The most classic and frequent way of representing particle size distributions is the semi-logarithmic diagram. The sizes are represented on the abscissa axis using a base 10 logarithmic scale (generally in μm) and the ordinates on an arithmetic scale, from 0 to 100%.

Sometimes logarithmic normal representations are found (logarithmic abscissa and ordered according to the Gaussian normal distribution).

There are also special ordinate distributions, such as that of Rosin-Rammler (1933) or that of Gaudin-Schumann (1948). At these benchmarks, the distributions are usually represented by one or two lines. They are used in granulometric separation work. They are derived from the following basic equation, with q (x) being the weight proportion of the particles for a given diameter x:.

Meteorology

In meteorology, the size distribution of raindrops according to their diameter (D) results from three processes that contribute to the formation of droplets: the condensation "Condensation (change of state)") of water vapor in a droplet, the accretion of small droplets into larger droplets, and collisions between droplets of similar size. Depending on the time spent in the cloud, the vertical movement within it and the ambient temperature, a very varied history will have accumulated and a distribution of diameters will range from a few tens of micrometers "Micrometer (unit of length)") to a few millimeters. Studying the particle size of droplets allows us to better understand these phenomena and calibrate weather radars.

Geology, geotechnics and construction

Granulometric analysis makes it possible to define various classes of materials regardless of their chemical nature. The following table corresponds to the French standard NF P18-560 used in particular in road construction:

Three other common classifications:

Other names are also derived from these concepts, for example the definition of granulated soils, which comprise more than 50% of elements with a granulometry greater than . They are divided into two families:

In the oil industry, where the English language has a marked presence, the most frequently used names, directly derived from the C. K. Wentworth classification, are the following:[6][7]​.

Sifting

This is the oldest method and is still widely used because it is the most economical. It consists of measuring the weight of the material that passes through a sieve with a calibrated mesh. The sieves are superimposed, reducing the mesh and the weight of the material retained in each sieve is measured.

This operation can be carried out dry, and by vibrating the entire sieve column in the case of relatively large grain sizes. When the grain population has some very fine elements, a depression can be used to form a controlled air current. When the grain size is smaller than , it is necessary to operate under a stream of water (or alcohol for non-water-soluble products). Each residue is dried and weighed.

Sedimentometry

The method consists of measuring the sedimentation time required for fines in a water column, that is, the rate of fall of the particles.

From Stokes' law, the size of the grains is determined, being:.

There are different methods:

The Martin scale measures the amount of material deposited in a tray as a function of time. With the Andreasen pipette, the concentration of the suspension is measured at a given time and at a given height. X-ray sedimentometry measures the absorption of radiation by the suspension at a given height and a given time that depends on the concentration.*[2]​.

Analytical centrifugation

The principle of centrifugation is identical to that of sedimentation, the fractionation of particles or droplets dispersed in a carrier liquid (continuous phase) is deposited according to their differences in size and density, as described by Stokes' law. Here the value of "g" is variable and is calculated from the angular velocity of the centrifuge, the mass of the sample and the distance from the center of rotation. This technique is separative, centrifugation allows the fractionation of the particles and an optical device allows the different fractions to be quantified. This approach is recommended for the resolution of multimodal polydisperse systems. Each separate fraction can be analyzed independently of the other populations present in the sample. The difference with conventional sedimentometry is that it can accelerate the migration of nanoparticles or nanoobjects and discriminate down to 10 nm, the lower limit of quantification.

The suspension or emulsion to be analyzed is inserted without prior dilution into a transparent container and passed through with a beam of light radiation (visible, X-ray, infrared...). The main advantage of this technique is that it allows obtaining a particle size distribution independent of the optical properties of the dispersed materials. Changes in optical density due to the displacement of the fractions are monitored during centrifugation to determine the migration rate and a grain size distribution weighted by the migration speed of the objects Q(v) is obtained. This distribution can be converted into intensity, mass or volume, although it will be necessary to determine the density of the particles and the viscosity of the carrier liquid to solve the Stokes equation and calculate the equivalent spherical diameter.[3][4]​.

Nanoparticles are among the transparent and colorless compositions that absorb infrared radiation.[5]​.

laser diffraction

The laser granulometer is based on the principle of light diffraction. Suspended particles (in water or an air stream) diffract the light emitted by a laser beam. The spatial distribution of this light, a function of particle size, is recorded by an array of photodiodes. The analysis of this distribution in the focal plane allows the proportion of each dimensional class to be determined. The interpretation is carried out using Fraunhofer's theory. However, this method is limited on the one hand by the wavelength of the laser beam and by the transparency of the grains. In fact, Fraunhofer's theory assumes particles that are opaque but also significantly larger than the wavelength of light. Therefore, new methods have been developed to analyze the spatial distribution of light based on the Rayleigh-Mie theory. In this case, diffraction, refraction, reflection and absorption of light by the grains are taken into account. This allows measurements of much smaller sizes.

Image analysis

In this method, a photograph of the grains is taken with a microscope. The resulting image is analyzed using specialized computer programs, capable of counting and sizing the number of pixels associated with the image of each of the particles, and then associating them with an ellipse (or a square, or a rhombus) that defines the general shape of the grain. In this way, a numerical and geometric description of the granular set is obtained that allows establishing distributions in number, surface and shape (granulomorphism). Image analysis also allows the color of the grains to be determined, which makes it possible to establish differentiated curves depending on the nature of the grains.

The most classic and frequent way of representing particle size distributions is the semi-logarithmic diagram. The sizes are represented on the abscissa axis using a base 10 logarithmic scale (generally in μm) and the ordinates on an arithmetic scale, from 0 to 100%.

Sometimes logarithmic normal representations are found (logarithmic abscissa and ordered according to the Gaussian normal distribution).

There are also special ordinate distributions, such as that of Rosin-Rammler (1933) or that of Gaudin-Schumann (1948). At these benchmarks, the distributions are usually represented by one or two lines. They are used in granulometric separation work. They are derived from the following basic equation, with q (x) being the weight proportion of the particles for a given diameter x:.

Meteorology

In meteorology, the size distribution of raindrops according to their diameter (D) results from three processes that contribute to the formation of droplets: the condensation "Condensation (change of state)") of water vapor in a droplet, the accretion of small droplets into larger droplets, and collisions between droplets of similar size. Depending on the time spent in the cloud, the vertical movement within it and the ambient temperature, a very varied history will have accumulated and a distribution of diameters will range from a few tens of micrometers "Micrometer (unit of length)") to a few millimeters. Studying the particle size of droplets allows us to better understand these phenomena and calibrate weather radars.

Geology, geotechnics and construction

Granulometric analysis makes it possible to define various classes of materials regardless of their chemical nature. The following table corresponds to the French standard NF P18-560 used in particular in road construction:

Three other common classifications:

Other names are also derived from these concepts, for example the definition of granulated soils, which comprise more than 50% of elements with a granulometry greater than . They are divided into two families:

In the oil industry, where the English language has a marked presence, the most frequently used names, directly derived from the C. K. Wentworth classification, are the following:[6][7]​.