Fractal Agglomerates Research Articles

Sintering of Polydisperse Nanometer-Sized Agglomerates

ABSTRACT In order to evaluate the sintering characteristics of polydisperse TiO2 and SiO2 fractal agglomerates consisting of nm-sized primary particles (nanoparticles), the change in size distribution of agglomerates in a heated pipe is measured using a differential mobility analyzer and a condensation nucleus counter. Change in the structure and the primary particle size of the agglomerates collected by a thermophoretic aerosol sampler is also measured by the transmission electron microscopy as a function of furnace temperature. Coalescence of the agglomerates and the growth of primary particles due to sintering are observed at temperatures corresponding to 50%–100% of the bulk melting points of the particle material. To model the changes in the size distribution of agglomerates and primary particles due to sintering, two-dimensional sectional representation of the size distribution is employed, and the population balance equation for sintering is solved numerically. The calculated results, considering a well-defined temperature history of the agglomerates, successfully explain the observed changes in the particle-size distribution and agglomerate structure.

On the aerodynamic behavior of fractal agglomerates

On the aerodynamic behavior of fractal agglomerates

Empirical formula for optical absorption by fractal aerosol agglomerates

An empirical formula for calculating the optical absorption of fractal aerosol agglomerates over a broad frequency range is derived based on extensive calculations made on five smoke agglomerates having a widely varying number of particles ranging from 12 to 372 and an almost constant fractal dimension in the 1.7-1.9 range. The expansion coefficients in the empirical formula were determined by least-squares curve fiting of numerical data obtained using the volume integral equation formulation (VIEF).(1) The formula satisfies the frequency dependence of the absorption at lower frequencies and up to the resonance frequency of the agglomerate. Expressions for the resonance frequency (f(0)), as well as the constant coefficients in the empiricial formula, are derived in terms of the structural dimensions, number and size of the primary particles, and the complex permittivity of the aerosol agglomerate. Numerical results obtained from the empirical formula are generally in good agreement with those calculated by the VIEF for soot particles with a magnitude of complex permittivity |epsilon*| in the 1-7 range. The average error in the absorption calculation is <5%. The formula thus provides a simple and inexpensive method for calculating the optical absorption of aerosol agglomerates, which otherwise require complicated and expensive methods of calculation. This formula also facilitates the implementation of the accurate VIEF results in large climate codes such as the general circulation model.

Resonance optical absorption by fractal agglomerates of smoke aerosols

The Volume Integral Equation Formulation (VIEF) and the method of moments solution procedure were utilized to calculate optical scattering and absorption by agglomerates of smoke aerosols of fractal structure. The general solution procedure was described elsewhere (Iskander et al., 1989), while the emphasis in this paper is placed on examining the effect of the size and index of refraction of the primary particles on the optical properties of the agglomerates. The obtained results show that the fractal theory (Berry and Percival, 1986, Optica Acta 33, 577–591) may be in as much error as 50% in the resonance frequency range when the effective length of the agglomerate is of the order of a wavelength of the incident radiation. At off-resonant frequencies, the results from the fractal theory and the utilized numerical procedure are in agreement to within 10–20 per cent. Since at resonance the interaction effects between the primary particles are strong, the obtained results suggest that these effects are not totally and accurately accounted for in the fractal theory. Additional comparisons between the VIEF results and experimental observations are also included in this paper.

Light Scattering and Absorption by Fractal Agglomerates and Coagulations of Smoke Aerosols

Abstract We used the volume integral equation formulation to calculate the light scattering and absorption of five types of fractal agglomerates with fractal dimensions in the range from 1·7 to 1·9. Results for the absorbed power, absorption, and scattering cross-sections are calculated for three different polarizations of the incident electromagnetic wave with respect to the agglomerates. The obtained results were found to be polarization-dependent with the amount of variation dependent on the frequency of the incident radiation. Furthermore, the obtained scattering and absorption results were compared with those based on the fractal theory, and some differences were observed. Specifically, it is noted that the absorption cross-section of the agglomerates is different from that obtained from multiplying the number of primary particles by the absorption of a single particle. The average difference is approximately 25% at lower frequencies (λ = 10 μm) and is about 15% at higher frequencies (λ = 0·5 μm). Th...

Deposition rates from polydispersed particle populations of arbitrary spread

AbstractFor particle deposition from log‐normal polydispersed aerosol streams by one or more of several mechanisms described by piecewise‐power‐law mass transfer coefficients, we derive useful relations between actual total mass deposition rates and the ‘reference’ rate one would calculate by imagining that all particles in the mainstream population had the average particle volume v(=ϕp/Np). Included here are diffusion or inertial mechanisms for laminar‐ or turbulent‐boundary layers, free‐molecular or continuum diffusion at high Peclet numbers of dense spherical particles, or fractal agglomerates. The mainstream particle volume distribution is considered to be log‐normal with arbitrary ‘spread’ parameter, thereby generalizing earlier results for “coagulation‐aged” (self‐preserving) distributions. Further generalizations include transitions between important particle transport mechanisms, opening the way to efficient, finite‐analytic methods for predicting mass deposition rates for arbitrary, size‐dependent particle capture efficiencies.

Fractal agglomeration during crystallization of Pd‐Si alloy films

SUMMARYFractal agglomeration or irregular hole formation has been obtained during the crystallization of evaporated Pd‐Si alloy films. The morphologies of the fractal‐like structures observed by TEM are similar to patterns simulated by computer according to the Witten‐Sander diffusion‐limited aggregation (DLA) model. The scale‐invariance was tested by the density‐density correlation method and the size‐radius of gyration method. The results from these two methods show that fractal‐like structures in the specimens with different compositions have different fractal dimensions; 1·58·0·04 and 1·78·0·04 for Pd‐Si 62 at.% and Pd‐Si 44 at.% alloy films, respectively. A model is proposed for describing the formation process.