Direct numerical simulation of nanoparticle coagulation in a temporal mixing layer via a moment method

Direct numerical simulations of coagulating aerosols in two-dimensional, incompressible, iso-thermal mixing layers are performed. The evolution of the particle field is obtained by utilizing a moment method to approximate the aerosol general dynamic equation. We use a moment method which assumes a lognormal function for the particle size distribution and requires the knowledge of only the first three moments. This approach is advantageous in that the number of equations which are solved is greatly reduced. A Damköhler number is defined to represent the ratio of convection to coagulation time scales. Simulations are performed for three flows: Damköhler numbers of 0.2, 1, and 2. The spatio-temporal evolution of the first three moments along with the mean diameter and standard deviation are discussed.     

Daubechies小波对流化床压力波动的分解研究

由于小波具有紧支集的正交特性，作为一种信号处理方法已引起了越来越多的关注和重视。基于床层压力波动信号的小波分析已用于流态化的研究。但由于在采用多大紧支集的Daubechies小波时具有一定的随意性，对相同的信号，应用不同紧支集的Daubechies小波可能会得到不同的结果。为了了解小波分析的误差，本文对流化床不同测量位置的压力波动信号用不同紧支集的Daubechies小波族在1-9尺度下进行分解和重构，对比重构信号和原始信号发现，紧支集为[-1，2]的Dau2小波用于压力波动信号分析时误差最小，为压力波动Daubechies小波分析的最优小波。而紧支集为[-9，10]的Daul0小波分解误差最大，其次为紧支集为[-4，5]的Dau5小波。     

A moment model for simulating raindrop scavenging of aerosols

The dynamics of a polydispersed aerosol size distribution, scavenged by precipitation, are numerically studied. The collision efficiency formula proposed by Slinn (Precipitation Scavenging in Atmospheric Sciences and Power Production—1979, Division of Biomedical Environmental Research, US Department of Energy, Washington, DC, USA, 1983, Chapter 11) and the moment method were introduced to represent the particle removal mechanism by raindrops and the aerosol size distribution, respectively. Consequently, the dynamics of the particle size distribution were reduced to a set of ordinary differential equations using the moment approach. A generalized raindrop distribution, including two widely used distributions; the Marshall–Palmer (MP) and Krigian–Mazin (KM) raindrop distributions, was adopted.Our model results have shown that raindrops with smaller diameters, and narrower distributions, collect aerosols more efficiently. Further, it was shown, in the small particle size region that the geometric mean diameter increases, while in the large particle region it decreases. For the two size ranges, the geometric standard deviations decrease with time, and a scavenging gap, the minimum particle removal efficiency region, exists between these particle size ranges.The dynamics of the particle size distributions, the MP and KM raindrop distributions, in the small particle range, show that the effects of the overestimation in the MP distribution were not as great as expected. Also, this study ascertained that the conventional parameterization of the constant collision efficiency introduces significant errors for estimating the particle size distribution dynamics by wet scavenging.     

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.     

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).     

Size diffusion for the growth of newly nucleated aerosol

Size diffusion is often regarded as a problem encountered with the numerical solution of the general dynamic equation for aerosols. We investigate here the real size diffusion arising in the solution of the more fundamental discrete rate equations, which treat condensation and evaporation on a molecular basis. The spreading of the aerosol distribution in molecular number content is obtained from previously derived moment equations, and is verified by numerical calculations. When the condensing material is volatile and its supersaturation is low, spreading values are very significant in the nanometer size range. The spreading of the aerosol distribution in radius tends to a constant value at large sizes, but this corresponds to a fall-off in the geometric standard deviation of the size distribution in the logarithm of the radius. Experimental examination of distributions at small sizes has the potential to give information on the volatility of the condensing material.     

Aerosol size distribution from elutriator efficiency measurements

A method for obtaining approximate cumulative particle size distributions with high flow rate elutriators has been developed. Several multiple channel elutriators of different capacities are used to sample the aerosol simultaneously and in parallel. From their measured efficiencies, a mixture of monodisperse aerosols is found analytically which yields these efficiencies for each elutriator. The cumulative size distribution is inferred from the composition of the monodisperse aerosol mixture.     

