Although particles can assume all regular geometric shapes, and in most instances highly irregular shapes, most particle size measurements are based on the so-called ‘equivalent spherical diameter’. This is the diameter of a sphere that would behave in the same manner as the test particle being measured in the same instrument. For example, the electrical sensing zone method [1] is a commonly used technique for determining particle sizes. Its principle is based on the momentary increase in the resistance of an electrolyte solution that results when a particle passes through a narrow aperture between two electrodes. The resistance change is registered in the electronics as a rapid pulse. The pulse height is proportional to the particle volume and therefore, the particles are sized as equivalent spheres.

Stokes’ law [2] is another concept around which several instruments are designed to give particle size or size distributions. Stokes’ law is used to determine the settling velocity of particles in a fluid medium as a function of their size. Equation is a useful from of Stokes’ law

Where D is the particle diameter, n is the coefficient of viscosity, V is the settling velocity, g is the gravitational constant, and Ps and Pr are the densities of the solid and the fluid, respectively.

Allen [3] gives an excellent discussion of the various experimental methods associated with sedimentation size analysis. Regardless of the experimental method employed, nonspherical particles will be measured as larger or smaller equivalent spheres depending on whether the particles settle faster or more slowly than spheres of the same mass. Modification of Stokes law have been used in centrifugal devices to enhance he settling rates but are subject to the same limitations of yielding only the equivalent spherical diameter.

Optical devices, based upon particle attenuation of a light beam or measurement of scattering angles and intensity, also give equivalent spherical diameters.

Permeametric methods are often used to determine average particle size. The method is based upon the impedance offered to the fluid flow by a packed bed of powder. Again, equivalent spherical diameter is the calculated size.

Sieving is another technique that sizes particles according to their smallest dimension but gives no information on particle shape.

Electron microscopy techniques can be used to estimate particle shape. A limitation is that only relatively few particles can be viewed.

Attempts to measure surface area based on ay of the above methods will give results significantly less than the true value, in some cases by factors of 10³ or greater depending upon particle shape, surface irregularities and porosity. At best, surface areas calculated from particle size will establish the lower limit by the implicit assumptions of sphericity or some other regular geometric shape, and by ignoring the highly irregular nature of real surfaces.

[1] ISO 13319 (2000) Determination of particle size distributions – Electrical sensing zone method, International Organization for Standardization, Geneva, Switzerland.

[2] Orr Jr. C. and Dalla Valle J.M (1959) Fine Particle Measurement, Macmillan, New York.

[3] Allen T. (1981) Particle Size Measurement, Chapman and Hall, London.