Definitions of particle size

The motion of a particle, and its separation in a cyclone, obviously depends on its size, amongst other important factors, such as its density, shape, and tangential velocity. By the term size we normally mean the diameter. The particle diameter can be defined in different ways, and one should be aware which one is used in a given context. Clift et al. (2005) and Allen (1990) review this issue. We mention here the definitions that are most relevant for cyclones. 

The volume equivalent diameter is the diameter of a sphere with the same volume as the actual particle s. The surface equivalent diameter is the diameter of a sphere with the same surface area as the actual particle. The surface/volume diameter is the diameter of a particle with the same surface-to-volume ratio as the actual particle. 

To illustrate this, a cylindrical particle with height 2L and diameter L is shown in Fig. 2.3.1, together with its equivalent spheres. 

Very central to cyclone technology is the dynamically equivalent particle diameter. This is the diameter of an equi-dense sphere that has the same terminal velocity as the actual particle. Calculating this can be difficult in the range of intermediate Reynolds numbers, or when the Cunningham correction is significant. In the region where Stokes drag law applies, we call it the Stokesian diameter. 

A similar measure, which is widely used in aerosol science, is the aerodynamic particle size . This is the diameter of a sphere of density 1000 kg/rr that has the same terminal velocity as the actual particle in air at normal temperature and pressure in a gravity field. 

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Particle shape plays an important role in particle size determination. The simplest definition of particle size diameter is based on a sphere, which has a unique diameter. In reality, however, many particles are not well represented by this model. Figure 1 illustrates the variety of shapes that may be found in particle samples [1]. As the size of a particle increases, so does its tendency to have an irregular shape [2], complicating statistical analysis. Particle shape coefficients have been derived for different geometries [3], and various equivalent diame-... 

Particle size measurement is one of the essential requirements in almost all uses of colloids. However, our discussion in Section 1.5 makes it clear that this is no easy task, especially since even the definition of particle size is difficult in many cases. A number of techniques have been developed for measuring particle size and are well documented in specialized monographs (e.g., Allen 1990). Optical and electron microscopy described in the previous section can be used when ex situ measurements are possible or can be acceptable, but we also touch on a few nonintrusive methods such as static and dynamic light scattering (Chapter 5) and field-flow fractionation (see Vignette II Chapter 2) in other chapters. 

Only a minority of systems of industrial interest contain powders with a uniform particle size, i.e. monodisperse. Most systems generally show a distribution of sizes (polydisperse) and it is then necessary to define the average dimension. There are many different definitions of particle size,1 2 the most commonly used, particularly in fluidisation, is the so called volume-surface mean or the Sauter mean diameter. This is the... 

Two commonly encountered definitions of particle size are Feret s diameter and Martin s diameter. These refer to estimates of approxi-... 

As with the different definitions of particle size, the choice is made of a shape factor most relevant in the application in question. The following is a list of the definitions of the most frequently used, simple shape factors. 

The same type of problem is encountered in the definition of particle size distribution since the starting assumption is that all particles have the same shape. In this case, the particle size distribution is defined as the relationship between a given particle size and the frequency, or number of particles, with that certain diameter or size. Matyi et al. (143a) discuss in detail for a given particle size distribution the several features that can be interpreted as the average size. We refer the reader to this review article. 

Particle size of spherical particles is their diameter, while the size of particles with irregular shapes is more difficult to be determined. Therefore, it is important to have a definition of particle size. For particles with irregular shapes, their size can be... 

Natural soils, despite their lack of homogeneity, can be assorted in fractions or subfractions by reference to their particle size. The definition of particle size in this case refers to the maximum size of the particle that is incorporated in the soil. This type of assortment is quite useful to engineers, since it is directly connected to the mechanical behaviour of the soil material. The basic fractions of soils are boulders, cobbles, gravels, sand, silt and clay. 

An excellent discussion of the definition of particle size has been given by Bailey, Beattie, and Booth (146), and a more recent and broader discussion of particle size and shape is given by Underwood (147). 

If an irregularly shaped particle is allowed to settle in a liquid, its terminal velocity may be compared with that for a sphere of the same density settling under similar conditions. For laminar flow, the sphere diameter can be calculated from Stokes law and is commonly referred to as the Stokes diameter. Using a microscope, individual particles are observed and measured. In this case, the particle size is commonly determined from the projected area of the particles projected area diameter) or a linear dimension measured parallel to some fixed direction Feret s diameter or Martin s diameter). Some definitions of particle size are given in Table 3.3. 

Some of these analytical techniques allow the definition of particle size, either directly from the PDF or from X-ray scattering peak broadening (XSPB), small-angle X-ray scattering (SAXS), and dynamic light scattering (DLS) (Waychunas, 2001). 

H. Heywood, Numerical Definitions of Particle Size and Shape. Chem. Ind., 15(1937) 149-154. 

The atmospheric environment is composed of a number of gases in which particles are suspended. As a consequence, millions of particles are inhaled with every breath. A surface area the size of a tennis court is available in the lungs for the deposition of these particles. This huge surface area is in direct contact with the atmospheric environment, and is thus the primary target for inhaled particles. Usually particles in the diameter range of 0.01-10 pm are deposited in the lungs and are therefore available for interactions with pulmonary surfaces. Unfortunately, however, different definitions of particle size ranges are in use so that data are often not comparable. We were not able to cope with this problem, but we hope that Table 1 will help in the interpretation of the presented data. 

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