Particle size

The particle size of a spherical object can be unambiguously and quantitatively defined by its diameter. However, a typical material object is likely to be irregular in shape and non-spherical. The above quantitative definition of particle size cannot be applied to non-spherical particles. There are several ways of extending the above quantitative definition to apply to non-spherical particles. Existing definitions are based on replacing a given particle with an imaginary sphere that has one of the properties identical with the particle.

Volume-based particle size

Volume-based particle size equals the diameter of the sphere that has the same volume as a given particle. Typically used in sieve analysis, as shape hypothesis (sieve's mesh size as the sphere diameter).

${\displaystyle D=2{\sqrt[{3}]{\frac {3V}{4\pi }}}}$

where

${\displaystyle D}$: diameter of representative sphere

${\displaystyle V}$: volume of particle

Area-based particle size

Area-based particle size equals the diameter of the sphere that has the same surface area as a given particle. Typically used in optical granulometry techniques.

${\displaystyle D={\sqrt[{2}]{\frac {4A}{\pi }}}}$

where

${\displaystyle D}$: diameter of representative sphere

${\displaystyle A}$: surface area of particle

In some measures the size (a length dimension in the expression) can't be obtained, only calculated as a function of another dimensions and parameters. Illustrating below by the main cases.

Weight-based (spheroidal) particle size

Weight-based particle size equals the diameter of the sphere that has the same weight as a given particle. Useful as hypothesis in centrifugation and decantation, or when the number of particles can be estimated (to obtain average particle's weight as sample weight divided by the number of particles in the sample). This formula is only valid when all particles have the same density.

${\displaystyle D=2{\sqrt[{3}]{\frac {3W}{4\pi dg}}}}$

where

${\displaystyle D}$: diameter of representative sphere

${\displaystyle W}$: weight of particle

${\displaystyle d}$: density of particle

${\displaystyle g}$: gravitational constant

Aerodynamic particle size

Hydrodynamic or aerodynamic particle size equals the diameter of the sphere that has the same drag coefficient as a given particle.

Another complexity in defining particle size in a fluid medium appears for particles with sizes below a micrometre. When a particle becomes that small, the thickness of the interface layer becomes comparable with the particle size. As a result, the position of the particle surface becomes uncertain. There is a convention for placing this imaginary surface at a certain position suggested by Gibbs and presented in many books on interface and colloid science.[4][5][6][7][8][2]

In Materials science and Colloidal chemistry, the term colloidal particle is about a small amount of matter having size typical for colloids and with a clear phase boundary. The dispersed-phase particles have a diameter between approximately 1 and 1000 nanometers. Colloids are heterogeneous in nature. Invisible to the naked eye, and always move in a zig-zag motion known as the Brownian motion. The scattering of light by colloidal particles is known as Tyndall effect.[10]