Modal Aerosol Dynamics Modeling

ABSTRACT

The derivation of the governing equations for modal aerosol dynamics (MAD) models is presented. MAD models represent the aerosol size distribution as an assemblage of distinct populations of aerosol, where each population is distinguished by size or chemical composition. The size distribution of each population is approximated by an analytical modal distribution function; usually by a lognormal distribution function. By substituting the MAD representation of aerosol size distributions into the governing equation for aerosol processes, the governing differential equations for MAD models are derived. These differential equations express the time dependence of the moments of the aerosol size distribution and are called Moment Dynamics Equations (MDEs). The MDEs for Continuously-Stirred Tank Aerosol Reactors (CSTARs) are also derived.     

Measurements of Kelvin-Equivalent Size Distributions of Well-Defined Aerosols with Particle Diameters > 13 nm

During the 1979 workshop of the working group on ultrafine aerosols, different experimental techniques for measuring the number concentration and size of ultrafine aerosol particles were compared. In the present paper we report on a comparison of different particle size measuring techniques for ultrafine aerosols. Well-defined monodisperse aerosols with electrical mobility particle diameters ranging from 13 to 100 nm were generated using an electrical aerosol classifier. Kelvin-equivalent size distributions of these aerosols were determined by means of a process-controlled expansion chamber, the size-analyzing nuclei counter (SANC). To this end the considered aerosol was humidified and the number concentration of the droplets growing in the expansion chamber was measured for stepwise increase in supersaturation. At a quite well defined critical supersaturation, a significant increase in the measured droplet concentration, and thus the onset of heterogeneous nucleation, was observed. By means of the Kelvin-Gibbs equation this critical supersaturation is related to the Kelvin-equivalent diameter of the aerosol particles. Measurements were made on NaCl and dioctyl phthalate (DOP) aerosols. For NaCl particles the Kelvin diameter was found to be larger by a factor of about 4 than the electrical mobility diameter, as determined by the electrostatic aerosol classifier. This is explained by the solubility of the NaCl particles. For DOP particles, however, the Kelvin diameter agrees quite well with the electrical mobility diameter. The Kelvin size distributions were found to be quite narrow, indicating a high monodispersity of the generated aerosol as well as a satisfactory size resolution of the SANC. Thus different experimental techniques, based on completely different principles, yielded similar measurement results.     

Size Dependence of the Ratio of Aerosol Coagulation to Deposition Rates for Indoor Aerosols

A thorough understanding of the importance of aerosol coagulation and deposition relative to each other as modifiers of the particle size distribution plays an important role in the proper selection of conditions to estimate the deposition rate coefficient. In this work, a theoretical analysis was conducted for investigating the size-resolved ratio of coagulation to deposition for different types of size distributions using the Simpson integral method. The theoretical model was subsequently qualitatively validated by experiments in a completely mixed and ventilated aerosol chamber. Both experimental and theoretical studies show that the ratio of the rates of coagulation to deposition is strongly dependent on the total particle number concentration and the geometric mean diameter of the aerosol. A variation of the ratio of coagulation to deposition by several orders of magnitude for aerosols with differing size distributions was found. Thus the previously employed criterion for the negligence of coagulation based solely on the total particle number concentration was shown to be insufficient to accurately judge whether an aerosol is suited for the estimation of the deposition rate coefficient. Aerosols with wide size distributions are not recommended for use in the estimation of the deposition rate coefficient. The study provides a method to understand the role of coagulation and deposition for indoor aerosols.

Copyright 2013 American Association for Aerosol Research     

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.     

