Transformation of Chord Length Distributions into Particle Size Distributions Using Least Squares Techniques

ABSTRACT

For the characterization of particulate systems, various measuring techniques exist. Many of these assume that the particles are spherical in order to compute a particle size distribution (PSD) from the measured data. However, in many applications the shape of the particles deviates from a sphere, and as a consequence the computed PSD will contain errors because of this violated assumption. Measuring techniques that do not require this a priori assumption are, for example, those that measure the chord lengths of the particles. A disadvantage of the latter techniques is that the interpretation of the chord length distribution (CLD) is less transparent than the interpretation of a shape-based PSD (the PSD given an assumed particle shape). To facilitate the interpretation of a CLD, an algorithm based on least squares optimization techniques is presented. This algorithm computes the shape-based PSD that best explains the measured CLD and can, for example, discriminate spheres from rods using information of the CLD only. Knowledge about the type of PSD (e.g., Gaussian or log-normal) is not required.