Simulation of Aerosol Dynamics: A Comparative Review of Algorithms Used in Air Quality Models

A comparative review of algorithms currently used in air quality models to simulate aerosol dynamics is presented. This review addresses coagula tion, condensational growth, nucleation, and gas particle mass transfer. Two major approaches are used in air quality models to represent the particle size distribution: (1) the sectional approach in which the size distribution is discretized into sections and particle properties are assumed to be constant over particle size sections and (2) the modal approach in which the size distribution is approxi mated by several modes and particle properties are assumed to be uniform in each mode. The sectional approach is accurate for coagulation and can reproduce the major characteristics of the evolution of the particle size distribution for condensa tional growth with the moving-center and hybrid algorithms. For coagulation and condensational growth, the modal approach provides more accurate results when the standard deviations of the modes are allowed to vary than it does when they are fixed. Predictions of H₂SO₄ nucleation rates are highly sensitive to environ mental variables and simulation of relative rates of condensation on existing particles and nucleation is a preferable approach. Explicit treatment of mass transfer is recommended for cases where volatile species undergo different equilib rium reactions in different particle size ranges (e.g., in the presence of coarse salt particles). The results of this study provide useful information for use in selecting algorithms to simulate aerosol dynamics in air quality models and for improving the accuracy of existing algorithms.     

Temporal Characteristics of Aerosol Optical Depths and Size Distribution at Visakhapatnam,India

Aerosol spectral optical depths and size distribution derived from the direct solar flux measurements at nine discrete wavelengths in the visible and near IR region for a period of about 10 years exhibit a gradual increase in the aerosol spectral optical depths from 1994-1997. There was a very large increase in the optical depths during 1991 after the volcanic eruption of Mt. Pinatubo and its effect persisted until 1993-94. The size distribution during 1988-1996 (excluding 1991, 1992, and 1993) remained bimodal in nature with an increase in the small particle number density with year. The aerosol optical depths and size distribu tions at Visakhapatnam also show some short period changes, characterizing the high sensitivity of the coastal urban aerosol system to the mesoscale weather. The observed features have been explained on the basis of the aerosol genesis based on local sources, sinks, and the prevailing weather.     

Description of Aerosol Dynamics by the Quadrature Method of Moments

ABSTRACT

The method of moments (MOM) may be used to determine the evolution of the lower-order moments of an unknown aerosol distribution. Previous applications of the method have been limited by the requirement that the equations governing the evolution of the lower-order moments be in closed form. Here a new approach, the quadrature method of moments (QMOM), is described. The dynamical equations for moment evolution are replaced by a quadrature-based approximate set that satisfies closure under a much broader range of conditions without requiring that the size distribution or growth law maintain any special mathematical form. The conventional MOM is recovered as a special case of the QMOM under those conditions, e.g., free-molecular growth, for which conventional closure is satisfied. The QMOM is illustrated for the growth of sulfuric acid-water aerosols and simulations of diffusion-controlled cloud droplet growth are presented.     

A new splitting wavelet method for solving the general aerosol dynamics equation

In this paper, a new and robust splitting wavelet method has been developed to solve the general aerosol dynamics equation. The considered models are the nonlinear integro-partial differential equations on time, size and space, which describe different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. The proposed method reduces the complex general aerosol dynamic equation to two one-dimensional splitting equations in each time interval, and further the wavelet method and the upstream finite difference method are proposed for solving the particle size directional and the spatial directional splitting equations. By the method, the aerosol size spectrum is represented by a combination of Daubechies’ wavelets and substituted into the size-directional splitting equation at each time step. The class of Daubechies’ wavelets in the wavelet-Galerkin scheme as trial and weight functions has the advantages of both compact support and orthonormality which can efficiently simulate the sharp shape distribution of aerosols along the particle size direction. Numerical experiments are given to show the efficient performance of the method.     

