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

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

A numerical aerosol model Fractal Aggregate Moment Model (FAMM) to simulate simultaneous nucleation,coagulation, surface growth,and sintering of fractal aggregates

Particles generated from high-temperature processes often attain an aggregate structure, with physical and chemical properties and health impacts dependent on the particles’ size and morphology. A numerical aggregate model is a useful tool to produce well-controlled ceramic particles and to predict the production of particulate air contaminants. Although extensive efforts have been directed at developing accurate and fast-running numerical aerosol codes that can model the formation and growth of aerosol aggregates using the framework of the log-normal (LN) moment method, none developed thus far can account for the bimodal particle size distribution and aggregate morphology simultaneously. In this study, two previous models, a bimodal LN model for spherical particles and a unimodal LN model for fractal aggregates, are extended to fabricate a bimodal LN model for fractal aggregates. By tracing five time-dependent variables for the particle phase, the present model can predict the formation of nucleus particles from a gas precursor and the change in the particle size distribution and morphology. Nucleation, surface growth, intramodal and intermodal coagulation, sintering, and condensational obliteration are taken into account. Numerical experiments performed for validating the new model showed that it is a robust and efficient tool for predicting both aggregate particle size distribution and morphology. The proposed model is expected to be a useful tool for simulating the formation and growth of fractal aggregate particles in multidimensional spatial domains requiring a fast-running aerosol model.

Copyright © 2019 American Association for Aerosol Research     

Computational Modeling of Silicon Nanoparticle Synthesis: I. A General Two-Dimensional Model

A two-dimensional model has been developed for silicon nanoparticle synthesis by silane thermal decomposition driven by laser heating in a tubular reactor. This fully coupled model includes fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics which includes particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, and coagulation processes. A moment method, based upon a lognormal particle size distribution, and a sectional method are used to model the aerosol dynamics. The simulation results obtained by the two methods are compared. The sectional method is capable of capturing the bimodal behavior that occurs locally during the process, while the moment method is computationally more efficient. The effect of operating parameters, such as precursor concentration, gas phase composition, inlet gas velocity and laser power input, on the characteristics of the particles produced are investigated. Higher temperature generates more large particles with higher precursor conversion. Shorter residence time, from high inlet velocity, produces more small particles at the cost of lower precursor conversion. Increasing H₂ concentration suppresses particle formation by reducing the rates of gas phase and surface reactions, leading to fewer and smaller particles. In addition, the relative importance of the interconnected mechanisms involved in the particle formation is considered. The results make clear that spatial variations in reaction conditions are the primary source of size polydispersity and generation of non lognormal overall size distributions in a laser-driven process like that considered here.     

Simulation of nano-particle formation in a wall-heated aerosol reactor including coalescence

The initial stage of particle formation during gas phase synthesis is characterized by a high concentration of particles that undergo rapid coagulation. The surface area of the agglomerates is reduced by coalescence. In this study a model is presented that accounts, in addition to nucleation and coagulation, for the shape of the particles by tracing both the particle volume and the total surface area density of the agglomerates. A moment model, based on a unimodal lognormal size distribution gives the concentration, polydispersity, and average volume of the particles as a function of space and time. The total surface area density of the particles is determined by solving an additional transport equation, incorporating a linear decay law to describe the decrease in surface area of a coalescing structure. The aerosol dynamics are calculated in combination with the convective and diffusive particle transport in a spatially inhomogeneous aerosol reactor.     

Multicomponent Aerosol Dynamics of the Pb-O2 System in a Bench Scale Flame Incinerator

A study was carried out to understand the formation and growth of lead particles in a flame incinerator. A bench scale flame incinerator was used to perform controlled experiments with lead acetate as a test compound. A dilution probe in conjunction with real-time aerosol instruments was used to measure the evolution of the particle size distribution at different locations in the flame region. A multicomponent lognormal aerosol model is developed accounting for the chemistry of the lead-oxygen system, and various aerosol dynamic phenomena such as nucleation, coagulation, and condensation. Reasonable agreement is obtained between the predictions of the model using appropriate kinetic parameters and the experimental results.     