Coagulation of highly concentrated aerosols

A number of material synthesis processes such as flame, plasma and laser ablation have been developed for production of films and powders at low pressure and high temperature. At these conditions particle growth typically takes place by coagulation in the free molecule and transition regimes. As economic manufacturing of these materials favors operation at high particle concentrations, classic coagulation theory may not be sufficient to describe the ensuing aerosol dynamics, especially if fractal-like particles are formed. The coagulation rate of highly concentrated, polydisperse aerosols is investigated here from the free molecule to the continuum regime by solving the corresponding Langevin dynamics (LD) equations. The LD simulations are validated by monitoring the attainment of the self-preserving size distribution (SPSD) for dilute particle volume fractions, φ_s, below 0.1%. High particle concentrations in the free molecule regime lead to deviations of the aerosol dynamics from the kinetic theory of gases especially during instantaneous coalescence (completely inelastic particle–particle collisions) resulting in slower coagulation rates and slightly narrower SPSDs than in conventional dilute aerosols. In the transition regime, the coagulation rate of highly concentrated aerosols is progressively higher than that for dilute aerosols as growing particles enter the continuum regime where coagulation rates are 2–30 times higher than that of classic Smoluchowski theory. At high particle concentrations (φ_s>1%), a SPSD is approached (σ_g,n=1.42) that does not exhibit the characteristic minimum at the transition regime of dilute aerosols. A relationship is developed for the aerosol coagulation rate of highly concentrated aerosols from the free molecule to continuum regime.     

Measuring Average Particle Size for Fluidized Bed Reactors by Employing Acoustic Emission Signals and Neural Networks

Average particle size is one of the key parameters of fluidized bed reactors. A novel method to measure the average particle size in fluidized bed reactors by acoustic emission (AE) signal is proposed. The measurement of the average particle size by AE is superior to other methods since it is inherently safe to use and it is also a non‐invasive method. AE signals originating from different particle sizes were 8‐level decomposed by a Daubechies wavelet of order 3 after being denoised with a sym8 wavelet filter combined with the rigrsure threshold method. Principal component analysis (PCA) was applied to overcome the complex collinearity and reduce the number of input variables of the neural network. A feed‐forward back propagation neural network with two hidden layers was used to predict the average particle size according to the principal components. The results show that this soft‐measuring model is suitable for measuring the average particle size in the fluidized bed reactors by online AE. It achieved high accuracy when applied to a model‐scale fluidized bed.     

Simultaneous Use of Polystyrene Latex Particles of Different Sizes to Evaluate Performance of a Cyclone and Impactor

Monodisperse and polydisperse aerosols were produced to evaluate the effect of particle size on cyclone and impactor performance. Monodisperse aerosols were generated from polystyrene latex and divinylbenzene particles. Polystyrene aerosols were also generated by mixing several monodisperse aerosols of different sizes. The mixture ratio of monodisperse aerosols was found by trial and error to generate polydisperse aerosols. Generated polydisperse aerosols had multimodal aerosol size distribution, which had the same peak point as shown in the size distribution of monodisperse particles. The results show the collection efficiency curves of a cyclone and impactor, when generating monodisperse particles were coherent with those for polydisperse ones. Our findings show that the size distribution and the size range of test aerosols can be easily determined by mixing monodisperse particles of known particle sizes, using a time saving procedure.     

Modulation of silica layer properties by varying the granulometric state of tetraethyl orthosilicate precursor aerosols during combustion chemical vapor deposition (CCVD)

Abstract

For the purpose of silica surface layer modulation, a pneumatic-controlled two-substance atomizer with inertia-based coarse droplet separation was operated at different system pressures for tetraethyl orthosilicate precursor aerosol supply during combustion chemical vapor deposition. A comprehensive testing study was performed to characterize the atomizer’s performance characteristics, initial precursor aerosols at the atomizer’s outlet, transformed aerosols before combustion, combustion aerosols and formed layers. Laser diffraction spectrometry, differential electrical mobility analyses and condensation particle counting were used for aerosol characterization with regard to particle size and particle production quantities. Layers were characterized by scanning electron microscopy, atomic force microscopy, spectral ellipsometry, water contact angle measurements and light transmission concerning geometric properties (thickness, surface structure and roughness) and physical behaviors (i.e., optical behaviors, hydrophobicity). Results show a quasi-linear relationship of the ejection mass flow of the pneumatic-controlled atomizer and geometric layer properties which again show a direct relationship to the physical properties. No correlation was found between the aerosols before combustion and the combustion aerosols since the majority of combustion aerosol particles are synthesized solely from the gas phase based on evaporated precursor material.