Determination of the aerosol particle size distribution by means of the diffusion battery: Analytical inversion

The algorithm of the analytical inversion of aerosol size distribution is proposed in this work. As the diffusion battery separates particles into several fractions according to their diffusivity, the total spectrum can be represented as the sum of spectra of fractions. Analytical formulas are derived to calculate mean diameters for particles in different fractions using diffusion battery penetrations as input parameters. The spectra of fractions are approximated by lognormal functions. Two analytical solutions for the aerosol size distribution inversion problem are discussed. The sizing accuracy of analytical solutions is investigated, comparing them with the measurements through transmission electron microscopy using the laboratory-generated NaCl aerosol. The agreement is demonstrated to be within 10% accuracy. It is shown that in case of two-mode size distribution, the spectrum components are well resolved for rather distant peaks (modal diameters of 10 and 300?nm) and poorly resolved for nearby modes (50 and 300?nm). To improve the peak resolution, the procedure of spectrum correction is applied demonstrating an excellent peak separation. Finally, the peak resolution is experimentally verified for the laboratory-generated two-mode spectra of tungsten oxide–NaCl aerosol with the modal diameters of 10 and 60?nm, respectively. Both analytical solutions demonstrated good peak resolution.

Copyright © 2018 American Association for Aerosol Research     

Study of Visibility Degradation Due to Coagulation,Condensation, and Gravitational Settling of the Atmospheric Aerosol

This work studies the evolution in time of the light extinction coefficients of the single-component spherical aerosols after a given mechanism of removal (coagulation, heterogeneous nucleation, and gravitational settling) as a function of time. The well-known equations of scavenging are applied to 3 atmospheric environments (clear, hazy, and urban) that represent the aerosol particle size distributions (PSDs) in the countryside, the industry, and the city, respectively. The aerosol scattering and absorption coefficients are determined from the single particle light extinction efficients, K s ( m , p ) and K a ( m , p ), where m is the complex refractive index of each particle and p = ~ D p / u , the dimensionless parameter relating the particle diameter D p to the wavelength u of the incident light. The single particle light extinction efficiences K s and K a can be derived theoretically by Mie's solution to Maxwell's equations (van de Hulst 1981; Kerker 1969). From this study it is inferred that gravitational settling predominates with respect to coagulation and condensation since the visual range is increased considerably. Besides, gravitational settling is the main mechanism for removal of respirable aerosol in comparison to condensation and coagulation and is close to 6 times better than rainout (García Nieto et al. 1994).     

Determination of Arbitrary Moments of Aerosol Size Distributions from Measurements with a Differential Mobility Analyzer

A method to determine arbitrary moments of aerosol size distributions from differential mobility analyzer measurements has been proposed. The proposed method is based on a modification of the algorithm developed by Knutson and Whitby to calculate the moments of electrical mobility distributions. For this modification, the electrical mobility and the charge distribution have been approximately expressed by power functions of the particle diameter. To evaluate the validity of the approximation, we have carried out numerical simulations for typical size distributions. We have found that for typical narrowly distributed aerosols such as polystyrene latex particles and particles that arise in the tandem differential mobility analyzer configuration, the distribution parameters can be accurately determined by this method. For a log-normally distributed aerosol, the accuracy of the distribution parameters determined by this method has been evaluated as a function of the geometric standard deviation. We have also compared the accuracy of the proposed method with other existing methods in the case of the asymmetric Gaussian distribution.     

Development and Preliminary Validation of a Modal Aerosol Model for Tropospheric Chemistry: MAM

This paper presents a modal aerosol model (MAM) developed to be used in three dimensional air quality models. MAM, which represents the aerosol distribution with four modes, has the advantage of simplicity and speed efficiency associated to modal models, while mass transfer is modeled with a dynamic approach. To assess the ability of MAM to represent mass transfer, MAM is compared to a size-resolved model based on the dynamic approach and to a version of MAM based on an equilibrium approach. Comparisons are done using measurements of inorganic species made in Japan as initial conditions. Furthermore, it is shown that MAM combined with a well chosen mode splitting scheme is able to deal accurately with the simultaneous occurrence of strong nucleation/condensation and coagulation, as may be observed in high nucleation episodes.     

Simulation of Aerosol Dynamics: A Comparative Review of Mathematical Models

A comparative review of mathematical models of aerosol dynamics is presented. Three approaches are considered that are based on continuous, discrete (sectional), and parametrized (lognormal) representations of the aerosol size distribution. Simulations of coagulation and diffusion-limited condensation are performed with these modeling approaches for three case studies typical of clear, hazy, and urban atmospheric aerosol concentrations. The relative accuracies and computational costs of models based on these approaches are compared. The models based on a continuous size distribution provide an accurate solution for both coagulation and condensation. Sectional approaches simulate coagulation very well but require a fine size resolution to minimize numerical diffusion in the simulation of condensation. The parametrized model based on log-normal modal size distributions is computationally efficient but tends to overestimate the rate of coagulation and the peak aerosol concentration resulting from condensational growth. The results of this study provide useful information for the selection of an aerosol model, depending on the accuracy requirements and computational constraints associated with a specific application.     

