Particle formation and surface processes on atmospheric aerosols: A review of applied quantum chemical calculations

Aerosols significantly influence atmospheric processes such as cloud nucleation, heterogeneous chemistry, and heavy-metal transport in the troposphere. The chemical and physical complexity of atmospheric aerosols results in large uncertainties in their climate and health effects. In this article, we review recent advances in scientific understanding of aerosol processes achieved by the application of quantum chemical calculations. In particular, we emphasize recent work in two areas: new particle formation and heterogeneous processes. Details in quantum chemical methods are provided, elaborating on computational models for prenucleation, secondary organic aerosol formation, and aerosol interface phenomena. Modeling of relative humidity effects, aerosol surfaces, and chemical kinetics of reaction pathways is discussed. Because of their relevance, quantum chemical calculations and field and laboratory experiments are compared. In addition to describing the atmospheric relevance of the computational models, this article also presents future challenges in quantum chemical calculations applied to aerosols.     

Nucleation simulations using the fluid dynamics software FLUENT with the fine particle model FPM

This work is an assessment of the capabilities of the FLUENT-FPM software package to simulate actual nucleation experiments. In the first step, we verified the FPM condensation routine with the NEWALC code. Next, homogeneous nucleation of n-butanol, n-pentanol, and n-hexanol in a laminar flow diffusion chamber (LFDC) was simulated and the results were compared to experimental data and an earlier model, which was described by Lihavainen and Viisanen (2001) and will be called femtube2 in the following. Models based on classical nucleation theory typically give too small nucleation rates for alcohol vapors. Also, the FPM underestimates particle production by several orders of magnitude, the factor being a constant for each nucleation isotherm (i.e., at constant nucleation temperature). However, experimental observations beyond exact particle concentrations can be reproduced. We found a behavior similar to the experiment for the dependence of the concentration of nucleated particles N on the flow rate. After correcting the FPM nucleation rate by a constant factor, experimentally found vapor depletion effects could be simulated. Comparing the FPM and femtube2, we observed that the FPM systematically predicts lower saturation ratio values. Further investigation of vapor depletion showed significant differences between the FPM and the femtube2 model. Furthermore, FPM simulations confirm the earlier found carrier gas effect (Lihavainen and Viisanen, 2001).     

A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

CFD simulation of shear-induced aggregation and breakage in turbulent Taylor-Couette flow

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of approximately 10 microm latex spheres suspended in an aqueous solution undergoing turbulent Taylor-Couette flow was carried out. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method). Excellent agreement between the CFD-QMOM and experimental results was observed for two Reynolds numbers in the turbulent-flow regime.     

Mean-field kinetic nucleation theory

A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.     

CFD simulation of aggregation and breakage processes in laminar Taylor-Couette flow

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of approximately 10 microm latex spheres suspended in an aqueous solution undergoing laminar Taylor-Couette flow was carried out according to the following program. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method) and with predictions using spatial average shear rates. The mean particle size evolution predicted by CFD and QMOM using appropriate kinetic expressions that incorporate information concerning the particle morphology (fractal dimension) and the local fluid viscous effects on aggregation collision efficiency match well with the experimental data.     

Numerical prediction of absolute crystallization rates in hard-sphere colloids

Special computational techniques are required to compute absolute crystal nucleation rates of colloidal suspensions. Using crystal nucleation of hard-sphere colloids as an example, we describe in some detail the novel computational tools that are needed to perform such calculations. In particular, we focus on the definition of appropriate order parameters that distinguish liquid from crystal, and on techniques to compute the kinetic prefactor that enters in the expression for the nucleation rate. In addition, we discuss the relation between simulation results and theoretical predictions based on classical nucleation theory.     

