Mean particle diameters. From statistical definition to physical understanding

Mean particle diameters may be used to describe and to model physical, chemical, or physiological properties of products or materials containing dispersed phases. There are different notation systems for these mean diameters, which may cause much confusion. This equally applies to their nomenclature. This article introduces the Moment-Ratio definition system and evaluates briefly the ISO definition system. The ISO system appears to have serious drawbacks. Mean particle diameters can be estimated from histograms of size distributions by Summation (M-R system) and by Integration (ISO system) over the histogram intervals. Summation tends to be more accurate than Integration and is less sensitive to low values of the lower limit of size distributions. The Summation method equations are straightforward and generally applicable. The mathematical formulas of the Integration method are difficult to apply in daily practice, and their complexity may easily hide the physical background of a mean particle diameter. A coherent nomenclature system for denoting mean particle diameters is recommended. This nomenclature system does not contain any ambiguities and clearly conveys the physical meanings of mean particle diameters. This article deals also with an empirical method to select the proper type of mean diameter to describe a physical, chemical, or physiological property of a product or material containing dispersed phases. After calculation of the mean diameters from experimental data, the relationships between the product property and these mean diameters are investigated statistically. The selection method has been illustrated by two examples. The dataset of each example consists of a set of particle size distributions and the corresponding physical product properties that are influenced by the particle sizes. Hypotheses are formulated to explain the types of selected mean diameters. Sharing results from all over the world of applications of the developed selection method will lead to a buildup of knowledge of physical meanings and application areas of the types of mean particle diameters, which will support decision making in product development.