Characterization of particle populations in flow and processing systems by moment distribution functions

Abstract

The moment distribution functions (MDF) for characterization of particle populations are defined, with respect to one-and multidimensional random variables. It is shown that the MDF provides the relative weight that is attributed to a property of interest which can be used to characterize the particles with regard to their physical and chemical nature. The number distribution function of particle size is defined as the fundamental distribution, which is then used to formulate multidimensional MDF of size dependent variables, such as momentum, energy and their fluxes. Applications of known densities as the fundamental size distribution provide MDFs that can fit typical skew size distributions. The MDF that involves the normal distribution is shown to produce this effect. Specific size distributions are defined for fractions of particles in which the efficiency of size reduction is constant. The expectation of the specific size distribution, for a particle population that is characterized by a nonuniform efficiency across its size fractions, is shown to constitute a generalized size distribution. Alternatively, an ordinary size distribution may be resolved into specific size distributions. Finally, the order of the MDF and its use for cases of distributed momentum, energy, chemical potential, fluxes and for analysis of separation and filtration processes are discussed.