Premium
Note on light transmission through a polydisperse dispersion
Author(s) -
Curl Rane L.
Publication year - 1974
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690200130
Subject(s) - curl (programming language) , citation , library science , computer science , mathematics , world wide web
A recent paper of McLaughlin and Rushton (1973) presented an analysis of light transmission through a dense dispersion of spherical particles when only the unscattered light is received by the detector. They numerically generated samples from various drop size distributions and, using a relation for the probability of a light ray (in a parallel beam) not striking any of the drops, found that the total light transmission is a unique exponential function of the group al, where a is the interfacial area per unit volume, and 2 is the path length through the dispersion. They confirmed this numerically for four different drop size distributions. It may be shown that this result is theoretically exact for all drop size distributions, subject to certain idealizations. Actually, Calderbank (1958) showed this, in a rather elegant fashion, but used a distribution-free argument that obscured the fact that the result is independent of a drop size distribution. The Calderbank equation is equal to that obtained by McLaughlin and Rushton. The following derivation simplifies but generalizes the analyses of Otvos et al. (1957) and Gumprecht and Sliepcevich ( 1953a, 1953b). Assuming, as did McLaughlin and Rushton, a beam of parallel rays, and that scattered light (diffracted or refracted) is not received by the detector, the effective scattering cross section of a single drop of radius r is