Determination of the fiber-size distribution function in polydisperse dielectric fibrous materials

A simple method has been proposed for determining the average fiber length in unit volume of a polydisperse fibrous material as depending on fiber diameter. The method consists in the measurement of light attenuation as a function of the distance from an examined sample. The method entails comparison of the measured energy fluxes that reach a detector before and after scattering by an examined fibrous material sample and uses an integral relation that expresses the intensity of light transmitted through a random medium via the electric-field correlation function. Formulas have been found for the electric-field correlation function after the passage through a layer of a polydisperse fibrous material with random arrangement and orientation of fibers. The obtained correlation function enables one to derive an integral equation that expresses the logarithmic ratio of the energy fluxes reaching the radiation detector before and after the passage through a scattering medium via the fiber size-distribution function. Solution of this integral equation makes it possible to determine the fiber-size distribution function from the light attenuation measured as depending on the distance from the point of observation. Experiments have been carried out for several fibrous filters and relevant calculations have been presented. The results of the solution of the integral equation agree with the data obtained by other experimental methods and with visual processing of electron micrographs.