Diffusion Charging Of Aerosol Particles Research Articles

CoronaChargingFoam: An OpenFOAM based solver for multi-physical simulations of direct unipolar diffusion charging of aerosol particles

Diffusion charging of ultrafine aerosol particles is widely used in various fields and understanding the multi-physical phenomena during the charging processes is critical to the optimization of chargers and prediction of particle evolution in particulate systems. In this work, a numerical algorithm of unipolar aerosol diffusion charging is coupled with corona discharge, a combination of electric field, current continuity and heat transfer, and fluid flow enabling the modelling of multi-physics in direct charging processes. The governing equations are discretized based on the finite volume schemes. Methods of numerically calculating the ion-particle attachment coefficients are proposed and a class named niMixedFvPatchField describing the boundary condition of ion injection on the anode is defined on the basis of OpenFOAM libraries. Iteratively strategies are applied to uncouple the governing equations and the PISO (Pressure Implicit with Splitting of Operators) algorithm is used to solve the aerosol flow equations. A new solver labelled as coronaChargingFoam in the OpenFOAM framework is developed to implement the numerical algorithm and it is further validated by comparing four test cases: Laplacian electric field, electric field-charge coupling effect, ion-particle attachment coefficients, and charging efficiencies. Acceptable agreement level in all these comparisons verifies the fidelity of the solver implementation. Program summaryProgram Title: coronaChargingFoamCPC Library link to program files:https://doi.org/10.17632/vrfky24b8m.1Licensing provisions: GNU General Public License (either version 3 or any later version)Programming language: C++External routines/libraries: OpenFOAM (http://www.openfoam.org)Nature of problem: coronaChargingFoam solves the problem of aerosol charging dynamics in direct unipolar diffusion chargers in which the equations of diffusion charging are coupled with corona discharge, a combination of electric field, current continuity and heat transfer, and fluid flow enabling the modelling of multi-physics in direct charging processes.Solution method: coronaChargingFoam employs the Finite-volume method to discretize the governing equations. Iteratively strategies are applied to uncouple the multi-physical equations and the PISO algorithm is used to solve the flow fields. Simpson method and Fibonacci approach are employed in the calculation of ion-particle attachment coefficients. A new class, niMixedFvPatchField, is defined to describe the ion-injection boundary condition on the anode.Additional comments including restrictions and unusual features: The current version of the solver can only be applied in diffusion charging for monodisperse aerosol particles. This restriction will be relaxed in near future by adopting models for polydisperse particles and incorporating field charging mechanism.

An experimentally validated model of diffusion charging of arbitrary shaped aerosol particles

Particle shape strongly influences the diffusion charging of aerosol particles exposed to bipolar/unipolar ions and accurate modeling is needed to predict the charge distribution of non-spherical particles. A prior particle-ion collision kernel βi model including Coulombic and image potential interactions for spherical particles is generalized for arbitrary shapes following a scaling approach that uses a continuum and free molecular particle length scale and Langevin dynamics simulations of non-spherical particle-ion collisions for attractive Coulomb-image potential interactions. This extended βi model for collisions between unlike charged particle-ion (bipolar charging) and like charged particle-ion (unipolar charging) is validated by comparing against published experimental data of bipolar charge distributions for diverse shapes. Comparison to the bipolar charging data for spherical particles shows good agreement in air, argon, and nitrogen, while also demonstrating high accuracy in predicting charge states up to ±6. Comparisons to the data for fractal aggregates reveal that the LD-based βi model predicts within overall ±30% without any systematic bias. The mean charge on linear chain aggregates and charge fractions on cylindrical particles is found to be in good agreement with the measurements (~±20% overall). The comparison with experimental results supports the use of LD-based diffusion charging models to predict the bipolar and unipolar charge distribution of arbitrary shaped aerosol particles for a wide range of particle size, and gas temperature, pressure. The presented βi model is valid for perfectly conducting particles and in the absence of external electric fields; these simplifications need to be addressed in future work on particle charging.

