A new multi-axial particle shape factor--application to particle sampling

Because for a given sample size the sampling uncertainty increases with increasing particle mass, the mass of a representative sample depends on the particle mass during chemical, physical and biological analysis. Sampling theory can be used to formulate the quantitative relationship between the particle mass and the corresponding mass or weight of a representative sample. But in practice, especially for small particles, it is often easier to evaluate the particle size in dimension of length (e.g. μm) rather than in dimension of mass (e.g. μg). In order to be able to apply sampling theory to predict the mass or weight of a representative sample, a well-defined methodology that relates the mass of a particle to its size is required. We here propose a new multi-axial shape factor which requires information of multiple sizes of the particle of interest, whereas a uniaxial shape factor only needs one. In view of the information loss that is implicit in the use of a one-dimensional shape factor like the Brunton shape factor, the here-proposed new multi-axial shape is expected to perform better. Experimental data confirm the better performance of the new shape factor. A multi-segment generalisation of the new multi-axial shape factor is proposed.