Aerosol Coagulation Research Articles

Hybrid Monte Carlo Method for Simulation of Two-Component Aerosol Coagulation and Phase Segregation

The paper presents the development of a hybrid Monte Carlo (MC) method for the simulation of the simultaneous coagulation and phase segregation of an immiscible two-component binary aerosol. The model is intended to qualitatively model our prior studies of the synthesis of mixed metal oxides for which phase-segregated domains have been observed in molten nanodroplets. In our previous works ( J. Aerosol Sci. 32, 1479 (2001); Chem. Eng. Sci. 56, 5763 (2001); submitted for publication) we developed sectional and monodisperse models where the internal state of the aerosol particles was described. These methods have certain limitations and it is difficult to include additional physical effects into the framework. Our new approach combines both constant volume and constant number Monte Carlo methods. Similar to our previous models, we assume that the phase segregation is kinetically controlled. The MC approach allows us to compute the mean number of enclosures (minor phase) per droplet, average enclosure volume, and the width of the enclosure size distribution. The results show that asymptotic behavior of enclosure distribution exists that is independent of initial conditions, which is very close to the continuum self-preserving distribution. Temperature is a key parameter because it allows for a significant change in the internal transport rate within each droplet. In particular, increasing the temperature significantly enhances the Brownian coagulation rate and lowers the number of enclosures per droplet. As a result, the MC results indicate that the growth of the minor phase can be moderated quite dramatically by small changes in system temperature. These results serve to illustrate the utility of this synthesis approach to the controlled growth of nanoparticles through the use of a majority matrix to slow down the encounter frequency of the minor phase and therefore its particle size.

Experimental and Numerical Study of Aerosol Coagulation by Gravitation

The behaviors of aerosols having particle diameters of 1–5 μm were studied experimentally and the results were compared with numerical calculations. For the experimental study, a specially designed coagulation cylinder was developed and the moment method was used in the numerical predictions. The experimental results were characterized by the size parameters including the geometric mean diameter (GMD), the geometric standard deviation (GSD) and the particle number concentration (N). Particle distributions in the cylinder were measured at certain time intervals. In a closed cylinder, the mechanism governing aerosol behavior appeared to be gravitational coagulation. Separately, the numerical calculations were carried out using the moment method. The experimental results and the numerical predictions were in reasonable agreement. It is believed that the present work represents the first experimental study on gravitational coagulation.

Design of metal nanoparticle synthesis by vapor flow condensation

A systematic engineering study on continuous synthesis of bismuth metal nanoparticles by vapor condensation in tube flows is presented. Simulations of aerosol nucleation, condensation and coagulation are cast in a design diagram format to guide experimental studies on the effect of process parameters on product nanoparticle characteristics. Flow visualization, tracer gas analysis and computational fluid dynamics are used to unravel the effect of particle residence time distribution on product morphology during evaluation of alternate quenching designs for the metal vapor. Bismuth nanoparticles of average diameter 12– 37 nm , as determined by nitrogen adsorption and X-ray diffraction, were made by controlling the quenching gas flow rate, carrier gas flow rate and process pressure.

The role of fragmentation in defining the signature size distribution of diesel soot

The addition of fragmentation to the Schmoluchowski aerosol coagulation model significantly improves the prediction of the signature size distribution recently observed for light duty diesel exhaust particulate matter. Allowing fragmentation largely eliminates the asymmetric shape that is characteristic of self-preserving size distributions predicted by models that consider only coagulation and yields a very nearly lognormal distribution, in excellent agreement with diesel soot mobility size measurements. Interestingly, the addition of fragmentation does not really introduce any new adjustable parameters. The model assumes continuum dynamics, as appropriate for diesel engine combustion. The shape and width of the size distribution are independent of the overall fragmentation rate and only slightly dependent on whether the particles break into two equal pieces or pieces with a 2:1 mass ratio. Finally, the size dependencies of both the coagulation rate and the fragmentation rate are tied to the soot fractal dimension, which in agreement with the literature is chosen to equal 1.8.