Corona discharge in a cylindrical triode charger for unipolar diffusion aerosol charging

Abstract A cylindrical triode charger for unipolar diffusion charging of aerosol particles was designed, constructed, and evaluated. The corona discharge characteristics were studied in this cylindrical triode charger. For the process the current–voltage characteristics were determined, as were the ion number concentration, the nit product, and the mean charge per particle as a function of particle diameter. The discharge and charging currents, and ion number concentration in the charging zone of the charger increased monotonically with corona voltage. The negative corona had a higher current than the positive corona. At the same corona voltage, the ion number concentration in the discharge zone was larger than the charging current for positive and negative coronas, with values of about 197 and 32 times and 645 and 99 times for the ion-driving voltages of 0 and 310 V, respectively. The average ion penetration for positive and negative coronas was 0.64 and 0.19% and 3.62 and 1.93% for the ion-driving voltages of 0 V and 310 V, respectively. The higher flow rate, shorter residence time, gave a lower Nit product. By calculation 14% of charged particles of 10 nm in diameter were lost to the outer cylinder because of the electrostatic field effect. The charger does not use a sheath of air flow along the walls or the perforated screen opening, it has low diffusion and space charge losses due to the short column charging zone, and is a low complexity and inexpensive system. It worked as well as more sophisticated and expensive commercially available chargers.

Investigation on the Electrical Discharge Characteristics of a Unipolar Corona-Wire Aerosol Charger

In the present study, a simple corona-wire charger for unipolar diffusion charging of aerosol particles is designed, constructed, and characterized. Experimental characterizations of the electrostatic discharge in terms of current-voltage relationships of positive and negative coronas of the corona-wire charger are also presented and discussed. The charging current and ion concentration in the charging zone increased monotonically with corona voltage. The negative corona showed higher current than the positive corona. At the same corona voltages, the current in the discharge zone is about 600 times larger than the charging current. The ion number concentrations ranged within approximately 5.0 × 10 10 to 1.24 × 10 16 and 4.5 × 10 12 to 2 × 10 16 ions/m 3 in the discharge and charging zones, respectively. A numerical model is used to predict the behavior of the electric potential lines. Numerical results of ion penetration through the inner electrode are in good agreement with the experimental results.

Dependence of the Ion-Aerosol Equivalent Attachment Coefficient on the Ratio of Polar Conductivities in a Steady State

The article discusses certain theoretical problems of the diffusion charging of aerosol particles in a bipolar ion environment. The ratio of polar conductivities, induced by cluster ions of either polarity, may vary in a wide range. New results are obtained for the calculation algorithm of the ion-aerosol equivalent attachment coefficient in a steady state. Applying the Poisson sum formula, an analytical approximation equation is derived for the ion-aerosol equivalent attachment coefficient as a function of the ratio of polar conductivities and of the particle diameter. This equation could simplify calculations of ion-aerosol interaction characteristics in the range of sufficiently large particle diameters. A possibility for the creation of a related approximation equation for the range of smaller particle diameters is briefly outlined.

Unipolar diffusion charging of aerosol particles in the transition regime

This paper presents experimental results of unipolar diffusion charging of monodisperse combustion aerosols in the size range of 10–300 nm. A Hewitt-type corona charger was designed for the purpose of the investigation and tested in a Tandem-DMA experimental configuration with particles produced by a combustion aerosol generator (CAG). Measurements of the mean charge and the actual charge distribution of the monodisperse samples have been performed, while the apparatus allowed for the investigation of the effect of pre-existing charge of the aerosols. Results are compared with Fuchs' limiting-sphere theory and good agreement is found in most cases. Calculations with the birth-and-death method, using combination coefficients determined by the limiting-sphere theory, show that a Gaussian-type distribution fits well the experimental results. It is shown that pre-existing charge on the particles, as long as it is lower than the mean charge dictated by the operating conditions ( N i t product) of the charger, does not affect the final charging state of the aerosol. Using the classification column of a differential mobility spectrometer (DMS) we performed similar measurements at sub-atmospheric pressures. Variation of the pressure in the range of 250–1000 mbar appears to have an effect on the average number of charges acquired by the particles, although the differences among the measurements lie within the uncertainty levels of the experimental arrangement.

