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.     

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.     

Sectional Modeling of Aerosol Dynamics in Multi-Dimensional Flows

The integration of computational fluid dynamics (CFD) with computer modeling of aerosol dynamics is needed in several practical applications. The use of a sectional size distribution is desirable because it offers generality and flexibility in describing the evolution of the aerosol. However, in the presence of condensational growth the sectional method is computationally expensive in multidimensional flows, because a large number of size sections is required to cope with numerical diffusion and achieve accuracy in the delicate coupling between the competing processes of nucleation and condensation. The present work proposes a methodology that enables the implementation of the sectional method in Eulerian multidimensional CFD calculations. For the solution of condensational growth a number conservative numerical scheme is proposed. The scheme is based on a combination of moving and fixed particle size grids and a re-mapping process for the cumulative size distribution, carried out with cubic spline interpolation. The coupling of the aerosol dynamics with the multidimensional CFD calculations is performed with an operator splitting technique, permitting to deal efficiently with the largely different time scales of the aerosol dynamics and transport processes. The developed methodology is validated against available analytical solutions of the general dynamic equation. The appropriateness of the methodology is evaluated by reproducing the numerically demanding case of nucleation-condensation in an experimental aerosol reactor. The method is found free of numerical diffusion and robust. Good accuracy is obtained with a modest number of size sections, whereas the computational time on a common personal computer remained always reasonable.     

The Effects of Differential Diffusion on Nanoparticle Coagulation in Temporal Mixing Layers

The effects of size-independent diffusive transport on nanoparticle growth is studied by performing direct numerical simulation of nanoparticle coagulation in temporal mixing layers. The flow field is obtained by solving the incompressible Navier-Stokes equations, while the evolution of the particle field is obtained by using a nodal approach to approximate the aerosol general dynamic equation. Simulations are performed where particles diffuse according to their size and also where all particles have the same diffusivity. For the latter, the model assumes that all particles of different sizes have the same diffusivity as the smallest particles. The advantage of the second approach is the length scales that need to be resolved are larger, facilitating more affordable computations. Simulations are performed at two volume fractions to assess the effects of the models under different growth rates. The results indicate the use of size-independent diffusion coefficients predicts particle sizes and geometric standard deviations that are larger than those obtained with size-dependent diffusion coefficients.     

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.     

Mean field theory for condensation on aerosols and application to multi-component organic vapours

The timescale is calculated for a particle to equilibrate by vapour condensation from a surrounding volume equal to the volume per particle in an aerosol, and is compared to the timescale to transport vapour by diffusion to neighbouring particle volumes. For practically all aerosols, the diffusive timescale is much smaller, showing that vapour diffusion, and, in the same way heat conduction, ensure that the vapour concentration and temperature in the vapour–gas mixture assume mean field values with which the whole of the aerosol equilibrates. Recent claims that individual particles equilibrate with the mixture are refuted. The concept is applied to obtain equations for the condensation of organic vapours whose equilibrium with condensate is governed by absorption partitioning coefficients together with a Kelvin term at small sizes. These dynamic equations, which contain vapour production and condensational loss terms, have steady-state solutions when these terms are changing slowly with time. Such solutions are obtained for non-volatile and semi-volatile constituents, their difference being defined to be that the equilibrium concentration is small compared to the actual concentration in the non-volatile case. For semi-volatile material, the concentration will generally be maintained at a value close to equilibrium over plane surfaces, so that it cannot contribute to nucleation and growth at small sizes. As for water condensation in the atmosphere, particles need to reach a certain size to be activated for growth by condensation of semi-volatile organics.     

