Granulometry
Basic concepts
Particle size,Grain size,Size distribution,Morphology
Methods and techniques
Mesh scale,Optical granulometry,Sieve analysis,Soil gradation
Related concepts
Granulation,Granular material,Mineral dust,Pattern recognition,Dynamic light scattering
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Particle size is anotion introduced for comparingdimensions ofsolid particles (flecks),liquid particles (droplets), orgaseous particles (bubbles). The notion of particle size applies to particles incolloids, inecology, ingranular material (whetherairborne or not), and to particles that form a granular material (see alsograin size).

There are several methods for measuring particle size^[1] andparticle size distribution. Some of them are based onlight, other onultrasound,^[2] orelectric field, orgravity, orcentrifugation. The use of sieves is a common measurement technique, however this process can be more susceptible to human error and is time consuming. Technology such as dynamic image analysis (DIA) can make particle size distribution analyses much easier. This approach can be seen in instruments like Retsch Technology's CAMSIZER or the Sympatec QICPIC series of instruments. They still lack the capability of inline measurements for real time monitoring in production environments. Therefore, inline imaging devices like the SOPAT^[3] system are most efficient.

Machine learning algorithms are used to increase the performance of particle size measurement.^[4][5] This line of research can yield low-cost and real timeparticle size analysis.

In all methods the size is an indirect measure, obtained by a model that transforms, in abstract way, the real particle shape into a simple and standardized shape, like a sphere (the most usual) or acuboid (whenminimum bounding box is used), where thesize parameter (ex. diameter of sphere) makes sense. Exception is themathematical morphology approach, where no shape hypothesis is necessary.

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

The particle size of aspherical object can be unambiguously and quantitatively defined by itsdiameter. However, a typical material object is likely to be irregular inshape and non-spherical. The above quantitative definition ofparticle 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 imaginarysphere 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 insieve 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 samesurface area as a given particle. Typically used inoptical 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 (alength 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 incentrifugation anddecantation, 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 oraerodynamic particle size equals the diameter of the sphere that has the samedrag coefficient as a given particle.

Another complexity in definingparticle size in a fluid medium appears for particles with sizes below amicrometre. When a particle becomes that small, the thickness of theinterface 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 oninterface and colloid science.^{[6][7][8][9][10][2]}

There is an international standard on presenting various characteristic particle sizes, the ISO 9276 (Representation of results of particle size analysis).^[11] This set of various average sizes includesmedian size,geometric mean size,average size. In the selection of specific small-size particles is common the use of ISO 565 and ISO 3310-1 to the choice ofmesh size.

Inmaterials science andcolloidal chemistry, the termcolloidal particle refers to a small amount of matter having a size typical forcolloids and with a clear phase boundary. The dispersed-phase particles have a diameter between approximately 1 and 1000nanometers. Colloids are heterogeneous in nature, invisible to the naked eye, and always move in a random zig-zag-like motion known asBrownian motion. The scattering of light by colloidal particles is known asTyndall effect.^[12]

• Dynamic light scattering
• Grain size
• Laser diffraction analysis
• Micromeritics
• Dispersion Technology
• Sauter mean diameter

8.ISO Standard 14644-1 Classification Airborne Particles Cleanliness

• Colloidal chemistry
• Particles
• Size

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