The size of a spherical homogeneous particle is uniquely defined by its diameter. For a cube the length along one edge is characteristic, and for other regular shapes there are equally appropriate dimensions. With some regular particles, it may be necessary to specify more than one dimension. For example: cone, diameter and height; cuboid, length, width and height.Derived diameters are determined by measuring a size-dependent property of the particle and relating it to a linear dimension. The most widely used of these are the equivalent spherical diameters. Thus, a unit cube has the same volume as a sphere of diameter 1.24 units, hence this is the derived volume diameter.If an irregularly shaped particle is allowed to settle in a liquid, its terminal velocity may be compared with the terminal velocity of a sphere of the same density settling under similar conditions. The size of the particle is then equated to the diameter of the sphere. In the laminar flow region, the particle moves with random orientation, but outside this region it orientates itself to give maximum resistance to motion so that the free-falling diameter for an irregular particle is greater in the intermediate region that in the laminar flow region. The free-falling diameter, in the laminar flow region, becomes the Stokes diameter. Stokes' equation can be used for spherical particles, up to a Reynolds number of 0.2, at which value it will give a diameter under-estimation of about 2%. Above 0.2 corrections have to be applied. Corrections may also be applied for non-spherical particles, so that the derived diameter is independent of settling conditions becoming purely a function of particle size. These diameters are particularly useful for characterizing suspended particles in the atmosphere and other cases where the settling behaviour of suspended solids is being examined.For irregular particles, the assigned size usually depends upon the method of measurement, hence the particle sizing technique should, wherever possible, duplicate the process one wishes to control. Thus, for paint pigments, the projected area is important, while for chemical reactants, the total surface area should be determined. The projected area diameter may be determined by microscopy for each individual particle, but surface area is usually determined for a known weight or volume of powder. The magnitude of this surface area will depend on the method of measurement, permeametry, for example, giving a much lower area than gas adsorption. The former gives the surface T. Allen, Particle Size Measurement © T. Allen 1981
