Mean Particle Diameters. Part V: Theoretical Derivation of the Proper Type of Mean Particle Diameter describing a Product or Process Property

Abstract

AbstractMean particle diameters may be used to model the physical, chemical, or physiological properties of products or materials if these properties depend on the dispersed phases of the products. The type of mean diameter physically related to such product properties will give the best description. A theoretical approach was developed to derive this proper type of mean diameter $ \overline D_{p,q} $. These mean diameters $ \overline D_{p,q} $ are defined according to the Moment‐Ratio (M–R) definition system. They are expressed as the 1/(p–q)‐th power of the ratio of the p‐th and the q‐th raw moment of the number density distribution of the particle sizes. A number of examples from the areas of evaporation, heat transfer, and turbulent two‐phase flow are used to illustrate the theoretical approach. Particle‐particle interactions were not taken into account. Each example starts from a single‐particle model for a physical product property. The sum of contributions of all particles to this product property leads to a relationship between the product property and the relevant type of mean particle diameter $ \overline D_{p,q} $ (M–R system). The examples given also demonstrate the physical relevance of the nomenclature system for mean particle diameters $ \overline D_{p,q} $, developed earlier. The described theoretical derivation of the proper type of $ \overline D_{p,q} $ supports the empirical selection method of $ \overline D_{p,q} $, developed earlier, because it emphasizes that these mean diameters have clear physical meanings, from which physical hypotheses concerning the physical properties of the products may be derived.