Pore size distributions of foams from chord distributions of random lines: Mathematical inversion and computer simulation

Abstract

A method is developed to determine pore size distributions of solid foams from optical or electron micrographs of fracture surfaces. The pores are approximated by spheres, and the chord lengths of random lines drawn through the micrographs are measured. Two methods are developed for smoothing the experimental chord length distribution: one by Fourier analysis and the other by curve-fitting to a multimodal modified Gaussian distribution function. Since the chord length distribution function (CDF) is an integral transform of the sphere diameter distribution function (SDF), a mathematical procedure is derived for inverting the CDF to obtain the SDF. Computer simulation using delta-function, unimodal, and bimodal SDFs are used to verify that the method gives very good approximations of the actual SDF, even when the data base includes fewer than 300 chord lengths. The method is applicable also to determining SDFs for spherical and sphere-like particles, and lends itself readily to automation.