Monte-Carlo simulation of unipolar diffusion charging for spherical and non-spherical particles

This paper presents a 3D Monte-Carlo model that simulates diffusion charging of aerosol particles in positive unipolar environments. Calculations are performed for N i t products up to 5×10 12 ions m −3 s (with N i being the ion concentration and t the charging time), and particles with diameter 5– 1000 nm , covering a wide range of Knudsen numbers at atmospheric pressure. Apart from the average charge, the code allows for the calculation of the charge distribution which is shown to be well described by Gaussian statistics for monodisperse particles. Standard deviations of the charge distribution calculated with the source-and-sink approach show good agreement with the Monte-Carlo results. Comparison of the Monte-Carlo calculations with Fuchs’ limiting-sphere theory shows good agreement for the whole size range and highlights the importance of the image force effect for smaller particles. The diffusion-mobility theory of the continuum regime matches the simulation results for the larger particle sizes while differences with Fuchs’ limiting-sphere theory in this regime are relatively small. Simulations of non-spherical particles show the power of the code to easily handle more complicated situations. Results of rectangular-shaped and elongated chain-aggregate particles show different charging behaviour compared to theoretical predictions, and indicate the importance of the assumptions for the surface distribution of charges on the particle. In contrast, calculations of 3D cross-shaped aggregate particles, despite having a very irregular geometry, indicate that the spherical shape assumption is reasonable.

Diffusion charging of aerosol nanoparticles with an excess of bipoloar ions

The equations of diffusion charging of aerosol particles in a bipolar ion environment have no analytical transient solution. Such a solution can, however, be obtained in the special but important case of a relatively high ion concentration and aerosols with a particle size of a few nanometres, for which the probability of multiple charging is vanishingly small. The analytical transient solution obtained has an application to nanoaerosol particle size distribution measurement by electric mobility analysis. It also allows determination of the mean aerosol residence time required to attain the stationary charge distribution as a function of the ion concentration and physical properties (mass, mobility), this result having a practical application to the design of charging devices for aerosol nanoparticles.

Bipolar charging of ultrafine particles in the size range below 10 nm

Bipolar diffusion charging of aerosol particles in the size range of 2.3–10 nm was studied experimentally. Charging probability for WO x nanoparticles as a function of particle size was measured using an 241Am aerosol neutralizer for aerosol charging and a tandem DMA (Reischl type) with a VIE-06 Faraday cup electrometer for aerosol measurement. In spite of small deviations in the predictions from the theory of N. Fuchs on bipolar aerosol charging at 2–4 nm range, the theory was seen to be valid. Correction of the deviations may be performed by adjusting the free parameters in the theory (ion mass and mobility). As a rule of thumb, the charging probability of 2 nm particles was seen to be around 0.6% for negative and around 0.4% for positive particles.

Bipolar Ion and Electron Diffusion Charging of Aerosol Particles in high purity argon and nitrogen

AbstractThe bipolar diffusion charging process is studied theoretically for aerosol particles in high purity argon and nitrogen. The Fuchs theory is extended by the incorporation of the free electron charging of the aerosol particles. The ion parameters for positive and negative ions are assumed to be identical. The influence of the free electrons explains the differences between the mean mobility and mean mass of negative and positive ions. The ratio of the electron number concentration to the number concentration of negative ions is used to fit the curves, calculated by the extended model, to the experimentally determined bipolar charge distribution in argon and nitrogen. The extended Fuchs model was found to be rather insensitive to variations in the mobility and mass compared with the model with four different ion parameters. Further experimental studies of the bipolar charge distribution in a gas mixture of pure nitrogen and sulfur hexafluoride, SF6, indicate the importance of the free electrons in the bipolar diffusion charging process.