Aerosol diffusion battery: The retrieval of particle size distribution with the help of analytical formulas

A new algorithm is proposed for the determination of aerosol particle size distribution from a set of screen diffusion battery penetrations. The idea is to determine the size spectra of the fractions of particles separated by the sections of diffusion battery, so the total size distribution is the sum of the spectra of fractions. The spectrum of each fraction is approximated by the lognormal function, which is defined by two parameters: the standard geometric deviation (SGD) and geometric mean diameter. The SGD value is chosen to be 1.35 for each fraction. The geometric mean diameters of fractions are calculated from the diffusion battery penetrations. For this purpose, analytical formulas are derived to link the mean single-fiber collection efficiency for each fraction with the experimentally measured penetrations. Then the mean diameters of fractions are calculated from the collection efficiencies using the fan model filtration theory. To achieve a better size resolution, numerical approach is proposed to calculate the particle size spectrum using the analytical solution as an initial approximation. The validity of the analytical and numerical solutions is investigated by comparing them with the spectra determined by means of transmission electron microscopy and gravity settling. For this purpose, the aerosol is generated using the evaporation-nucleation technique, Collison-type nebulizer, and hot-wire bulb generator. It is found that the analytical solution demonstrates a good sizing accuracy but relatively poor size resolution, while the numerical approach results in both good sizing accuracy and good size resolution for the two-mode aerosol.

Copyright © 2018 American Association for Aerosol Research     

叶栅通道内湿蒸汽非平衡凝结流动的数值模拟

过冷度是各种凝结现象产生、发展的直接驱动力,叶栅通道内湿蒸汽成核过程通常集中在喉部下游很窄的区域内,水滴数目和水滴半径分布则受到边界层和尾迹影响。针对叶栅通道内跨音速非平衡凝结流动参数分布陡峭、变化敏感的特点,采用具有较好激波捕获效果的高分辨率二阶TVD格式进行离散。利用时间推进法对控制方程进行求解,建立了凝结流动的数值解法,模拟与实验结果相吻合,验证了模型的准确性。研究了叶栅通道内非平衡凝结流动的基本物理现象,讨论了进口过冷度对凝结特性的影响,归纳了叶栅通道内压力、成核率、水滴数、水滴半径、蒸汽湿度的变化规律。研究表明:进口过冷度对非平衡凝结流动特性有重要影响。     

Analytic and numerical calculations of the formation of a sulphuric acid aerosol in the upper troposphere

Analytic and numerical calculations are performed on the production of sulphuric acid aerosol in conditions of a very large nucleation event observed in the upper troposphere. The numerical results feature a growing peak in the size distribution whose magnitude is reproduced well analytically, and are consistent with the observed particle number concentration at sizes greater than 25 nm (measured dry diameter), but suggest that most of the aerosol was at unobserved smaller sizes. Because of growth and coagulation, number concentrations of the aerosol rapidly become independent of the number initially nucleated, so that conclusions as to the nucleation process, either homogeneous or ion-induced nucleation, cannot easily be drawn from existing atmospheric observations. The final concentration is very insensitive to the magnitude of the SO₂ source, but, if condensation on, and coagulation with, a remnant background aerosol occurs, such nucleation events will be cut off for source magnitudes less than a specific value. Anthropogenic emissions of SO₂ which exceed this value can produce higher aerosol number concentrations in the atmosphere with consequences for the indirect effect of aerosols on the climate.     

A Bimodal Integral Solution of the Dynamic Equation for an Aerosol Undergoing Simultaneous Particle Inception and Coagulation

A model is developed from the general aerosol dynamic equation, using a bimodal integral formulation that includes particle formation and growth by coagulation in the free molecular regime. The particle inception mode accounts for the introduction of newly formed particles which, through coagulative collisions with one another, constitute the source of the particles in the growth mode. A numerical solution for the system of the first three moments of the particle volume distribution function is discussed, under the assumption of a logarithmic-normal behavior of the two modes of the size distribution function. The bimodal integral solution is subject to a detailed comparison with the MAEROS sectional model for the case of an aerosol that undergoes free molecular coagulation occurring simultaneously with particle formation by a Gaussian source pulse, under flamelike conditions.     

Depth-resolved impact of integration process on porosity and solvent diffusion in a SiOCH low-k material

The impact of plasma etching and chemical wet cleaning on solvent diffusion in porous network of a SiOCH low-k dielectric material is studied. Characterization of porosity and pore size distribution by means of ellipso-porosimetry and positron annihilation lifetime spectroscopy are presented. The results are compared with solvent diffusion kinetics, measured using probe molecules of different polarity, surface energies and molecular sizes. Infrared spectroscopy, Doppler broadening of annihilation radiation and time-of-flight secondary ion mass spectrometry measurements are also performed to investigate material modifications causing variations of diffusion kinetics.     

