Projected area diameter, calculation

Example 1. Calculate the equivalent projected area diameter surface area diameter and volume diameter of a particle with a projected area of 30.00 pm, perimeter of 24.58 pm and thickness of 0.40 pm as shown in Figure 4A. 

The circle diameter equivalent to the projected area was calculated. Such diameter of the initial snow crystal was also calculated using the same method. We calculated 250 400 crystals in each layer. In this paper, we use the statistically averaged diameter and the growth rate, which is the amount of change in the diameter per unit time. 

The value of the shape coefficients can be calculated for various equivalent sphere diameter bases. Let subscript a = projected area diameter v = volume diameter s -surface area diameter St = Stokes diameter m = mesh size. The volume of particles may be expressed as kjc/= k,xj = Aye/ = fexs/ = krfcj. Hence K = k/Xt/x f and so on. 

The first two columns on the left-hand side show the results firom the laboratory and are for projected area diameter. The calculation shows the respective means and the specific surface. 

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. 

Similar definitions give a in terms of dp or d/, but for simplicity, we consider only tty, defined in terms of dp. Table 20.2 gives volume shape factors for geometric shapes and mineral dusts. The volume shape factor based on projected area diameter has a maximum value of n/6 = 0.52, for a sphere. For regular geometric shapes, a can be calculated for irregular shapes, it must be determined experimentally by a combination of two or more measurement methods. The equivalent volume diameter is related to the volume shape factor by... 

There are various methods for the determination of the surface area of solids based on the adsorption of a mono-, or polymolecular layer on the surface of the solid. These methods do not measure the particle diameter or projected area as such, but measure the available surface per gram or milliliter of powder. The surface measured is usually greater than that determined by permeability methods as the latter are effectively concerned with the fluid taking the path of least resistance thru the bed, whereas the adsorbate will penetrate thru the whole of the bed as well as pores in the powder particles. These methods appear to be more accurate than surface areas calculated from weight averages or number averages of particle size because cracks, pores, and capillaries of the particles are included and are independent of particle shape and size... 

The primary size measurement is based on the area of the silhouette. A simple count of the pixels and the consideration of the calibration (pm2/pixel for example) give the projected area, A. This is valid for any cell, even elongated ones [76]. Geometrical correction might be necessary to take into account the shape of the support, like in the case of spherical microcarriers [77]. An equivalent diameter (Deq) is subsequently calculated ... 

No. of primnry particles X - Projected area Penetration. j M (calculated ncc. coeflicient v Numerical derivation) Envelop diameter (calculated acc. Numerical derivation) 2w, nm] Radins of gyration Rg nm] Fractnl dimension D, Fractal prefactor... 

In addition, to the projected area, an equivalent diameter could also be calculated based upon the particle s surface area. The equation for the surface area of a sphere is ... 

For example, particles can be photographed and the area of the particle projection can be measured. The equivalent diameter of a hypothetical sphere with the same projection area can then be calculated (Figure 21). In similar ways, other equivalent diameters can be determined such as diameters equivalent to spheres with the same volume, mass, specific surface area, sedimentation velocity in gases or liquids, etc. Sometimes, equivalent diameters are not unequivocal and may be limited in validity by the assumptions on which the physical models are based. 

Using this method. Park et al. [81] analysed TEM images of diesel particles and showed that the projected area equivalent diameter nearly equals the mobility diameter in the mobility size range from 50 to 220 nm. Doubly charged particles and possible fragments were observed for the DMA-classified particles. The fractal dimension calculated from the TEM images of mobility-classified aggregates was 1.75. The... 

The interspacing and diameter/thickness of the yarn is often used to calculate what is termed the fabric s cover factor , meaning the actual area the solid part of the fabric covers when the fabric is laid on a surface. From a more practical sense, this is the fraction of a fabric surface area that comprises the fibres/filaments. Neglecting the very small interfibre interstices. Fig. 8.24 depicts the projected areas seen in this way for a plain-weave structure, which can be used to obtain a calculated estimate of the fabric porosity. 

The numerical values of and a, for a particular sample, which will depend on the kind of linear dimension chosen, cannot be calculated a priori except in the very simplest of cases. In practice one nearly always has to be satisfied with an approximate estimate of their values. For this purpose X is best taken as the mean projected diameter d, i.e. the diameter of a circle having the same area as the projected image of the particle, when viewed in a direction normal to the plane of greatest stability is determined microscopically, and it includes no contributions from the thickness of the particle, i.e. from the dimension normal to the plane of greatest stability. For perfect cubes and spheres, the value of the ratio x,/a ( = K, say) is of course equal to 6. For sand. Fair and Hatch found, with rounded particles 6T, with worn particles 6-4, and with sharp particles 7-7. For crushed quartz, Cartwright reports values of K ranging from 14 to 18, but since the specific surface was determined by nitrogen adsorption (p. 61) some internal surface was probably included. f... 

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