Experimental particle size distributions and their representation by log—hyperbolic functions

Abstract

Following previous studies by Bagnold and Barndorff-Nielsen et al., the present work employs the log—hyperbolic function to fit experimentally measured particle size distributions originating from quite different experiments. It is shown that the log—hyperbolic function permits a satisfactory representation of all size distributions studied in this work. Hence, it appears that experimental particle size distributions are well described by the four characteristic parameters occurring in the log—hyperbolic function. These parameters can therefore be employed to study similarities or differences between particle size distributions and/or to describe temporal and spatial variations of distributions. The function was applied to the following particle size distributions: 1. — Mass—size distribution of a sand sample 2. — Size distribution of diamonds 3. — Size distribution of river bed sediments 4. — Size distribution of glacio-fluvial sediments 5. — Measurements of aerosol distributions 6. — Particle size distributions in sprays 7. — Molecular weight distributions A brief account of previous work is given and the major properties of the log—hyperbolic function are described. Experimental particle size distributions of sand, diamonds, river bed sediments, spray droplets, aerosols, and polymer molecules are fitted by the log—hyperbolic function and it is shown that it satisfactorily applies to all distributions.