A SIMPLIFIED DESCRIPTION OF CHAR COMBUSTION

A simplified analysis of carbonaceous particle combustion is presented that includes the effects of pore diffusion and growth as well as gas-phase heat and mass transfer. The combustion dynamics are described by time-dependent equations for particle temperature, radius and a number of intraparticle conversion variables. These are coupled to pseudosteady equations for gas-phase transport and internal reaction and diffusion. The differential equations for gas-phase transport are reduced by quadrature to a nonlinear boundary condition to the intraparticle boundary value problem. Numerical calculations are performed for conditions relevant to pulverized coal combustion. An analytical solution of the intraparticle problem, pertinent to the regime of strong diffusional limitations, reduces the intraparticle solution into a set of two quadratures which drastically simplifies the numerical calculations. The simplified intraparticle solution is in excellent agreement with the full solution at 1800 K free stream temperature and fair agreement at 1500 K.     

The Behavior of Constant Rate Aerosol Reactors

An aerosol reactor is a gaseous system in which fine particles are formed by chemical reaction in either a batch or flow process. The particle sizes of interest range from less than 10 Å (molecular clusters) to 10μm. Such reactors may be operated to study the aerosol formation process, as in a smog reactor, or to generate a product such as a pigment or a catalytic aerosol. Aerosol reactors can be characterized by three temporal or spatial zones or regions of operation for batch and flow reactors, respectively. In zone I, chemical reaction results in the formation of condensable molecular products which nucleate and form very high concentrations of small particles. The number density depends on the concentration of preexisting aerosol. Zone II is a transition region in which the aerosol number concentration levels off as a result of hetergeneous condensation by the stable aerosol. In zone III coagulation becomes sufficiently rapid to reduce the particle number concentration. There may be a zone IV in which agglomerates form. Chemical reaction may continue to generate condensable material throughout the various zones. This paper deals with reactors in which aerosol material is generated at a constant rate. Design parameters of interest are the particle size distribution, number density, surface area, and mass loadings. For ideal systems composed of spherical coalescing particles, these can be predicted theoretically for certain limiting cases. However, the irregular agglomerates which may form in zone IV are more difficult to characterize theoretically.     

In-situ characterization of ultrafine particles by laser-induced incandescence: sizing and particle structure determination

The laser-induced incandescence (LII) method is applied to the in situ size analysis of aerosol particles of different origin at room temperature. A detailed theoretical model of the particle heating and cooling for the different size fractions incorporating a solution of a Fredholm integral equation of the first kind is used to retrieve the particle size distribution from the time-dependent aerosol thermal emission detected after a ns laser pulse. The results are compared with TEM data of deposited aerosol particles along with online measurements employing a differential mobility analyzer (DMA). Besides the size distribution, the LII signal contains information on the internal structure of particle agglomerates, which can be obtained by analyzing the changes in the measured size distribution with the laser pulse energy. The objective of the paper is an evaluation of LII for its capability to measure the size distributions of various types of aerosols in the size range about 5–200 nm and to determine the primary particle sizes in the case of agglomerated particles.     

Solvent size effect on the static and dynamic properties of polymer chains in athermal solvents

The static and dynamic properties of polymer chains in athermal solvents with different sizes are studied by molecular dynamics method. With increasing solvent size, the radius of gyration and the diffusion coefficient of the polymer decay fast until a critical solvent size is reached. For the polymer diffusion coefficients, this decay only depends on the solvent size; while for the radius of gyration of polymers, this decay depends on both solvent size and the length of the polymers. The increase of solvent size also makes the polymer tend to be thicker ellipsoid until a critical solvent size is reached. The static scaling exponent of the polymer also shows the solvent size dependence. Moreover, four regions are identified where the polymers show different dynamic behaviors according to the dynamic structure factors of the polymer.     