A Newton–Cotes quadrature approach for solving the aerosol coagulation equation

This paper presents a direct approach to solving the aerosol coagulation equation. Newton–Cotes formulas are used to discretize the integral terms, and the semi-discrete system is built using collocation. A semi-implicit Gauss–Seidel time integration method is employed. The approach generalizes the semi-implicit method of Jacobson and is more accurate.

A model for two-component aerosol coagulation and phase separation: a method for changing the growth rate of nanoparticles

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 have also generated NaCl/metal aerosols in which the metal nanoparticle is enveloped within a salt droplet. In both systems the nanoparticles were grown in the molten state. In this paper we propose a model which 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 phase segregation process is kinetically controlled. The results indicate that a steady state behavior can be reached in which the characteristic time for aerosol coagulation and the characteristic time for the growth of the minority phase coincide such that the number of distinct segregated entities within each aerosol droplet is constant. The results suggest what we believe to be an important concept that can be utilized in materials synthesis. This is that the major phase can be used to moderate the growth rate of the minor phase by changing the characteristic encounter frequency and therefore the eventual growth rate of the minority phase. In particular, temperature, which does not play an important role in aerosol coagulation, is seen to be a very sensitive parameter for the growth of the minority phase nanoparticles. We discuss the parameter space necessary for this to occur.

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.

On the formation, growth and composition of nucleation mode particles

Taking advantage of only the measured aerosol particles spectral evolution as a function of time, a new analytical tool is developed to derive formation and growth properties of nucleation mode aerosols. This method, when used with hygroscopic growth-factors, can also estimate basic composition properties of these recently-formed particles. From size spectra the diameter growth-rate can be obtained, and aerosol condensation and coagulation sinks can be calculated. Using this growth-rate and condensation sink, the concentration of condensable vapours and their source rate can be estimated. Then, combining the coagulation sink together with measured number concentrations and apparent source rates of 3 nm particles, 1 nm particle nucleation rates and concentration can be estimated. To estimate nucleation rates and vapour concentration source rates producing new particle bursts over the Boreal forest regions, three cases from the BIOFOR project were examined using this analytical tool. In this environment, the nucleation mode growth-rate was observed to be 2–3 nm hour−1, which required a condensable vapour concentration of 2.5–4×107 cm−3 and a source rate of approximately 7.5–11×104 cm−3 s−1 to be sustained. The formation rate of 3 nm particles was =1 particle cm−3 s−1 in all three cases. The estimated formation rate of 1 nm particles was 10–100 particles cm−3 s−1, while their concentration was estimated to be between 10,000 and 100,000 particles cm−3. Using hygroscopicity data and mass flux expressions, the mass flux of insoluble vapour is estimated to be of the same order of magnitude as that of soluble vapour, with a soluble to insoluble vapour flux ratio ranging from 0.7 to 1.4 during these nucleation events.

Effects of second order processes in aerosol monitoring

We present a general-purpose mathematical model for pollution concentration studies. The model is an approximate solution for the time dependence of size distribution that takes into account processes like aerosol coagulation and condensation among others. Our model is validated by representative experiments using standard aerosol monitoring devices that measure light scattering, particle cross section, particle bound polycyclic aromatic hydrocarbons and number concentration, showing an excellent agreement with the experimental data. The results demonstrate that aerosol coagulation has to be taken into account when monitoring aerosol particles. We also show that the simultaneous application of different sensors reveals new information about the physical and chemical properties of the aerosol.

