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ABSTRACT
Aerosol particles are formed by chemical transformations in diverse systems including the atmosphere, fossil fuel combustors, aerosol synthesis reactors, and semiconductor processing equipment. This article discusses solutions to the aerosol population balance equations that account for nucleation, coagulation, wall deposition, scavenging by preexisting particles, and dilution with particle-free air in spatially homogeneous systems when a condensing species is produced by gas phase reactions at a constant rate. Two nucleation mechanisms are considered: classical nucleation due to competing rates of condensation and evaporation, and chemical nucleation due to acid-base reactions. The equations, which apply to a single component system (two components, the acid and base, are included for acid-base nucleation), are cast in a dimensionless form. This leads to dimensionless parameters (dimensionless rate constants) that characterize the importance of each process. When these parameters are sufficiently small, the corresponding process (scavenging by pre-existing particles, wall deposition, dilution, and cluster evaporation) has an insignificant effect and nucleation approaches the collision-controlled limit. Because the dimensionless parameters vary inversely with the square root of the reaction rate, the collision-controlled limit is reached for any chemical system provided the reaction rate is high enough. The numerical solutions quantify the effects of each process for low rates of gas-to-particle conversion where the dimensionless parameters become sufficiently large. They also illustrate how data for sub 10 nm number distributions can provide insights into the nucleation process.
© 2017 American Association for Aerosol Research
EDITOR:
Nomenclature
| AFuchs | = | aerosol surface area concentration, corrected to account for transition regime condensation |
| [A] | = | concentration of free acid |
| = | dimensionless concentration of free acid | |
| [B] | = | concentration of free base |
| [B˜] | = | dimensionless concentration of free base |
| βij | = | collision frequency function for clusters that contain i and j monomer |
| βij fm | = | free molecular expression for i-j colisions |
| cij | = | dimensionless free molecular collision function for i-j clusters |
| ciA | = | |
| Cw | = | Chamber wall loss constant as defined by Kürten et al. (Citation2014) |
| dp | = | particle diameter |
| = | dimensionless particle diameter | |
| Ds | = | diffusion coefficient for species s |
| Ej | = | Monomer evaporation rate constant from size j clusters |
| kA+B | = | forward rate constant for the reaction A+B→AB, assumed equal to the A + B collision rate |
| EAB | = | evaporation rate constant for the reaction AB→A+B |
| KAB | = | equilibrium constant for A+B⇔AB |
| kb | = | Boltzmann's constant |
| Kn | = | Knudsen Number = |
| ms | = | mass of species s |
| n(dp) | = | number distribution function of preexisting aerosol |
| Nj | = | concentration of clusters that contain j monomer |
| = | dimensionless concentration of clusters that contain j monomer | |
| Nsat | = | saturation vapor concentration of condensing monomer |
| R | = | rate of monomer formation by gas phase reaction |
| Qdil | = | volumetric flow rate of particle free air entering a rigid reactor |
| t | = | time |
| T | = | absolute temperature |
| v1 | = | monomer volume = m1/ρ |
| Vchamber | = | volume of rigid chamber |
Greek
| δ2j | = | Kronecker delta function ( = 1 for j = 2, and = 0 for j≠2) |
| λ | = | mean free path |
| ρ | = | particle density |
| σ | = | surface tension |
| τ | = | dimensionless time |
Funding
This research was supported by the US Department of Energy's Atmospheric System Research, an Office of Science, Office of Biological and Environmental Research program, under grant number DE-SC0011780.
