charged as predicted by theory.     

Challenges of measuring nascent soot in flames as evidenced by high-resolution differential mobility analysis

Nascent soot particles with mobility diameters ≤10 nm were measured in an ethylene/air premixed flame to shed light on the challenges and potential artifacts affecting studies on soot inception by differential mobility analysis (DMA) techniques. The size distribution functions (SDFs) of particles with charge acquired either naturally or diffusively upon ion seeding were measured at several positions in the flame using rapid-dilution probing and a high-resolution DMA for different values of the ratio of dilution ratio to residence time (DR/Δt). The SDFs are roughly bimodal with a sub-3 nm mode and a larger one that appears either downstream in the flame or for low DR/Δts. Soot nuclei smaller than 3 nm preferentially acquire positive charge, which brings into question the assumption of steady-state charging probability of flame sampled soot nuclei in the bipolar diffusion neutralizer. The approximately polarity-symmetric lognormal SDF of larger particles is attributed to nuclei coagulation. Naturally charged particles increase in number when lowering DR/Δt, suggesting either their collisional charging by flame chemi-ions or particle nucleation by condensation of neutral molecules on ions or both. The critical conditions for suppressing particle coagulation and charge redistribution in the sampling system were not achieved under most conditions, despite the fact that values of DR/Δts were more favorable to such a suppression in the present experiment as compared to other studies in the literature. As a result, the identification of this “asymptotic” regime, which is critical to determine the parent SDFs and the charge state of nascent soot in the flame, is still elusive.

© 2016 American Association for Aerosol Research     

A novel bipolar charger for submicron aerosol particles using carbon fiber ionizers

A simple and novel bipolar charging device using carbon fiber ionizers was developed to neutralize submicron aerosol particles without the generation of ozone. The ion currents of the positive and negative ions generated by carbon fiber ionizers were so chosen as to optimize particle neutralization. The particle penetration, charging probability and charge distribution resulting from the charger were investigated and compared to those from a Kr-85 radioactive neutralizer for the particles in the size range of 20–120 nm. Size distributions for various laboratory-generated aerosols (sodium chloride, ammonium nitrate, ammonium sulfate and glutaric acid) neutralized by the charger were also investigated and compared to those obtained without neutralization. Particle penetration in the charger was over 90% for particles larger than 20 nm. Charging probability and charge distribution for the charger were in good agreement with those from Kr-85 neutralizer and with theoretical estimations. Size distributions observed for the charger and Kr-85 neutralizer were also in good agreement for particles of different concentrations and various chemical compositions. The newly developed bipolar carbon fiber charger can neutralize submicron particles, at least as effectively as currently available radioactive neutralizers and with negligible ozone generation which is its major advantage.     

Monte Carlo simulation of pneumatic tribocharging in two-phase flow for high-inertia particles

Pneumatic transport, triboelectrostatic experimentation studying the removal of carbon from fly ash has shown the importance of particle charging on process performance. To further elucidate the influence of particle charging, a tribo-electrification model for charging spherical particles in vertical pipes is proposed. Unlike previous numerical approaches, the charging mechanism is studied in the framework of a charge relaxation process in which the equilibrium charge for uniform and localized charge distributions on the particle surfaces are determined. A recently proposed statistical model was also adopted to evaluate particle-wall collisions for wall-bounded flows, taking into account the influence of particle-particle collisions. Effects of particle concentrations, along with particle size and turbulence intensity, are also investigated. Model predictions are compared with experimental results, with good agreement found if the charge is assumed to be distributed on small surface sector of the particles. After defining suitable probability density functions for the variables considered, a Monte Carlo analysis is employed for simulating particle charge distributions and compared with published measurements to identify the important parameters during particle tribocharging.     