Effect of coagulation on the particle charge distribution and air conductivity

The steady state charge distribution on submicron‐size charged aerosols is calculated from the ion‐aerosol balance equations including the effects of both the ion‐particle charging mechanism as well as the coagulation of charged aerosols. The particle charge distribution is found to depend on the aerosol concentration and the ionization rate. The results show that for a given ionization rate the fraction of singly charged aerosols increases up to a critical value of aerosol concentration and then decreases with further increase in the aerosol concentration. However, the fractions of multiply charged aerosols show a steady increase with the aerosol concentration. The variation of the polar conductivity with aerosol concentration shows that the inverse relationship between them exists only up to a critical value of aerosol concentration which is decided by the prevailing ionization rate. Above this critical value the polar conductivity shows an increase with the aerosol concentration. Further, it is shown that though the polar conductivity is mainly due to small ions in a clean environment, the charged aerosols may dominantly contribute to the polar conductivity in a polluted atmosphere. For aerosols having larger mean radii the contribution of multiply charged aerosols becomes appreciable for higher values of aerosol concentration and is almost comparable to that of the small ions.

A Model for the Viscous Coalescence of Amorphous Particles

A model is presented for coalescence by viscous flow in two-particle systems, a phenomenon of interest in such diverse processes as the coagulation of air pollutant aerosols, glass and polymer sintering, and the coagulation of liquid suspensions. The model achieves computational efficiency by incorporating an empirical analytical function to describe the fluid interface, making it particularly suited to incorporation into aerosol dynamics models under conditions where coalescence-limited growth can occur. The dynamics of the interfacial evolution in the coalescing pair are approximated by employing a modification to the boundary integral approach in which a single surface point is used to solve the equations for the surface velocities. Model predictions of dimensionless shrinkage and neck growth obtained using this modeling approach compare favorably to those of existing finite-element models reported in the literature and provide a basis for more complex models to approximate multiple particle coalescence.

On the formation, growth and composition of nucleation mode particles

Taking advantage of only the measured aerosol particles spectral evolution as a function of time, a new analytical tool is developed to derive formation and growth properties of nucleation mode aerosols. This method, when used with hygroscopic growth-factors, can also estimate basic composition properties of these recently-formed particles. From size spectra the diameter growth-rate can be obtained, and aerosol condensation and coagulation sinks can be calculated. Using this growth-rate and condensation sink, the concentration of condensable vapours and their source rate can be estimated. Then, combining the coagulation sink together with measured number concentrations and apparent source rates of 3 nm particles, 1 nm particle nucleation rates and concentration can be estimated. To estimate nucleation rates and vapour concentration source rates producing new particle bursts over the Boreal forest regions, three cases from the BIOFOR project were examined using this analytical tool. In this environment, the nucleation mode growth-rate was observed to be 2–3 nm hour−1, which required a condensable vapour concentration of 2.5–4×107 cm−3 and a source rate of approximately 7.5–11×104 cm−3 s−1 to be sustained. The formation rate of 3 nm particles was =1 particle cm−3 s−1 in all three cases. The estimated formation rate of 1 nm particles was 10–100 particles cm−3 s−1, while their concentration was estimated to be between 10,000 and 100,000 particles cm−3. Using hygroscopicity data and mass flux expressions, the mass flux of insoluble vapour is estimated to be of the same order of magnitude as that of soluble vapour, with a soluble to insoluble vapour flux ratio ranging from 0.7 to 1.4 during these nucleation events.

Asymptotic Particle Size Distributions Attained during Coagulation Processes

The effects of the collision kernel on the self-preserving size distribution and on the gelation phenomenon of aerosol coagulation were investigated. An analytical solution for the asymptotic width of log-normally preserving size distribution during coagulation was obtained as a function of the degree of homogeneity using arbitrary shape of homogeneous collision kernels. From the solution obtained, it was shown that when the degree of homogeneity is larger than 1, self-preserving size distribution does not exist, and gelation occurs. A very accurate numerical coagulation simulation method, the sectional method, was also used for calculating the self-preserving particle size distribution for some specific classes of coagulation kernels and the results were compared with the analytical solution obtained by the log-normal method.

