Characterization of particle size based on fine and coarse fractions

Abstract

The mathematical modelling and analysis of particle or droplet size distributions have been extensively investigated in the chemical engineering literature. One such mathematical description is the Rosin–Rammler model that has found extensive application in milling and crushing operations and size distributions obtained from spray nozzles. The Rosin–Rammler function is represented by two parameters: mean size and n-value (width of distribution) and a goodness-of-fit factor is often also given. The increasing importance of granulation operations in the pharmaceutical and chemical process industries and the advent of processes other than spray drying have limited the scope of applications of the Rosin–Rammler function. There is also increasing emphasis on quality control, which is expressed as limits on proportions of fines and coarse particles. Therefore it has been postulated that simply measuring the fractions of coarse and fine particles in an assembly can provide the necessary and sufficient data for quality control, without loss of accuracy with respect to Rosin–Rammler. A sound, mathematically rigorous, yet simplified and practical approach has been formulated that aims to address the needs of both powder manufacturers and scientists. This paper shows that for every Rosin–Rammler distribution there is a coarse and fines fraction that maps uniquely to a Rosin–Rammler curve. Consequently, the coarse and fines fractions, which are of main interest anyway, can be used to describe the Rosin–Rammler distribution without any loss of data integrity. The advantages of the approach may be summarized as follows: (i) a particle size distribution can be expressed with confidence by using two real, comprehensible numbers; (ii) a particle size distribution as measured by sieving is simplified to the use of two sieves, the coarse and fines sieves; (iii) analysis of data is reduced to the calculation of two parameters, the coarse/fines fraction and the coarse+fines fraction; (iv) the approach allows the conventional Rosin–Rammler parameters dm and n to be determined; (v) extremely rapid checks can be made on fines and coarse levels of the process output and whether or not changes in process parameters/conditions have led to the required outcomes; (vi) the approach can be adapted to any mathematical expression that closely describes the particle size distribution; (vii) the influence of coarse and fine particles on the Rosin–Rammler mean size and n-value can be comprehended, in particular the fact that for any mean size and n there will exist a unique coarse and fines level.