Numerical and experimental simulations of diffusion charging of non-spherical aerosol particles by dense bipolar ions

Numerical and experimental simulations have been conducted for the time history of the diffusion charging process on the surface of aerosol particles by dense bipolar ions under continuum conditions. The range of conditions treated in the numerical simulations include positive-negative ion diffusion coefficient ratio from 0 to 1, aerosol particle radius from 0.1 to 10 μm, Debye ratio R_p/λD from 0 to 1 (equivalent to maximum charge density up to N₁ = 10¹² cm⁻³ for an ion temperature of 300 K), the major-to minor axis ratios of prolate spheroids, L, from 1 to 100. The experimental simulation was conducted by using a conductive dummy particle suspended by a thin shielded wire, and the charged particle deposition current flux was measured and the bipolar environments. Then the effect of particle surface charges was simulated by imposing an electric potential on the dummy particles. The results show that, (1) for small ion density (R_{p/λD 10⁻²}); the present results are in good agreement with model of Chang et al. (1978, 1983). (2) the aeroso particle charging speed and charging limit increase with increasing Debye ratio; (3) for larger Debye ratio, bipolar charging is faster than unipolar charging; (4) the effect of particle shape L is observed to be significantly influenced by Debye ratios: (5) the charging limit of the aerosol particle increases with L.     

Charging of Ultra-Fine Aerosol Particles by an Ozone-Free Indirect UV Photo-Charger

Particle charging by indirect photoemission may be an alternative to charging methods based on corona discharge or on bipolar charging by radioactive ion sources. An indirect charger using a low energy UV radiation is introduced and characterized in detail. Depending on the carrier gas, photoelectrons or ions formed by electron-attachment charge the particles by diffusion charging. The achieved charging efficiency is in the range of 20–70% for particle sizes of 20 to 100 nm. It can easily be modulated by a small voltage applied to the photoemitter. To achieve stable electron emission, glassy carbon with its very inert surface is used as photoemitter. Particle losses are very small. The charge distribution has been measured by a tandem DMA setup. The experimental results are compared with the theory of unipolar diffusion charging based on the Fuchs’ combination probability of ions with the particles. The charger characterization has been performed by carbon particles in a size range of 20–100 nm, produced by a spark discharge generator.

Copyright 2013 American Association for Aerosol Research     

Numerical analysis of frictional charging and electrostatic interaction of particles

Triboelectrification due to frictional contacts between particles and surfaces is prevalent in many powder handling processes. Aiming to explore the friction-induced electrostatic charging behavior, a discrete element method (DEM) is developed for the first time in the current article, in which a frictional charging model and electrostatic interaction models are implemented. The charge accumulation on both the particles and the surface in a rotational container is then analyzed numerically and experimentally to evaluate the developed DEM. The numerical results for the frictional electrification between insulant particles and an insulant wall agree well with the experimental measurement. It is also shown that both the net charge on the particles and the degree of the particle dispersion are a function of the charging time. Moreover, it is revealed that the friction-induced particle charge enhances particle dispersion, and increases the granular temperature due to the electrostatic interactions.     

Performance of bipolar diffusion chargers: Experiments with particles in the size range of 100 to 900 nm

Accurate measurement of particle size distribution using electrical-mobility techniques requires knowledge of the charging state of the sampled particles. A consistent particle charge distribution is possible with bipolar diffusion chargers operated under steady-state condition. Theoretical steady-state charge distributions for bipolar charging are well established but recent studies have shown that the performance of particle chargers is a strong function of particle size, particle concentration, ion source, and charger operating conditions. Most of these studies have focused on particles smaller than 100 nm and the applicability of these results for particles larger than 100 nm must be investigated. In this study, experimentally obtained singly-charged and doubly-charged fractions are compared against theoretical predictions for particles in the size range of 100 to 900 nm. The experimental results show that the commercial soft X-ray charger performs as theoretically-predicted over the range of conditions studied while the performance of other commonly used radioactive chargers (⁸⁵Kr and ²¹⁰Po) are dependent on source strengths, flowrates, particle charge polarities, and particle sizes. From measurements of particle residence times and ion concentrations in different test bipolar chargers, prior observations of flowrate-dependent charging fractions can be explained. Additionally, the results from this study are used to determine an acceptable time period for usage of the commercial TSI 3077A ⁸⁵Kr chargers for steady-state charging as a function of flowrate.

Copyright © 2018 American Association for Aerosol Research     

Effect of an external electric field on the charge distribution of electrostatic coagulation

This article analyzes the effect of an external electric field on the charge distribution of bipolar and unipolar charged particles numerically by solving the coagulation equation for charged particles, based on the analytical expression for the coagulation coefficient [Wang, L. Z., Zhang, X. R., & Zhu, K. Q. (2005). An analytical expression for the coagulation coefficient of bipolarly charged particles by an external electric field with the effect of Coulomb force. Journal of Aerosol Science, 36, 1050–1055]. For symmetric bipolar charged particles, the external electric field does not change the symmetry of the initial charge distribution as the coagulation time increases. In addition, the particle number concentration decays monotonically during coagulation regardless of the magnitude of the particle charge. For asymmetric bipolar charged and unipolar charged particles, however, the particle number concentration does not decay monotonically for each value of charge during coagulation, due to the effect of an external electric field.     