Modeling and experimental evaluation of an aerosol generator for very high number currents based on a free turbulent jet

In this paper we report on theoretical and experimental work on aerosol formation in a free turbulent jet. A hot DEHS vapor issues through a circular nozzle into slowly moving cold air. Vapor concentration and temperatures are such that particles are formed via homogeneous nucleation close to the nozzle upon mixing with the surrounding air. The vapor is completely quenched in the nucleation regime so that further particle growth is controlled by coagulation. A simple growth dynamics model is presented and the theory is used to design a generation system that produces liquid aerosols at a very high number current [up to 10¹² particles (s)]. The aerosol properties can be controlled by two easily adjustable parameters. The aerosol properties are related to these parameters by simple scaling laws. The results of measurements of the number current and the average particle size support these scaling laws.     

Sintering Time for Silica Particle Growth

The formation and growth of gas-made silica particles by co-agulation and sintering is investigated theoretically. A model for the characteristic time for silica sintering is proposed defining a minimum primary particle diameter above which macroscopic expressions are applied. The value of the minimum primary particle diameter is selected consistently with molecular dynamics simulations. The proposed characteristic sintering time is tested using a monodisperse model for aggregate dynamics by coagulation and sintering. The model predictions are compared with experimental data for silica formation and growth in premixed flames and hot wall aerosol flow reactors by oxidation of hexamethyl-disiloxane (HMDSO) and silicon-tetrachloride (SiCl₄).     

Particle size distribution of PM-10 and heavy metal emission with different temperature and HCl concentrations from incinerators

Emission characteristics of particulate matter and heavy metals from 12 small waste incinerators, whose capacity ranged from 25 to 200 kg/h of waste, were investigated to determine the factors affecting the particulate matter generation and growth mechanisms. The ratio of fine particles to coarse particles increased with the flue gas temperature. Particulate matter showed bimodal forms in particle size distributions. The finer particle mode in particle size distribution shifted toward the coarser particle mode with a decrease in flue gas temperature. Experimental results were in agreement with coagulation theory: It is thought that the coarser particles were mechanically generated and the finer particles were generated by gas-to-particle conversion mechanisms such as nucleation, condensation, and coagulation. Heavy metal enrichment in finer particulate matter was also observed and related to particle formation and growth from vaporized metals. Emission of all heavy metals except zinc was affected by hydrogen chloride concentrations, while some metal emissions such as manganese, chromium, and copper were not varied with flue gas temperature. This paper is dedicated to Professor Dong Sup Doh on the occasion of his retirement from Korea University.     

Modeling of the monomer role and the coalescence limitation in primary particle growth

The general dynamic equation (GDE) has been numerically solved to simulate the growth of ultrafine particles (UFPs) in a tubular aerosol reactor, approximating the particle size distribution by a lognormal function. The GDE includes all the terms describing diffusion, thermophoresis, nucleation, condensation and coagulation. We have also considered the efficiency of liquid-like coagulation to primary particles. The data calculated from our model were compared with those from the previous model and also with some experimental results from a TiO₂ UFP generator. The condensation term, which we split from a single coagulation term in the previous model, well described the monomer contribution to the particle growth. Introduction of one adjustable parameter, the efficiency of coagulation, was successful in limiting the growth of primary particles and fit the experimental data.     

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.     

The Effect of van der Waals and Viscous Forces on Aerosol Coagulation

An analysis is carried out to determine the combined effect of van der Waals and viscous fluid forces on coagulation of spherical aerosol particles in the free molecular, transition, and continuum regimes. The effect of viscous forces is taken into account by modifying the particle diffusion coefficient. An asymptotic solution is substituted for the classical formulation of viscous forces. The results of free molecular and continuum regimes are then extended to the transition size range by an interpolation formula.     