The duomodule. Part 1: Hydrodynamic investigations

On-line plasma detoxification requires two circulation: the separation of the plasma from the patients blood, in a first circulation, and a plasma fractionation, in a second circulation, before the detoxified plasma returns back to the patient. These processes can be realised in one single step by use of a duofilter. The duofilter is a modular construction integrating two different hollow fibre filters in one common module housing. In this paper the liquid flow and the pressure distribution in the duofilter module system is calculated based, on the one hand, on the laws of hydrodynamics, and on the other hand, on the finite volume method, where each part in the duofilter is scrutinized separately and supplemented with a computational simulation program for liquid flow. The data from such calculations are compared with experimental investigations. The results of both, calculation methods and the experimental technique, demonstrate correspondence. On this basis the module equipment can be optimized with respect to its performance.     

Homogeneous nucleation of n-nonane and n-propanol mixtures: a comparison of classical nucleation theory and experiments

The homogeneous nucleation rates for n-nonane-n-propanol vapor mixtures have been calculated as a function of vapor-phase activities at 230 K using the classical nucleation theory (CNT) with both rigorous and approximate kinetic prefactors and compared to previously reported experimental data. The predicted nucleation rates resemble qualitatively the experimental results for low n-nonane gas phase activity. On the high nonane activity side the theoretical nucleation rates are about three orders of magnitude lower than the experimental data when using the CNT with the approximate kinetics. The accurate kinetics improves the situation by reducing the difference between theory and experiments to two orders of magnitude. Besides the nucleation rate comparison and the experimental and predicted onset activities, the critical cluster composition is presented. The total number of molecules is approximated by CNT with reasonable accuracy. Overall, the classical nucleation theory with rigorous kinetic prefactor seems to perform better. The thermodynamic parameters needed to calculate the nucleation rates are revised extensively. Up-to-date estimates of liquid phase activities using universal functional activity coefficient Dortmund method are presented together with the experimental values of surface tensions obtained in the present study.     

Complete thermodynamically consistent kinetic model of particle nucleation and growth: numerical study of the applicability of the classical theory of homogeneous nucleation

A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.     

由成核率数据拟合饱和蒸汽压力

Saturated vapor pressure was calculated from the nucleation experimental data using the thermodynamically consistent nucleation theory in which the effect of real gas is considered. The cubic polynomial fit equations of saturation pressure for several substances were obtained based on the calculation. The results of the calculations were compared to those of thermodynamic equilibrium equation and the empirical equation and applied to the predictions of the classical nucleation theory. The results show that the saturation pressures estimated from the nucleation data agree fairly well with those of empirical equations for the substances investigated, and this indicates that the predictions from the classical nucleation theory are close to the experimental data.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

Non-empirical LCAO-MO-SCF-CI calculations on organic molecules with Gaussian type functions

This paper (Part I) describes the theoretical and computational bases of some non-empirical calculations on small organic molecules to be reported in later papers (Parts II et seq). Approximate solutions for the usual fixed nucleus electronic Hamiltonian, in the term of wave functions composed of Slater determinants, are discussed, with particular emphasis on their computational utility. Possible choices of basis functions, from which to form the determinants are examined, and the advantages of Gaussian type functions (GTF) centered on the component atoms are pointed out. Some of the properties of molecules which can be calculated using such approximate wave functions are outlined. Finally an attempt is made to discuss the current limitations of non-empirical calculations of the type described here, and some guesses are made about their future. Brief outlines as a set of appendices are given of the mathematical formalism and computational details of the calculations.     

Copolymerization of ethylene and vinyl acetate at low pressure: Determination of the kinetics by sequential sampling

In behalf of a detailed study on the course of copolymerization reactions, this paper describes an improved and generally applicable experimental method and an efficient computational procedure to match. The experimental method is based on quantitative gas chromatography, and permits frequent measurement of the monomer feed composition throughout (co)polymerization processes at pressures up to 40 kgf/cm² ( = 38.7 atm). The given method is applied to the study of the radical copolymerization of ethylene with vinyl acetate in a series of kinetic experiments, at 62°C and 35 kgf/cm² ( = 33.9 atm) in tert-butyl alcohol, in which 20–40% conversion is reached. Monomer feed composition and degree of conversion are entered into a computational procedure based on nonlinear least-squares methods applied to the integrated version of the copolymer equation. The experimental data, covering a region of ethylene molar feed fractions between 0.24 and 0.74 and copolymer concentrations up to 8 wt-%, are precisely consistent with the usual model. The respective reactivity ratios are r?_e = 0.743 ± 0.005 and r?_v = 1.515 ± 0.007.     

