Range of Validity of the Rayleigh-Debye-Gans Theory for Optics of Fractal Aggregates
The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, includingx [subscript p] = 0.01-1.0, |m - 1| = 0.1-2.0, N = 16-256, and D[subscript f] = 1.0-3.0. The percent differences between both scattering theories were presented as error contour charts in the |m- 1|x[subscript p] domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (D f â‰ˆ 1.0) to compact clusters (D [subscript f] ~ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for |m - 1| to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (x[subscript p] ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.
T. L. Farias et al., "Range of Validity of the Rayleigh-Debye-Gans Theory for Optics of Fractal Aggregates," Applied Optics, Optical Society of America, Jan 1996.
The definitive version is available at https://doi.org/10.1364/AO.35.006560
Mechanical and Aerospace Engineering
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© 1996 Optical Society of America, All rights reserved.