FORMATION OF SULPHURIC ACID AEROSOLS AND CLOUD CONDENSATION NUCLEI: AN EXPRESSION FOR SIGNIFICANT NUCLEATION AND MODEL COMPRARISON

A new analytical expression has been derived to predict atmospheric conditions where homogeneous water–sulphuric acid nucleation will have a significant effect on aerosol and cloud condensation nuclei population. In the expression, the condensational sink due to pre-existing aerosol particles and source due to chemical production of sulphuric acid have been taken into account. The analytical expression has been derived using a sectional aerosol dynamic model including nucleation, condensation, coagulation, deposition and sulphuric acid formation in the gas phase. In the present study we have also compared the sectional model with modal and monodisperse models. All models may be used for predicting the onset of significant new particle formation. However, the computationally more efficient models—monodisperse, modal, and sectional with low number of sections—over- or underpredict particle formation in some situations.     

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.     

Design and Characterization of a Fluidized Bed Aerosol Generator: A Source for Dry,Submicrometer Aerosol

A fluidized bed aerosol generator has been designed and built for the purpose of generating a constant output of dry, submicrometer particles with a large number density. The output of the fluidized bed for generating aerosol particles from dry soot powder has been characterized using a differential mobility analyzer and a condensation particle counter. The particle size distribution is bimodal, with a mode in the submicrometer diameter size range and a mode in the supermicrometer diameter size range. The larger diameter mode is fully separated from the smaller mode and can thus be easily removed from the aerosol flow using impaction techniques. The distribution in the submicrometer size range is nearly log-normal, with a count median diameter falling between 0.1 and 0.3 micrometers. A number density of greater than 10⁵ particles cm^-3 of soot particles in the submicrometer range can be produced, constant to within 25% (1 standard deviation) over a 4 h time period. The number density of particles produced in the submicrometer range was found to vary with the ratio of soot to bronze beads in the bed mixture, whether or not a feed system was used, and nitrogen flow rate through the fluidized bed and feed system.     

Recent advances in nanoparticle size measurement with a particle growth system combined with an optical particle counter-A feasibility study

A particle growth system (PGS) of original design is presented here, which, when combined with an opticle particle counter has the same function as a condensation nucleus counter (CNC). After an experimental study validated by a numerical model of transfers in a continuous-flow condenser, a relationship of unambiguous dependence is established between the droplet sizes and the size of the primary particles when the latter are between 4 and 20 nm. Furthermore, when aerosol sample is made up of an ultrafine fraction and a fine fraction (about 50 nm), the size distribution of the droplets obtained from the PGS is shown to be bimodal too. Finally, the activation efficiency of our PGS is found to be of the order of 100% for particles as small as 4 nm.     

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.     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

Parameterization of the effect of sub-grid scale aerosol dynamics on aerosol number emission rates

A method for parameterizing sub-grid scale aerosol dynamics of freshly emitted aerosol is developed. This approach is based on the calculation of the probability that a given particle emitted inside a computational grid cell will survive and be available for transfer outside the cell. This survival probability is calculated as a function of the emitted particle size, the pre-existing aerosol size distribution and the grid-cell mean advection time scale. The approach can be used in three-dimensional chemical transport models (CTMs) of all scales, from urban to global. The parameterization's results are evaluated against the predictions of a detailed one-dimensional aerosol dynamics model under a variety of atmospheric conditions. The parameterization agrees well with the dynamic model when the mean emitted particle size is smaller than that of the existing particles. Finally, the method for applying the sub-grid coagulation parameterization to a CTM is discussed.     

A New Moment Method for Solving the Coagulation Equation for Particles in Brownian Motion

A new numerical approach for solving coagulation equation, TEMOM model, is first presented. In this model, the closure of the moment equations is approached using the Taylor-series expansion technique. Through constructing a system of three first-order ordinary differential equations, the most important indexes for describing aerosol dynamics, including particle number density, particle mass and geometric standard deviation, are easily obtained. This approach has no prior requirement for particle size spectrum, and the limitation existing in the log-normal distribution theory automatically disappears. This new approach is tested by comparing it with known accurate solutions both in the free molecular and the continuum regime. The results show that this new approach can be used to solve the particle general dynamic equation undergoing Brownian coagulation with sufficient accuracy, while less computational cost is needed.