William H. Marlow

Derivation of aerosol collision rates for singular attractive contact potentials

A rigorous derivation is given of the collision rate for spherical aerosol particles in the free‐molecular regime interacting via an attractive potential which diverges at particle contact. The Lifshitz–van der Waals and electrical image potentials are two examples of such particle interactions that play important roles in aerosol dynamics. The method employed in the derivation of this extended free‐molecular collision rate is then used to derive an expression for transition regime collision rates by means of Fuchs’ method. This is the first time that the influence of a particle interaction potential upon the collision rate has been incorporated into the Fuchs formula. Results of computations employing the extended free‐molecular formula derived here are compared with published data and the computations used in their interpretation. By utilizing the same interaction potentials as in those interpretative computations, the corrected free‐molecular formula is shown to improve the data fits.

Separation and analysis of aerosol sulfate species at ambient concentrations

Sampling and analysis techniques appropriate for the determination of the chemical composition of sulfate in aerosol particles are described. These techniques are applied to the speciation of sulfate in ambient air-borne particles with time resolution of one hour or less and with size discrimination in the size range below 0.25 μm. Initial East Coast data are reported indicating the dominance of sulfuric acid and its ammonianeutralization products in ambient sulfate-containing particles. Data from a comparison study of several analytical techniques for aerosol sulfate and related species are highly correlated. Diffusion sampling experiments for size-segregated chemical composition determination indicate that 12 of airborne sulfate is in particles <0.3 μm dia. Hourly variations in sulfate chemical composition at 3 RAMS sites in and near St. Louis, MO. are documented for a one-day intensive experiment and are correlated with air-mass backward trajectories and area primary sources.

Lifshitz–van der Waals forces in aerosol particle collisions. I. Introduction: Water droplets

Collision rates among water droplets are computed by the application of results of a current paper which gives a rigorous expression for free‐molecular collisions between aerosol particles with a singular, attractive contact potential and the extension of that expression throughout the transition regime via Fuchs’ interpolation method. An expression for the Lifshitz–van der Waals attractive potential recently derived by Kiefer et al. is modified to include a physically motivated, frequency‐dependent retardation factor and is used with experimental data for water’s frequency‐dependent dielectric susceptibility. This expression is employed in the computation of the ratio of the collision rate incorporating the interaction potential to the collision rate omitting the potential for various pairs of water particles of 1, 10, 100, and 1000 nm radii at 0.1, 1.0, and 10.0 atm. pressures. A graph of this ratio for a pair of 200 nm radius particles as a function of pressure is given and shown to display similar pre...

Unipolar charging of small aerosol particles

Abstract Calculations are presented of the unipolar charging rate of small aerosol particles in the transition and free molecule regimes of Knudsen number. Numerical results for the charging rate in the transition regime are obtained from a constant collision frequency model of the Boltzmann equation. These results confirm experimental observations that the unipolar charging rates for larger particle charges are only weakly pressure dependent even when the Knudsen number is relatively small. Also, the modification of the near free molecular unipolar charging rate by ion-neutral molecule collisions, is found to depend importantly and in a complex manner on particle size and total particle charge when the image force is included in the ion-particle interaction.

Calculations of bipolar charging of aerosols

Abstract The acquisition of electric charge by the particles of an aerosol is a subject which heretofore has received only incomplete treatment, much of it based upon intuitive considerations. In this paper we present a rigorous treatment of the subject based upon the difference equations for charging of monodisperse and polydisperse aerosols in the presence of ions of both signs but unequal mobilities. The stochastic equations are written and the conditions of their solution are described for positive and negative small ions of mobilities 1.4 cm2/V-sec and 1.9 cm2/V-sec, respectively. Numerical calculations are presented of the time-dependent charge distributions and small ion number densities. Their relation to small-ion production, aerosol particle number concentration, and polydispersity is discussed. These results are compared where possible with calculated and experimental results of other workers. These calculations demonstrate for the first time that for bipolar charging a significant difference arises in polarity between the larger and smaller particle components of a polydisperse aerosol owing to unequal charging rates.

Detecting harmful gases using fluctuation-enhanced sensing with Taguchi sensors

Sensing techniques are often required to not only be versatile and portable, but also to be able to enhance sensor information. This paper describes and demonstrates a new approach to chemical signal analysis that we call fluctuation-enhanced sensing. It utilizes the entire bandwidth of the sensor signal in contrast to more conventional approaches that rely on the dc response. The new principle holds prospects for significantly reducing the necessary number of sensors in artificial noses and tongues, and it can provide improved sensitivity.

Calculations of the Equilibrium Vapor Pressure of Water over Adhering 50–200-nm Spheres

Treatments of condensation on aerosols generally assume the particles to be spherical implying that the condensate presents a positively curved surface to the surrounding vapor. In contrast, the region between two adhering spheres supports a pendular ring of condensation which may result in a condensate-vapor interface with negative curvature. According to the Kelvin equation, the equilibrium vapor pressure over such surfaces is depressed relative to a planar surface and therefore the substrate particle shows entirely different condensational characteristics than for an isolated sphere of similar size and composition to the adhering spheres. In this paper, literature results are utilized to develop general approaches to the calculation of the curvature of the pendular ring of condensation between two macroscopic spheres (radii > 10 nm) that may differ in size and composition. Results of calculations for specific cases are given for spheres of 50, 100, and 200 nm and for a range of condensate-substrate con...

BGK equation solution of coagulation for large knudsen number aerosols with a singular attractive contact potential

Abstract Aerosol coagulation rate expressions in the presence of singular attractive contact potentials such as the van der Waals potential and the electrical image potential are obtained by integrating the characteristics of the BGK equation. The rate expression consists of two parts: (A) the free-molecule regime (Kn → ∝) enhancement, and (B) the first-order correction for a finite but large Knudsen number. For situations involving either the van der Waals or image potential, we present closed form best-fit equations for data calculated from the theory. The experimental data of ionic charging of Pui et al. (9) and data on ultrafine particle coagulation rate of Okuyama et al. (10, 11) are compared with the predictions from the present theory and the empirical Fuchs matching method. We have considered the situations of a combined van der Waals, coulombic, and image potential. The conditions where either coulombic, image, or van der Waals forces predominate are determined.

Size effects in aerosol particle interactions: The Van der Waals potential and collision rates☆

Abstract Three effects which are explicitly dependent on aerosol particle size are identified and discussed. They are focussed about the particle collision rate and how it relates to the properties of the gas, the particle, and the particles interaction potential energy which play roles in particle-particle collision rates. By incorporating the conduction electronic free path effect for conductors into the frequency-dependent dielectric constants of silver and graphite, particle size effects in the Lifshitz-Van der Waals potentials for identical pairs of 1 nm and 100 nm particles are evaluated. Water and tetradecane particle interaction potentials for the same size particles are also calculated to illustrate size effects due to the retardation of the interaction. These potentials are then used to calculate the enhancement of the particle collision rates above their value in the absence of any potential at various gas pressures. The roles of the interaction potential in collision among identical pairs of particles of differing compositions is also briefly discussed.

CHEMICAL COMPOSITION OF SULFATE AS A FUNCTION OF PARTICLE SIZE IN NEW YORK SUMMER AEROSOL

Aerosol samples from a New York City site have been collected by a variety of sampling techniques during August, 1976 and analyzed for sulfate and related cationic species as a function of particle size from > 7 ..mu..m to 0.95, but there is an indiction of other variable sources of strong acid which somewhat confound the data.