Scale-adaptive simulation of liquid mixing in an agitated vessel equipped with eccentric HE 3 impeller

The current study presents the results of a numerical simulation of hydrodynamics in an agitated vessel equipped with an eccentric HE 3 impeller. CFD (computational fluid dynamics) simulations were carried out using ANSYS 14.0 software. Time-dependent simulations of turbulent flow were carried out using the SAS-SST (scale adaptive simulation-shear stress transport) method coupled with the SM (sliding mesh) method. The results of the calculations are presented as contours of velocity in different cross-sections of the agitated vessel, as well as profiles of components of velocity vector and turbulence kinetic energy and its dissipation rate. The iso-surface of vorticity, which shows the region of possible vortex existence, is also presented. A numerically obtained data set of impeller power number was used to calculate the averaged impeller power number. This value was compared with the experimental data with good results. The relationship between impeller position and fluctuation of the impeller power number was also analysed.     

Numerical Modeling of an RF Argon–Silane Plasma with Dust Particle Nucleation and Growth

A one-dimensional numerical model and simulation results are presented for a capacitively-coupled radio frequency parallel-plate argon–silane dusty plasma. The model includes self-consistently coupled numerical modules, including a plasma fluid model, a sectional aerosol model, and a simple chemistry model to predict rates of particle nucleation and surface growth. Operating conditions considered include 13.56 MHz frequency, 100 mTorr pressure, a 4-cm electrode gap, gas flow through the top electrode with a 30:1 ratio of argon to silane, and applied radio frequency voltage amplitude of either 100 or 250 V. In the higher voltage case two lobes of relatively large particles are formed by ion drag, while fresh nucleation occurs in the void between these lobes. It is shown that the reason that fresh nucleation occurs in the void involves an interplay among several coupled phenomena, including nanoparticle transport, the plasma potential profile, and trapping of silicon hydride anions that drive nucleation in this system.     

Analysis of droplet behavior in a de-oiling hydrocyclone

A mechanical separation process in a de-oiling hydrocyclone is described in which disperse oil droplets are separated from a continuous water phase. This separation process is influenced by droplet breakage and coalescence. Based on experimental data and simulation results in a stirred tank, a modified breakage model, which can be applied to droplet breakage in the de-oiling hydrocyclone, is developed. Then, a simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics (CFD) with population balances. The homogenous discrete method and the inhomogeneous discrete method are applied for solving the population balance model (PBM). The investigations show that the numerical results obtained by the simulation model coupled with the modified PBM using the inhomogeneous discrete method are in good accordance with experimental data under a high flow rate. According to this simulation model, the effect of three different inlet designs on the separation efficiency of the de-oiling hydrocyclone has been discussed. The results indicate that the separation efficiency of the de-oiling hydrocyclone can be improved with an appropriate inlet design.     

Experimental studies of the vapor phase nucleation of refractory compounds. VI. The condensation of sodium

In this paper we discuss the condensation of sodium vapor and the formation of a sodium aerosol as it occurs in a gas evaporation condensation chamber. A one-dimensional model describing the vapor transport to the vapor/aerosol interface was employed to determine the onset supersaturation, in which we assume the observed location of the interface is coincident with a nucleation rate maximum. We then present and discuss the resulting nucleation onset supersaturation data within the context of nucleation theory based on the liquid droplet model. Nucleation results appear to be consistent with a cesium vapor-to-liquid nucleation study performed in a thermal diffusion cloud chamber.