Measurement equivalent diameter

Predic tions from Eq. (14-201) ahgn well with the Tatterson data. For example, for a velocity of 43 iti/s (140 ft/s) in a 0.05-m (1.8-inch) equivalent diameter channel, Eq. (14-201) predicts D32 of 490 microns, compared to the measured 460 to 480 microns. 

Particle diameter is a primary variable important to many chemical engineering calculations, including settling, slurry flow, fluidized beds, packed reactors, and packed distillation towers. Unfortunately, this dimension is usually difficult or impossible to measure, because the particles are small or irregular. Consequently, chemical engineers have become familiar with the notion of equivalent diameter of a partiele, which is the diameter of a sphere that has a volume equal to that of the particle. 

Also, in cases where the dimensions of a regular particle vary throughout a bed of such particles or are not known, but where the fractional free volume and specific surface can be measured or calculated, the shape factor can be calculated and the equivalent diameter of the regular particle determined from Figure 2. 

Massimilla et al. (M5) measured the rate of absorption of carbon dioxide in water from a mixture of carbon dioxide and nitrogen. Used as solid phase were silica sand particles of average equivalent diameter 0.22 mm, or glass ballotini of average equivalent diameter 0.50 and 0.80 mm. Columns of 30-and 90-mm i.d. were used, and the column height was varied from 100 to 1200 mm. 

Indeed, it is easy to define the size (sizes) of simple particles (e.g., in the case of spherical globules or cylinders). But, for many real PSs, the form of particles and pores is complicated. The sizes of complicated particles or pores are expressed with equivalent diameters (sizes). The particular choice of an equivalent is directed by measuring the technique or other reasons. Following are some frequently used expressions for equivalent diameters [52] ... 

Interrelation between different equivalent diameters is derived from the relations between the real values of the volume of solid Vs and surface area A of a particle with equivalent diameters Di and D-, where i and j are the methods of measurement or types of equivalent sizes. In a general case,... 

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 ... 

Selecki and Wasiak [54] have developed a modification of this technique which they named capillary method. Under the influence of a reduced pressure the foam moves continuously through a capillary tube with a known internal radius rin. The foam in the capillary is transformed into bubbles with extended cylindrical shape. By a lamp and two phototransistors the rate of film movement vy is measured, thus enabling to determine the equivalent diameter of each bubble... 

Stiegel and Shah34 reported the liquid holdup characteristics of a packed (with 0.318-cm polyethylene or 0.44-cm equivalent diameter packing) rectangular (16.8 cm x 2.06 cm) column. The column was approximately 122 cm high. The measurements were carried out with an air (in the flow range of 0 through 0.203 kg s 1 m 2) water system. The total liquid holdup was correlated by the relation... 

Often fibers have an irregular cross-section. The above method will give an equivalent diameter of a fiber having an irregular cross-section. One can also take a photograph of such a fiber and measure the area planimetrically. 

Where Sq is the surface area of a sphere with a diameter equal to the equivalent diameter (,5q = 4A) and is the surface area of the particle computed from the measured surface area. 

Schafer, [136] in a discussion on the accuracy of image analysis systems, states that the accuracy of area and equivalent diameter measurements is sufficient for most practical purposes. On the other hand he suggests improvements in the determination of perimeters and shape factors which he found to be unsatisfactory. 

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. 

This example shows that an irregularly shaped particle can have different values for the different equivalent diameters when they are calculated from different geometric properties, i.e., each type of equivalent diameter weights the particle based upon the property that was measured (Fig. 4B). 

In summary, not all equivalent diameters are equivalent to each other, unless the particles are perfect spheres this highlights the importance of reporting the type of particle size and method of measurement. Different equivalent diameters emphasize different properties of the particle as shown in Example 1, and these differences become more significant as the particles become more irregular. The choice of diameter is in part determined by the method of measurement, because different methods measure different... 

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