Copyright © 2020 American Association for Aerosol Research     

Development of polydisperse aerosol generation and measurement procedures for wind tunnel evaluation of size-selective aerosol samplers

Accurate development and evaluation of inlets for representatively collecting ambient particulate matter typically involves the use of monodisperse particles in aerosol wind tunnels. However, the resource requirements of using monodisperse aerosols for inlet evaluation creates the need for more rapid and less-expensive techniques to enable determination of size-selective performance in aerosol wind tunnels. The goal of recent wind tunnel research at the U.S. EPA was to develop and validate the use of polydisperse aerosols, which provide more rapid, less resource-intensive test results, which still meet data quality requirements necessary for developing and evaluating ambient aerosol inlets. This goal was successfully achieved through comprehensive efforts regarding polydisperse aerosol generation, dispersion, collection, extraction, and analysis over a wide range of aerodynamic particle sizes. Using proper experimental techniques, a sampler’s complete size-selective efficiency curve can be estimated with polydisperse aerosols in a single test, as opposed to the use of monodisperse aerosols, which require conducting multiple tests using several different particle sizes. While this polydisperse aerosol technique is not proposed as a regulatory substitute for use of monodisperse aerosols, the use of polydisperse aerosols is advantageous during an inlet’s development where variables of sampling flow rate and inlet geometry are often iteratively evaluated before a final inlet design can be successfully achieved. Complete Standard Operating Procedures for the generation, collection, and analysis of polydisperse calibration aerosols are available from EPA as downloadable files. The described experimental methods will be of value to other researchers during the development of ambient sampling inlets and size-selective evaluation of the inlets in aerosol wind tunnels.

© 2018 American Association for Aerosol Research     

The Coagulation Equation Under Time Reversal

In this article we examine the possibility of integrating backward in time the coagulation equation in order to find the aerosol particle size distribution at earlier times. In theory, time reversal solution of the coagulation equation allows backward prediction of past distributions in any circumstances. There are, however, a few restrictions on the practical use of this approach. First, the impossibility of working with infinitely small numbers in any computer prevents retrieval of past distributions when some particle concentrations have decayed to extremely small values. Second, the recovery of very narrow, quasi-monodisperse distributions is also problematic. In most practical situations in which not too narrowly distributed and not extremely concentrated aerosols coagulate for not too long periods of time, it is possible to predict back the original size distribution with high accuracy.     

A model for kinetically controlled internal phase segregation during aerosol coagulation

In previous studies of particle growth, we have synthesized binary metal oxide aerosols and have observed the evolution of internal phase segregation during growth of molten nanodroplets. We describe a new formulation of the aerosol general dynamic equation (GDE) that incorporates phase segregation in a binary aerosol. The model assumes that complete phase segregation is the thermodynamically favored state, that no thermodynamic activation energy exists, and that the segregation process is kinetically controlled. We develop a GDE formulation that involves the solution of a distribution function N_n(V), where N_n(V) is the number density of aerosols with volume V and n phase domains (which we might think of as enclosures). The GDE is solved using a two-dimensional sectional model, under the assumption that the phase coalescence of the minority phase is controlled by Brownian coagulation. For the purposes of these initial studies, the rate laws governing the enclosures (minority phase) assume a monodisperse particle size distribution. The dynamical behavior of such a system is presented.     

MADM-A New Multicomponent Aerosol Dynamics Model

A Multicomponent Aerosol Dynamics Model (MADM) capable of solving the condensation/evaporation equation of atmospheric aerosols is presented. Condensable species may be organic and/or inorganic. For the inorganic constituents the equilibrium model ISORROPIA is used to predict the physical state of the particle, i.e., whether the aerosol is liquid or solid. The mass transfer equations for the fluxes for solid atmospheric particles are developed. MADM is able to simulate aerosol deliquescence, crystallization, solid to solid phase transitions, and acidity transitions. Aerosols of different sizes can be in different physical states (solid, liquid, or partially solid and partially liquid). Novel constraints on the electroneutrality of the species flux between the gas and aerosol phases are presented for both liquid and solid aerosols. These constraints aid in the stability of the algorithm, yet still allow changes in aerosol acidity. As an example, MADM is used to predict the dynamic response of marine aerosol entering an urban area.