Numerical modeling of the performance of high flow DMAs to classify sub-2 nm particles

While there are several computational studies on differential mobility analyzers (DMA), there is none for high flow DMA to classify nanoparticles less than 3?nm. A specific design of a high flow DMA, a half mini DMA, is investigated to predict its performance through numerical modeling in the incompressible flow regime. The governing equations for flow field, electric field and aerosol transport are solved using COMSOL 5.3. The transfer function of the half mini DMA is compared with that of a nano DMA (TSI 3085). The results show that both the height of the transfer function and resolution (R) of the half mini DMA are much better than those of nano DMA in sub-2?nm particle size range. Finally, the transfer function of half mini DMA is evaluated for different values of aerosol flow rate to the sheath flow rate (q/Q). Comparison of the simulated transfer function with existing models from Knutson–Whitby and Stolzenburg is also elucidated. It is found that the former model overestimates the resolution; whereas the latter is close to the simulation results for q/Q above 0.067. This work provides a useful method to study the flow regimes and transfer function of a high flow DMA.

Copyright © 2018 American Association for Aerosol Research     

Rapid Check of Cascade Impactor Cut-Sizes using a Polydisperse Challenge Aerosol Calibration Method

A method has been developed to check the 50% cut-size values of cascade impactor stages. The method involves generating a broad-size, log-normally distributed aerosol that covers the range of 50% cut-sizes for the impactor being tested. The amount of deposit on each impaction plate is analyzed and a histogram of the resulting aerosol size distribution plotted, using the amount of aerosol collected on each impaction plate and the published values for the cut-sizes of the impactor in question. If the particle size distribution indicated by the histogram does not result in a log-normal distribution, one or more of the assumed cut-sizes of the impactor are in error. The incorrect cut-sizes of the impactor can then be adjusted until the curve is log-normal, and these adjusted cut-sizes are the correct values for the impactor stages.     

Absolute Mass and Size Measurement of Monodisperse Particles Using a Modified Millikan's Method: Part I—Theoretical Framework of the Electro-Gravitational Aerosol Balance

A new method for accurate mass and size measurement of monodisperse particles is proposed. In this method, charged aerosol particles are introduced into parallel plate electrodes similar to the Millikan cell, and the number of particles left suspended after a certainty holding time has elapsed is measured. The particle survival rate as a function of the voltage applied to the electrodes is used to determine the particle mass. The particle size is deduced by using the particle density which is determined in a separate experiment. The expression of the particle survival function, which is defined as the survival rate as a function of the mass, for particles with and without Brownian diffusion is derived. The sensitivity of this method to the number average diameter, as well as other size distribution parameters, is analyzed on the basis of the survival function.     

Size distribution dynamics of fuel-borne catalytic ceria nanoparticles

Ceria-based fuel additives in diesel engines when dosed at above a certain concentration into the fuel have been shown to lead into bimodal exhaust particle size distributions in a previous study. In order to model this complex problem it is assumed that the soot aggregate size distribution (where each aggregate consists of individual primary particles) evolves fast toward a constant total surface area (determined by the “open” non-coalesced fractal aggregate morphology) and this surface represents a sink for the ceria nuclei. The latter undergo kinetic aggregation among them as well as are simultaneously scavenged by the soot particles. The mathematical model is formulated in terms of an aerosol population balance equation for the ceria particles. The governing parameter in the resulting dimensionless population balance equation is the ratio of the total surface area of the soot aerosol over the initial additive surface area. The latter is proportional to the total additive mass if the ceria critical nuclei are assumed to consist of one molecule, an appropriate assumption for high surface tension, metal oxides like ceria. The experimental results show that the critical additive concentration at the onset of the bimodal shape of the exhaust size distribution scales linearly with the exhaust soot mass fraction, hence the soot aggregates must have a quite “open” fractal structure in order for their total area to be proportional to their total mass. Although simple population balance models may provide some insight into the problem of interest, the experimental results show that models accounting for more complex interactions of additive and soot particles (potentially involving incomplete accommodation) must be investigated in the future.     

