Effective Diameter of Agglomerates for Radiative Extinction and Scattering

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Abstract
This study examines the extinction and scattering characteristics of randomly oriented agglomerates consisting of closely-packed small identical spherical particles such as soot in flames. An equivalent sphere is introduced as one that exhibits similar scattering or extinction cross-section as the agglomerate and has the same refractive index as the primary particles. A simple analytical reasoning is presented that establishes the ratio of the diameter of this sphere to the diameter of the primary particles to be proportional to the cube root of the number of particles in the agglomerate. Simple expressions for the proportionality constants for various morphologies are developed. Previous studies in literature have used extensive numerical computations to empirically correlate the above proportionality without considering the proportionality constants. Scattering patterns for various morphologies are also predicted which have significance for optical diagnostic techniques.

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