Smoke Coagulation in Compartment Fire Modelling

The effect of coagulation on the total smoke particles concentration and mean particles volume fields is studied under the conditions of a compartment fire. An approximate analytical consideration of aerosol temporal behaviour accounting for the simultaneous action of aerosol generation, coagulation, and dilution is given, and two regimes of fast and slow coagulation are considered. A CFD model of compartment fire, including smoke aerosol generation and coagulation, is presented. The results of CFD simulation for a hydrocarbon burner sooting fire with smoke movement and coagulation in a two room compartment are analysed, where the regimes of coagulation and their key features predicted by means of analytical consideration are illustrated by numerical simulations. For a given geometry of the compartment, fuel type, and volumetric smoke generation rate, the coagulation rate was shown to be determined by the mean volume of the particles generated in the flame zone. In the limit of small particles generated (fast coagulation regime), the aerosol parameters far away the flame zone were found to be weakly dependent on those inside the flame zone due to a strong coagulation effect. In the opposite limit of large particles generated (slow coagulation regime), coagulation has no effect on the aerosol parameters. The approximate boundary between the two regimes has been defined.

MOMENT METHOD OF LOG-NORMAL SIZE DISTRIBUTION FOR COAGULATION PROBLEM: CONSTANT COLLISION KERNEL MODEL

ABSTRACT The accuracy of the moment method of log-normal size distribution for aerosol coagulation problem was investigated. The constant collision kernel coagulation problem was solved by the moment method as well as a very accurate numerical method (Landgrebe and Pratsinis, 1990) for the purpose. Approximate analytical solutions to the problem by different choices of moments were obtained and compared with the result of the accurate numerical model. During the analysis, solutions to the moments of the size distribution were obtained in exact form and it was discussed that the solutions can be used as a standard reference for ensuring the accuracy of any new numerical schemes for solving the coagulation equation. The time evolution of the particle size distribution was obtained by representing the size distribution with a log-normal size distribution function. Depending on the choice for three moments during the analysis, different solutions to the size distribution parameters were obtained. Three choices for moments were compared as an example. The use of the 0th, 1st and 2nd moments which has been conventionally used was proven to be most accurate for various polydispersity cases by comparing with a numerical result and is recommended to be used for future studies.

Numerical modelling of regional and global transport and coagulation of radioactive aerosol from hypothetical accidental sources

Numerical modelling of regional and global transport and coagulation of radioactive aerosol from hypothetical accidental sources

Observations of the evolution of the aerosol, cloud and boundary-layer characteristics during the 1st ACE-2 Lagrangian experiment

During the 1st Lagrangian experiment of the North Atlantic Regional Aerosol Characterisation Experiment (ACE-2), a parcel of air was tagged by releasing a smart, constant level balloon into it from the Research Vessel Vodyanitskiy. The Meteorological Research Flight's C-130 aircraft then followed this parcel over a period of 30 h characterising the marine boundary layer (MBL), the cloud and the physical and chemical aerosol evolution. The air mass had originated over the northern North Atlantic and thus was clean and had low aerosol concentrations. At the beginning of the experiment the MBL was over 1500 m deep and made up of a surface mixed layer (SML) underlying a layer containing cloud beneath a subsidence inversion. Subsidence in the free troposphere caused the depth of the MBL to almost halve during the experiment and, after 26 h, the MBL became well mixed throughout its whole depth. Salt particle mass in the MBL increased as the surface wind speed increased from 8 m s -1 to 16 m s -1 and the accumulation mode (0.1μm to 3.0 μm) aerosol concentrations quadrupled from 50 cm -3 to 200 cm -3 . However, at the same time the total condensation nuclei (>3 nm) decreased from over 1000 cm -3 to 750 cm -3 . The changes in the accumulation mode aerosol concentrations had a significant effect on the observed cloud microphysics. Observational evidence suggests that the important processes in controlling the Aitken mode concentration which, dominated the total CN concentration, included, scavenging of interstitial aerosol by cloud droplets, enhanced coagulation of Aitken mode aerosol and accumulation mode aerosol due to the increased sea salt aerosol surface area, and dilution of the MBL by free tropospheric air. DOI: 10.1034/j.1600-0889.2000.00087.x