A High Volume Apparatus for the Condensational Growth of Ultrafine Particles for Inhalation Toxicological Studies

A high volume (2500 LPM) system for the condensational growth of ultrafine particles was developed and evaluated using indoor air as a test aerosol. The main features of this system are the following: (a) ultrafine particles grow condensationally to supermicron sizes using high purity deionized water as a condensing medium; (b) the supersaturation ratio is adjustable and can be precisely controlled; (c) the system can operate for a wide range of ambient air temperature and relative humidity conditions; and (d) a thermal dryer is used to return the condensationally grown particles back to their original size. Restoring the original ambient size distribution and preserving the composition of the ambient ultrafine particles is very important for inhalation studies. The system is fully automated and has computerized feedback controls. In addition, saturation of the aerosol with water vapor occurs at close to ambient temperatures to minimize particle losses of volatile components. Saturation of sample air is obtained using a direct steam-injecting, fully modulating electric humidifier. The sample air after saturation is drawn through the supersaturator, which is a refrigerant-to-air heat exchanger and is cooled down to obtain the desirable supersaturation ratio. Supersaturation ratios can be precisely adjusted, with the optimum operational level found to be in the range of 2 to 3. The performance of the system was evaluated as a function of critical operation parameters, including the supersaturation ratio as well as the saturation and supersaturation temperatures. A series of virtual and conventional impactors was used to characterize the condensational growth of ultrafine particles. This new high volume apparatus was shown to grow ambient ultrafine particles to supermicron sizes with a particle size growth of approximately 1.8 w m. Particle losses in the system were found to be minimal (about 10%). The thermal dryer was used successfully to restore the grown particles back to their original size distribution. Particle concentration, aerosol temperature, and residence time (aerosol flow) are key parameters shown to affect the performance of the thermal dryer was used successfully to restore the grown particles back to their original size distribution. Particle concentration, aerosol temperature, and residence time (aerosol flow) are key parameters shown to affect the performance of the thermal dryer.     

Submicrometer Aerosol Mass Distributions of Emissions from Boilers,Fireplaces, Automobiles,Diesel Trucks,and Meat-Cooking Operations

The predominant peak in the mass distribution emitted from each source measured in this study occurs at or below about 0.2 μm in particle diameter, whereas the Los Angeles atmospheric aerosol contains peaks at a variety of sizes in the range between 0.1 and 1.0 μm in particle diameter, including peaks at sizes larger than 0.2 μm. This suggests that considerable modification of the primary aerosol size distribution occurs because of subsequent processes in the atmosphere. The data presented here are intended for use in defining the size distribution of the primary combustion source effluent for use with mathematical models of the evolution of the atmospheric aerosol size distribution.     

Coarsening of Faceted Crystals

The influence of the nucleation energy barrier on the capillary-driven coarsening of faceted crystals that exchange material by diffusion is quantified. Our calculations are based on the assumption that the transport of material between particles must happen in series with the nucleation of partial layers on flat facets. Using a numerical model based on this idea, we simulate the time evolution of distributions of crystals that are made up of perfect faceted crystals (without step-producing defects), crystals containing step-producing defects, and mixtures of the two types. We find that the coarsening of a distribution containing only perfect faceted crystals is arrested at a size where the nucleation energy barrier becomes prohibitive. This critical size ranges from a few nanometers to several hundred nanometers, depending on material parameters and experimental conditions. When a small fraction of the crystals have step-producing defects (for these crystals the nucleation energy barrier vanishes), they can grow to large sizes at the expense of the perfect crystals and a bimodal grain size distribution is created. Based on these results, we hypothesize that when abnormal coarsening is observed in nature, it results from the presence of a small number of crystals with step-producing defects.     

Simulation of Condensation Aerosol Growth by Condensation and Evaporation

A new numerical method is reported for the solution of the condensation—evaporation equation, a first-order hyperbolic equation. The solution and properties of the nonlinear integrodifferential equation arising when the mass of the condensing vapor is conserved are discussed. For aerosol evolution in the conserved case it is shown that there develops an asymptotic regime analogous to the asymptotic behavior found for the coagulation process.