Collision-Based Ionization: Bridging the Gap between Chemical Ionization and Aerosol Particle Diffusion Charging

In diffusion charging theory, it is assumed that each ion–particle collision leads to the transfer of charge from ion to particle, and that charge transfer will not occur upon collision between a vapor molecule and a charged particle. However, in chemical ionization, charge transfer can occur in two directions—from charge-donating ion to vapor molecule and back from charged vapor molecule to the original charge-donating species. Both aerosol diffusion charging and chemical ionization are collision-based charge transfer processes, and for particles only slightly larger than vapor molecules (aerosol clusters), the line between diffusion charging and chemical ionization becomes blurred. We examined the charge transfer from aerosol clusters (positively charged amino acid clusters) in the ～1.0 nm size range to neutral vapor molecules (trimethylamine) at atmospheric pressure by using a combined experimental and theoretical approach. It was found that for singly charged amino acid cluster ions composed of 1, 2, and 3 amino acid molecules, the rate of charge transfer to trimethylamine vapor molecules was clearly observable, particularly for clusters composed of 1 and 2 molecules. The charge transfer rate for singly charged clusters with 4 or more amino acid molecules was consistently close to 0, indicating that the rate of charge transfer from clusters to vapor molecules is size dependent. The charge transfer rates also varied with cluster's chemical composition. Overall, this study demonstrates that small aerosol clusters (～0.5 nm) can lose charge through collisions with vapor molecules, which is typically not considered in diffusion charging theories.     

The Effect of Particle Pre-Existing Charge on Unipolar Charging and Its Implication on Electrical Aerosol Measurements

We investigated the effect of particle pre-existing charges on unipolar charging. Particles carrying a defined number and polarity of pre-existing charges were used to study the unipolar charging process in a unipolar diffusion charger with positive ions. It was found that the particles initially carrying negative charges have almost the same amount of positive charges as the initially uncharged particles after passing the test charger; and the particles initially carrying more positive charges have more final charges. An analytical solution of a model for particle charge distribution of initially charged particles was provided for unipolar charging based on Fuchs' theory and the birth-and-death theory. The N _ion t value used in this model was obtained by fitting the experimental data of average charge on particles for initially uncharged particles. The results from the analytical solution show very good agreements with experimental data regarding the relationship between the pre-existing charge and the final charge on particles (50–200 nm in this study). Experimental tests of the response of Nanoparticle Surface Area Monitor (NSAM) against initially charged particles demonstrated that NSAM could have a large response deviation (more than 20% in the tested charge level) depending on the particle size and the amount of pre-existing positive charges on particles. Modeling of NSAM response showed similar deviation and predicted that when pre-existing charge is high enough, the NSAM response can be as large as 5 and 9 times of the uncharged particle response for alveolar and tracheobronchial surface area concentration, respectively.     

Capture of Viral Particles in Soft X-Ray–Enhanced Corona Systems: Charge Distribution and Transport Characteristics

The charge distribution of airborne MS2 bacteriophage nanoparticles and the efficiency of electrical-mobility–based capture mechanisms with bipolar charging were studied. MS2 virions form large agglomerated particles in a suspension. The average charge on airborne MS2 virions can be as high as one unit charge (negatively charged). The application of both soft X-ray irradiation and alpha rays from a Po-210 bipolar charger was shown to not only reduce the average charge on MS2 virion particles but also partially fragment the larger MS2 virion agglomerates, thereby increasing the number of ultrafine MS2 virion particles. A cylindrical electrostatic precipitator with a mounted soft X-ray emitter was used to determine the effectiveness of electrical capture methods for virus particles. At low applied voltages, it was found that the capture efficiency of ultrafine virus particles can be increased by applying in situ soft X-ray irradiation with electrostatic precipitation. It has also been shown that in the presence of both a positive and negative corona, virus particles are readily captured with log removal values exceeding 4. The unit developed and demonstrated in this work is a compact, low-pressure drop system that can be readily mounted in ventilation ducts or air supply systems to remove ultrafine particles such as viruses.