Six‐moment representation of multiple aerosol populations in a sub‐hemispheric chemical transformation model

This letter describes the first application of the Quadrature Method of Moments (QMOM) [McGraw, 1997] in a 3‐D chemical transformation and transport model. The QMOM simultaneously tracks an arbitrary (even) number of moments of a particle size distribution directly in space and time without the need for explicitly representing the distribution itself. The host 3‐D model, the Global Chemistry Model driven by Observation‐derived meteorological data (GChM‐O), has been previously described [Benkovitz et al., 1994]. The present implementation evolves the six lowest‐order radial moments for each of several externally‐mixed aerosol populations. From these moments we report modeled geographic distributions of several aerosol properties, including a shortwave radiative forcing obtained using the Multiple Isomomental Distribution Aerosol Surrogate (MIDAS) technique [Wright, 2000]. These results demonstrate the capabilities of these moment‐based techniques to simultaneously represent aerosol nucleation, condensation, coagulation, dry deposition, wet removal, cloud activation, and transport processes in a large scale model, and to yield aerosol optical properties and radiative influence from the modeled aerosol.

Observations of the evolution of the aerosol, cloud and boundary-layer characteristics during the 1st ACE-2 Lagrangian experiment

During the 1st Lagrangian experiment of the North Atlantic Regional Aerosol Characterisation Experiment (ACE-2), a parcel of air was tagged by releasing a smart, constant level balloon into it from the Research Vessel Vodyanitskiy. The Meteorological Research Flight’s C-130 aircraft then followed this parcel over a period of 30 h characterising the marine boundary layer (MBL), the cloud and the physical and chemical aerosol evolution. The air mass had originated over the northern North Atlantic and thus was clean and had low aerosol concentrations. At the beginning of the experiment the MBL was over 1500 m deep and made up of a surface mixed layer (SML) underlying a layer containing cloud beneath a subsidence inversion. Subsidence in the free troposphere caused the depth of the MBL to almost halve during the experiment and, after 26 h, the MBL became well mixed throughout its whole depth. Salt particle mass in the MBL increased as the surface wind speed increased from 8 m s-1 to 16 m s-1 and the accumulation mode (0.1μm to 3.0 μm) aerosol concentrations quadrupled from 50 cm-3 to 200 cm-3. However, at the same time the total condensation nuclei (>3 nm) decreased from over 1000 cm-3 to 750 cm-3. The changes in the accumulation mode aerosol concentrations had a significant effect on the observed cloud microphysics. Observational evidence suggests that the important processes in controlling the Aitken mode concentration which, dominated the total CN concentration, included, scavenging of interstitial aerosol by cloud droplets, enhanced coagulation of Aitken mode aerosol and accumulation mode aerosol due to the increased sea salt aerosol surface area, and dilution of the MBL by free tropospheric air.

COAGULATION OF SUSPENDED PARTICLES BY BROWNIAN MOTION FOR THE QUASI-SELF-PRESERVING CASE

ABSTRACT An analytic solution is developed for the aerosol coagulation problem in the transition regime. The size distribution of a coagulating aerosol is represented by log-normal functions and particle size distribution is assumed 10 pass through a series of quasi-self-preserving size distributions. The effects of Knudsen number on the Brownian coagulation are discussed along with the results. It is confirmed that after a sufficient period of elapsed time, a self-preserving log-normal size distribution develops whose geometric standard deviation remains unchanged. Such a distribution is found to be narrower than that for the continuum regime and depends upon the Knudsen number. It is shown that the current model serves as the upper bound for the transition regime coagulation problem while the continuum regime constitutes the lower bound. Good agreement was obtained when the present analytic solution was compared with existing numerical studies on transition regime coagulation for the regime up to the Knudsen number of about 1.