Particle size, characterization equivalent diameters

Besides mass concentration, atmospheric particles are often characterized by their size distribution. Aerosols are typically sized in terms of the aerodynamic equivalent diameter (dae) of the particle, usually expressed in micrometer (pm) or nanometer (nm) (Mark, 1998). Atmospheric particles are usually nonspherical and with unknown density. Therefore, the r/ae of a particle is usually defined as the diameter of an equivalent unit density sphere (p = 1 gctrf3) having the same terminal velocity as the particle in question (Mark, 1998 Seinfeld and Pandis, 1998). 

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

We get particles of different sizes. Each has a mass equivalent diameter," which is the diameter of a sphere with the same mass as the particle. One can characterize the sizes with a cumulative mass distribution such as in the upper part of Figure 14-6. This shows which mass fraction is in the particle with a diameter smaller than a certain value. The frequency distribution underneath is derived from the upper diagram it gives an indication of which diameters are most common. We can try to characterize the drops with a single diameter there are many different ways in which this can be done. They lead to parameters such as the c 32 (Sauter diameter), dso (mean diameter) and dmax (maximum... 

However, it is not easy to evaluate the particle size of a powder. For a large lump, it is possible to measure it in three dimensions. But if the substance is milled, the resulting particles are irregular with different numbers of faces and it would be difficult or impracticable to determine more than a single dimension.For this reason, a solid particle is often considered to approximate to a sphere characterized by a diameter. The measurement is thus based on a hypothetical sphere that represents only an approximation to the true shape of the particle. The dimension is thus referred to as the equivalent diameter of the particle. 

In the case of fumed powders, the results of particle size analysis depend veiy strongly on the characterization method. Each method measures a different particle property, from which sphere equivalent diameters are calculated. The underlying models assume homogeneous, spherical particles, which does not apply to the porous aggregates and agglomerates of these materials. 

An advantage of equivalent diameters is that they provide a unique characterization of particle size for the given method of measurement. In addition, the diameter gives information about the particle properties. For example, the equivalent surface diameter would give information about the surface area of the particle and the equivalent volume diameter would give information about the volume. Thus, if the density of the particles is known, the mass and properties important to pharmaceutical applications can be calculated. The numerical value for equivalent diameters derived from different geometric properties will only be identical in the case of perfectly spherical particles, and if the particle irregularity increases so will the differences between the different equivalent diameters. 

For non-spherical particles, a simple characterization is to specify the size in terms of an equivalent diameter, the diameter of spherical particle that would... 

In many cases, particularly for very small particles, surface area is a more appropriate characteristic to assess than some size based on an equivalent diameter. Particle surface area is important, for example, in paints and pigments or when chemical reactivity is an important property, as in the setting of cement. Precipitated materials are often characterized in this manner. Amongst the several techniques available, those based on permeability and gas adsorption are probably the most popular. 

Thus we see that the adhesion of irregular particles can be characterized by means of the average force of adhesion, which is determined from the distribution of the irregular adherent particles with respect to adhesive force, on the basis of equivalent size (diameter). The relationship between the average adhesive force and particle size is more complex for the irregular particles than for the equivalent-size spherical particles. For a certain size range of the irregular particles, there will be a maximum in adhesion. 

Dependence of Adhesive Force on Size of Irregularly Shaped Particles. Experiments have been performed [194] to characterize the relationship between the adhesion of irregularly shaped particles and the size of these particles. The equivalent diameter (see Section 14) was taken as a single parameter characterizing the size of irregularly shaped particles. 

If the particle size distributions are characterized by the average diameters at the cumulative masses of 10, 50, and 90%, the data scattering measured by different techniques can be represented by the diameter ratios at the cumulative masses of 10, 50, and 90%, or DRio, DR50, and DR90. Since the particle diameter measured by the electrical sensing zone technique is to be the equivalent volume diameter and is independent of the particle shape, its particle diameter is defined to be one. The particle diameters measured by other techniques are then ratioed with this diameter. The experimental results of DRjo, DR50, and DR90 are summarized in Table 5. It can be seen that the results of particle analysis from different techniques can be quite different. 