Aerosol Growth in a Steady-State,Continuous Flow Chamber: Application to Studies of Secondary Aerosol Formation

An analytical solution for the steady-state aerosol size distribution achieved in a steady-state, continuous flow chamber is derived, where particle growth is occurring by gas-to-particle conversion and particle loss is occurring by deposition to the walls of the chamber. The solution is presented in the case of two condensing species. By fitting the predicted steady-state aerosol size distribution to that measured, one may infer information about the nature of the condensing species from the calculated values of the species's molecular weights. The analytical solution is applied to three sets of experiments on secondary organic aerosol formation carried out in the U.S. Environmental Protection Agency irradiated continuous flow reactor, with parent hydrocarbons: toluene, f -pinene, and a mixture of toluene and f -pinene. Fits to the observed size distributions are illustrated by assuming two condensing products for each parent hydrocarbon; this is a highly simplified picture of secondary organic aerosol formation, which is known to involve considerably more than two condensing products. While not based on a molecular-level model of the gas-to-particle conversion process, the model does allow one to evaluate the extent to which the observed size distribution agrees with that based on a simple, two-component picture of condensation, and to study the sensitivity of those size distributions to variation of the essential properties of the condensing compounds, such as molecular weight. An inherent limitation of the steady-state experiment is that it is not possible to calculate the vapor pressures of the condensing species.     

Evolution of particle metrics in a buoyant aerosol cloud from explosive releases

Abstract

The detonation of high explosive (HE) material generates a cloud containing a high concentration of detonation products in the form of aerosol particles and gases. Modeling and simulation of aerosol metrics in an explosive cloud is a complex problem as it involves various processes such as chemical reaction, nucleation, volume expansion, and coagulation. Several models have been developed to study the atmospheric dispersion of these detonation products, but very few or no model is available to study the evolution of aerosol metrics at the early stage. In this work, we present a numerical model to simulate the temporal evolution of aerosol metrics in an expanding cloud by coupling transient thermodynamic properties with important microphysical processes. To illustrate the application, the numerical model is applied to a typical HE, and the aerosol particle properties such as size distribution, number concentration, and average size are estimated from the numerical results. These results will provide the essential input conditions for atmospheric dispersion models to estimate the atmospheric concentration and deposition of aerosol particles.

Copyright © 2020 American Association for Aerosol Research     

A diethylene glycol condensation particle counter for rapid sizing of sub-3 nm atmospheric clusters

Abstract

This article describes the modification of a laminar flow, thermally diffusive universal-fluid condensation particle counter (standard operation: 50% detection efficiency at 5?nm) to rapidly measure the size distribution of sub 3?nm aerosol. Sub 3?nm detection was achieved by using diethylene glycol as the working fluid, which enabled high instrument super-saturations while minimizing homogenous nucleation of the working fluid; a detection efficiency of 50% was achieved at 1.6?nm with laboratory-generated ammonium sulfate (AS) aerosol. Rapid aerosol sizing beneath 3?nm was achieved by inverting the measured grown droplet size distribution (1?s sampling) to recover the sampled aerosol size distribution. The developed inversion algorithm utilizes analytical kernel functions determined from the instrument response to pseudo-monodisperse AS aerosol from 1.5?nm to 20?nm, generated by a high-resolution DMA and a nano DMA. The inversion algorithm was tested numerically with assumed, idealized aerosol size distributions consistent with observed new particle formation events, yielding a reasonable agreement between inverted and assumed aerosol size distributions below 3?nm. This technique provides a measure of the aerosol size assuming an aerosol composition identical to that of the aerosol used to generate the experimentally determined kernel function.

