Estimation of Particle Size Distribution and Aspect Ratio of Non-Spherical Particles From Chord Length Distribution

TL;DR

This paper introduces a comprehensive algorithm to estimate particle size distribution and aspect ratio from chord length distribution data, enabling in situ analysis of non-spherical particles during manufacturing processes.

Contribution

The paper presents a novel algorithm that accurately recovers size and shape of non-spherical particles from CLD data without prior size or shape assumptions.

Findings

The algorithm successfully estimates particle size and aspect ratio from CLD data.

The thin cylinder model better fits experimental CLD data than the ellipsoid model.

Estimated particle parameters agree well with imaging results.

Abstract

Information about size and shape of particles produced in various manufacturing processes is very important for process and product development because design of downstream processes as well as final product properties strongly depend on these geometrical particle attributes. However, recovery of particle size and shape information in situ during crystallisation processes has been a major challenge. The focused beam reflectance measurement (FBRM) provides the chord length distribution (CLD) of a population of particles in a suspension flowing close to the sensor window. Recovery of size and shape information from the CLD requires a model relating particle size and shape to its CLD as well as solving the corresponding inverse problem. This paper presents a comprehensive algorithm which produces estimates of particle size distribution and particle aspect ratio from measured CLD data. While the algorithm searches for a global best solution to the inverse problem without requiring further a priori information on the range of particle sizes present in the population or aspect ratio of particles, suitable regularisation techniques based on relevant additional information can be implemented as required to obtain physically reasonable size distributions. We used the algorithm to analyse CLD data for samples of needle-like crystalline particles of various lengths using two previously published CLD models for ellipsoids and for thin cylinders to estimate particle size distribution and shape. We found that the thin cylinder model yielded significantly better agreement with experimental data, while estimated particle size distributions and aspect ratios were in good agreement with those obtained from imaging.