In many cases, irregular-shaped particles or a size distribution of particles can be treated as spheres with an equivalent diameter that gives the same sinface/volmne ratio as the irregular-shaped particle. The Saunter mean diameter, usually denoted t/j2, defined as the total volume divided by the total surface area, is a very common method used to characterize a size distribution of bubbles or drops. With this definition, the total volume can be calculated from the munber of particles multiphed by the volume of a sphere with diameter and the total sinface area can be calculated by multiplying the number of particles by the surface of the sphere. 

Most frequently, an aerosol is characterized by its particle size distribution. Usually this distribution is reasonably well approximated by a log-normal frequency function (Fig. 4A). If the distribution is based on the logarithm of the particle size, the skewed log-normal distribution is transferred into the bell-shaped, gaussian error curve (see Fig. 4B). Consequently, two parameters are required to describe the particle size distribution of an aerosol the median particle diameter (MD), and an index of dispersion, the geometric standard deviation (Og). The MD of the log-normal frequency distribution is equivalent to the logarithmic mean and represents the 50% size cut of the distribution. The geometric standard deviation is derived from the cumulative distribution (see Fig. 4C) by... 

Two important morphological parameters characterizing ball-milled powders are the particle and grain size of constituent phases within the powders. In our laboratory, the size measurement of the powder particles is carried out by attaching loose powder to sticky carbon tape and taking pictures under secondary electron (SE) mode in the SEM. The images are then analyzed by an image analysis software. The size of the powders is calculated as the particle equivalent circle diameter, ECD = AA/nf, where A represents the projected particle area. Usually from -300 to 700 particles are analyzed for each batch. 

The particles may be anisometric, i.e., deviate from the spherical form. Moreover, the particles may have a rough surface. The two cases cannot be fully separated because intermediates occur, but a sphere can have a rough surface and a platelet can be smooth. One parameter now is insufficient to characterize a particle. If all particles have approximately congruent shapes (think of a collection of screws of various sizes), it may be possible to use just one size parameter, e.g., length. For irregularly shaped but not very anisometric particles, as found in several powders, one often defines an equivalent sphere diameter. This can be defined in various ways, such as... 

The range of aperture sizes in most standard series extends from 125 mm to 20 pm. At the top end of the range particles must be carefully hand-placed on the sieve. At the lower end, sieving with the aid of a liquid is often needed to assist the flow of particles through the mesh. Particles that pass through a sieve are characterized by an equivalent sieve aperture diameter, the diameter of a sphere that would just pass through. Care needs to be taken to interpret this quantity, however, as explained in section 2.14.3 (see Figure 2.14). 

As demonstrated by the graphs of Figure 8.8 one can in some circumstances deal with bimodal distributions which are well separated. A wide ranging continuous size distribution is difficult to characterize by PCS. In general, PCS is an applicable method from 0.003 to several microns. As in many other methods, data for non spherical particles use the size of an equivalent sphere diameter in the presentation of the data. 

Other methods that detect a sphere of influence include those based on the Coulter principle which will also be reviewed at this conference. Here the data is reported in terms of a sphere of equivalent volume, irrespective of the shape or, in some situations, the state of the particulate interface. The method depends, essentially, on measuring the increase in resistance experienced between two electrodes as a particle passes between them and an essential requirement, therefore, is the presence of electrolyte in the measurement system. The method is realistically limited to particles down to about 1/jm in diameter, and there is no practical upper limit to the principle. The presence of electrolyte in the environment is an advantage in some situations since the effect is to suppress charge effects at the particle interface and this simplifies the measurement of the size of colloidal dispersions. Submicrometre dispersions can be measured but it should be noted that interference effects become more pronounced and there is less certainty about the magnitude of coincidence effects, quite apart from the intrinsic experimental difficulties of keeping orifices with diameters of less than 50um clean and operationally effective. Nevertheless, the Coulter principle has proved to be an invaluable technique for the detailed characterization of biological systems such as blood cells and, in some instances, bacterial suspensions. 

Since most particulate materials are irregularly shaped, the volumetric response is invaluable, as volume is the only single measurement which can be made of an irregular particle in order to characterize its size. In biological applications the size response is usually left calibrated in volume units (femtolitres, or cubic microns ), but industrially it is conventional to report the equivalent spherical diameter calculated from it. 

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