Copyright © 2018 American Association for Aerosol Research     

Wall Loss Rate of Polydispersed Aerosols

Wall loss rates of polydispersed aerosols in a stirred vessel were studied theoretically and experimentally. A formula for the poly- dispersity factor of the wall loss rate was derived using the moment method of log-normal size distribution and compared with numerical calculations. The representative theory of Crump and Seinfeld (1981) was used as the wall loss rate of monodispersed aerosols in which the Brownian diffusion, the turbulent eddy diffusion, and the gravitational settling are included as wall loss mechanisms. The results of the analysis show that the wall loss rate of a polydispersed aerosol is substantially higher than that based on a monodispersed size distribution model if the particle size distribution can be represented reasonably well by a log-normal function. The existing diagram showing the loss rate as a function only of the particle size was expanded to include the polydispersity effects. Experimental measurements of particle wall loss rate were performed by observing the time-dependent changes in particle number concentration for various stirring intensities in a cylindrical stirred chamber. It was shown that by correcting for the polydispersity effect, the dependence of the wall loss rate on particle size and stirring intensity agreed with the theory of Crump and Seinfeld (1981).     

Mathematical Modeling of Double-Stage Electrostatic Precipitators Based on a Modified Eulerian Approach

A new mathematical model has been developed to predict the performance of a double-stage electrostatic precipitator. This model is based on the Eulerian approach for particle dispersion taking into account the particle size distribution. In this model, by calculating the frequency size distribution of particles and particle concentration distribution simultaneously through a modified particle dispersion equation, the CPU time for solving the governing equations has been reduced significantly. In order to evaluate velocity distribution of the fluid, the k     

Online Nanoparticle Mass Measurement by Combined Aerosol Particle Mass Analyzer and Differential Mobility Analyzer: Comparison of Theory and Measurements

A combination of a differential mobility analyzer (DMA) and aerosol particle mass analyzer (APM) is used to measure the mass of NIST Standard Reference Materials (SRM®) PSL spheres with 60 and 100 nm nominal diameter, and NIST traceable 300 nm PSL spheres. The calibration PSL spheres were previously characterized by modal diameter and spread in particle size. We used the DMA to separate the particles with modal diameter in a narrow mobility diameter range. The mass of the separated particles is measured using the APM. The measured mass is converted to diameter using a specific density of 1.05. We found that there was good agreement between our measurements and calibration modal diameter. The measured average modal diameters are 59.23 and 101.2 nm for nominal diameters of 60 and 100 nm (calibration modal diameter: 60.39 and 100.7 nm) PSL spheres, respectively. The repeatability uncertainty of these measurements is reported. For 300 nm, the measured diameter was 305.5 nm, which is an agreement with calibration diameter within 1.8%.

The effect of spread in particle size on the APM transfer function is investigated. Two sources of the spread in “mono-dispersed” particle size distributions are discussed: (a) spread due to the triangular DMA transfer function, and (b) spread in the calibration particle size. The APM response function is calculated numerically with parabolic flow through the APM and diffusion broadening. As expected from theory, the calculated APM response function and measured data followed a similar trend with respect to APM voltage. However, the theoretical APM transfer function is narrower than the measured APM response.     

ON THE RETRIEVAL OF URBAN AEROSOL MASS CONCENTRATION BY A 532 AND 1064 nm LIDAR

Based on the hypothesis of a monomodal, lognormal size distribution, the uncertainty affecting the humid-mass retrieval from LIDAR data was estimated by considering our ignorance of the distribution width to be a source of error. The mass to backscatter ratio and its uncertainty were computed for six accumulation-mode aerosol models as a function of the backscatter angstrom coefficient (α) and of the relative humidity (RH). A mass to backscatter uncertainty of less than ±30% was obtained for all six models. We computed the mass and simulated the expected LIDAR backscatter at 532 and 1064 nm for a test data set of 14 “real-world” multimodal size distributions obtained from the literature. The possible presence of 0–20%–50% water-insoluble compounds in each aerosol mode was assumed. An urban-type accumulation mode and 10 different coarse mode compositions were considered, including dust-like aerosols. The aerosol mass concentration was derived by fitting the simulated LIDAR data at 532 and 1064 nm with a monomodal distribution of urban aerosols of “unknown” width. The relative over- or underestimation of the mass with respect to the real aerosol mass was expressed in terms of α and RH for the 10 coarse aerosol types. The LIDAR-derived mass turned out to be underestimated by 0 – 15% in the case of (NH₄)₂SO₄, NaCl, maritime, and H₂SO₄ coarse aerosols. In the case coarse dust aerosols, the range of underestimation was wider (0–30%). Absorbing aerosols showed a maximum underestimation of 40–50%.