SIMPLE MATHEMATICAL EXPRESSIONS FOR SPECTRAL EXTINCTION AND SCATTERING PROPERTIES OF SMALL-SIZE PARAMETER PARTICLES, INCLUDING EXAMPLES FORSOOT AND TIO2

Focusing on small size-parameter particles, this paper compares severa l easily-computable approximations to the Mie equations, including tho se by Rayleigh, Penndorf and Wiscombe, with only the first term of Mie -coefficient expansion, and the exact solution. A symbolic algebra alg orithm was also developed using Mathematica(tm) for solving the exact Mie equations, which is more than an order of magnitude shorter than a n available FORTRAN algorithm for the same purpose. The comparisons of the approximations and the errors incurred are evaluated for a wide r ange of complex refractive indices (1.0 less than or equal to n less t han or equal to 5.0 and 0.001 less than or equal to k less than or equ al to 50), and for the size-parameter range of 0.0 less than or equal to x less than or equal to 1.0. While the choice of approximation depe nds on the size parameter and the refractive index, the first-term app roximation is the best in most cases, with considerable reduction of c pu time. As a specific example, the extinction and scattering coeffici ents for soot and TiO2 particle suspensions are computed as a function of the size-parameter by the above-described approximations, by two o ther available approximations, and by the exact solution.