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# Particle size

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### Particle size

Particle size is a notion introduced for comparing dimensions of solid particles (flecks), liquid particles (droplets), or gaseous particles (bubbles).

The notion of particle size applies to

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 equals the diameter of the sphere that has the same volume as a given particle:
D = 2 \sqrt[3] {\frac{3V}{4\pi}}

where

D: diameter of representative sphere
V: volume of particle
• Weight-based particle size equals the diameter of the sphere that has the same weight as a given particle.
D = 2 \sqrt[3] {\frac{3W}{4\pi dg}}

where

D: diameter of representative sphere
W: weight of particle
d: density of particle
g: gravitational constant
• Area-based particle size equals the diameter of the sphere that has the same surface area as a given particle.
D = 2 \sqrt[2] {\frac{A}{4\pi}}

where

D: diameter of representative sphere
A: surface area of particle

Another complexity in defining particle size 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.[1][2][3][4][5][6]

Definition of the particle size for an ensemble (collection) of particles presents another problem. Real systems are practically always polydisperse, which means that the particles in an ensemble have different sizes. The notion of particle size distribution reflects this polydispersity. There is often a need for a certain average particle size for the ensemble of particles. There are several different ways of defining such a particle size.

• There is an international standard on presenting various characteristic particle sizes.[7] This set of various average sizes includes median size, geometric mean size, average size.

There are several methods for measuring particle size. Some of them are based on light, other on ultrasound, or electric field, or gravity, or centrifugation. They are briefly described in the section particle size distribution.

## References

1. ^ Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol.2, page.3.208, 1995
2. ^ Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989
3. ^ Dukhin, S.S. & Derjaguin, B.V. "Electrokinetic Phenomena", J.Willey and Sons, 1974
4. ^ Russel, W.B., Saville, D.A. and Schowalter, W.R. “Colloidal Dispersions”, Cambridge University Press,1989
5. ^ Kruyt, H.R. “Colloid Science”, Elsevier: Volume 1, Irreversible systems, (1952)
6. ^ Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", Elsevier, 2002
7. ^ ISO Standard 9276-5 "Representation of results of particle size analysis" (2004)
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