Bipolar Diffusion Charging of Aerosol Particles Under High Particle/Ion Concentration Ratios

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 smalle...

Simple Evaluation Method of Bipolar Diffusion Charging of Aerosol Particles and Its Application to Smoke Detectors

The diffusion charging of polydisperse and monodisperse aerosol particles by bipolar ions was theoretically studied under various conditions. Approximate equations in the simple form were derived to evaluate the changes in the particle charge and the ion number concentration. These approximate equations were applied to analyze the performance of the ionization-type smoke detector. The output response of an ionization-type smoke detector was experimentally tested with monodisperse aerosols, and the experimental response on the particle size and number concentration dependence were found to be explained by the simple approximate equations.

Bipolar diffusion charging of aerosol particles—I: experimental results within the diameter range 4–30 nm

Experimental results obtained on the fraction of charged particles of a monodisperse aerosol with a diameter of less than 10 nm can help to decide which of the charging theories most correctly describes the charging process in the whole particle size range. In this study the experimental results on bipolar diffusion charging of aerosol particles with a diameter between 4 and 30 nm are presented. A difference between the fraction of positively and negatively charged aerosol particles in equilibrium was measured, using a bipolar charger with equal negative and positive ion concentrations. The results were in best agreement with the bipolar charging theory of Fuchs, taking into account the different values of the physical parameters for negative and positive ions.

Theory of diffusion charging of arbitrarily shaped conductive aerosol particles by unipolar ions

The theory of diffusion charging of aerosol particles by unipolar ions having no external electric fields, is re-examined for arbitrary particle shape. For smaller effective Knudsen number (continuum limit), the time history of the charging of arbitrarily shaped particles can be obtained when the capacitance of the particles is known. For larger effective Knudsen numbers, the time history of the charging of arbitrarily shaped particles can be obtained when the capacitance and surface area of particles are known. Systematical analyses have been presented for bipolar sphere, oblate and prolate spheroids. The effect of gravitational motion of large aerosol particles on the charging process has been discussed.

Combined field and diffusion charging of aerosol particles in the continuum regime

The charging of aerosol particles by unipolar ions in an electric field has been studied theoretically by means of a numerical solution technique. The technique involves calculating the particle charging rate by solving the macroscopic ion diffusion equation in an electric field by relaxation and then integrating the particle charging rate to determine the particle charge as a function of charging time. Results are presented showing the dimensionless particle charge, γ, as a function of dimensionless time, τ, for various dimensionless electric fields, ω. The study provides a rigorous solution to the problem of combined field and diffusion charging of aerosol particles in the continuum regime. Comparison of the theoretical results with the experimental data of Hewitt (1957) and those of Smith et al. (1977) shows that there is good agreement between the theoretical and experimental results. The discrepancy between theory and experiment is of the same order of magnitude as the estimated uncertainties in the experimental data themselves.

Diffusion Charging of Aerosol Particles at Low Pressures

The diffusion charging of aerosol particles by unipolar ions has been studied experimentally over the pressure range, 0.0311 to 0.960 atm, using monodispersed aerosols of di-octyl phthalate. The ratio, a/λ, of the particle radius to the mean free path of ions has been varied over the range from 1.0 to 66. Within the accuracy of the experiments, the particle charge has been found to be independent of the ratio, a/λ, and well represented by the equation, np=9.00Dp ln (1+1.02×10−5N0tDp), where np is the number of elementary units of charge acquired by the particle, Dp is the diameter of the particle in microns, N0 is the number concentration of the ions to which the particle has been exposed in ions/cc, and t is the charging time in seconds. This equation agrees with a theoretical equation derived by White when the molecular weights of the positive ions used in the charging experiments are assumed to be equal to 16 times that of air or 460.