Shape classification of re-entrant particles I: The shape factor,

Abstract

The problem of quantifying re-entrant and non-uniform particle shapes until now has not been resolved. The development and generation of a shape factor, ▪ (shah), specifically designed to quantify re-entrant particle shapes is reported.The empirical factor ▪ is a machine-generated descriptor of particle shape; it may be calculated as an individual characteristic, but is most useful in describing the mean particle shape of a sample of bulk powder. As the shape of a particle becomes more re-entrant, the dimensionless value of ▪ increases.The shape factor is calculated from a knowledge of the number of downward pointing projections on a sample set of particles, e, and the total particle population of the sample, n, according to the formula ▪ = e/n. Using this relationship, re-entrant particles can be distinguished from non-re-entrant particles, which have a ▪ value of unity. The two variables, e and n, were measured using an image analysing computer. This method of measurement allows shape factors of particle populations to be calculated efficiently and accurately.The factor ▪ has been used to quantify the shape of re-entrant particles in different batches of habit-modified lactose powders. The shape factors of the different batches were found to increase with increasing particle size.The possible development of ▪ as a texture factor, for quantifying the surface roughness or texture of powder particles, is also discussed.