Selection of Relevant Characteristic Particle Size

An irregular particle can be described by a number of sizes. There are three groups of definitions the equivalent sphere diameters, the equivalent circle diameters and the statistical diameters. In the first group are the diameters of a sphere which would have the same property as the particle itself (e.g. the same volume, the same settling velocity, etc.) in the second group are the diameters of a circle that would have the same property as the projected outline of the particles (e.g. projected area or perimeter). The third group of sizes are obtained when a linear dimension is measured (usually by microscopy) parallel to a fixed direction. 

There is a wide variety of methods for particle size measurement which measure different types of particle size. When selecting a method, it is best to take one that measures the type of size which is most relevant to the property or the process which is under study. Thus, for example, in powder elutriation, pneumatic conveying or gas cleaning, it is most relevant to use one of the sedimentation methods which measure the Stokes diameter, i.e. the diameter of a sphere of the same density as the particle itself, which would fall in the gas at the same velocity as the real particle (assuming Stokes law). In flow through packed or fluidized beds, on the other hand, it is the surface-volume diameter (or diameter 

Very few, if any, practical particulate systems are mono-sized. Most show a distribution of sizes and, depending on the quantity measured, the distribution can be by number, surface or mass. Conversion from one type of distribution to another is theoretically possible but it assumes a constant shape factor throughout the distribution which often is not true and such conversion is in error. The conversions are therefore to be avoided whenever possible by choosing a measurement method which measures the desired type of distribution directly. Except for a few specialized applications like rating of filter media, the most relevant types in powder handling are usually the mass or the surface distributions. 

If a population of particles is to be represented by a single number, there are many different measures of central tendency or mean sizes. Those include the median, the mode and many different means arithmetic, geometric, quadratic, cubic, bi-quadratic, harmonic (ref. 1) to name just a few. As to which is to be chosen to represent the population, once again this depends on what property is of importance the real system is in effect to be represented by an artificial mono-sized system of particle size equal to the mean. Thus, for example, in precipitation of fine particles due to turbulence or in total recovery predictions in gas cleaning, a simple analysis may be used to show that the most relevant mean size is the arithmetic mean of the mass distribution (this is the same as the bi-quadratic mean of the number distribution). In flow through packed beds (relevant to powder aeration or de-aeration), it is the arithmetic mean of the surface distribution, which is identical to the harmonic mean of the mass distribution. 

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