Projected area diameters

As we just suggested, particle size and shape are important physical properties influencing powder flow and compaction. Particle size is a simple concept and yet a difficult one to quantitate. Feret s diameter, Martin s diameter, projected area diameter, specific surface diameter, Stokes diameter, and volume diameter are but several of the measurements that have been used to quantify particle size using a variety of methods. 

For irregularly shaped particles, the diameter of a particle may be estimated using one of several methods Feret diameter, Martin diameter, projected-area diameter, equivalent diameter, or aerodynamic diameter. The two most commonly used diameters, the Feret and Martin diameters, are relative to a randomly chosen reference line, typically the bottom edge of the viewing frame, where the Feret... 

Projected area diameter Projected area if the particle is resting in a stable position... 

Several diameter definitions are used in particle image measurements (Fig. 7). Martin diameter, the chord length which divides the projected particle into two equal areas with respect to a fixed dkection (29) Feret diameter, the projected length with respect to a reference dkection (30) and the diameter of equivalent surface area, the diameter of a ckcle the area of which is equivalent to the projected area of the particle in question (3). 

FIG. 20-5 Statistical (Martin s and Feret s) and projected area diameters for an irregular particle. 

Ggi, = mass velocity of liquid, Ib/hr (fF). For outside horizontal tubes, use projected area (diameter X length) of the tube, not the outside surface area. This assumes that only half of the tube is effective for bubble release. This does not apply to actual heat transfer area. 

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... 

To obtain a value for the dimensions of an irregular particle, several measurement approaches can be used Martin s diameter (defined as the length of a line that bisects the particle image), Feret s diameter (or end-to-end measurement, defined as the distance between two tangents on opposite sides of the particle parallel to some fixed direction), and the projected area diameter (defined as the diameter of a circle having the same area as that of the particle observed perpendicular to the surface on which the particle rests). With any technique, a sufficiently large number of particles is required in order to obtain a statistically valid conclusion. This is best accomplished by using a... 

D =(4SA/n)112 is the projected area diameter, equal to the diameter of a circle having the same area SA as the projected area of the particle resting in a stable position. For particles with size anisotropy, SA corresponds to the mean value derived from all possible orientations. 

Dh=4Sa/Pa is the hydraulic diameter, equal to the diameter of a circle with the same projection area to perimeter ratio. 

The second is the group R /pu2, in which R is the force per unit projected area of particle in a plane perpendicular to the direction of motion. For a sphere, the projected area is that of a circle of the same diameter as the sphere. 

If dp is the mean projected diameter, the mean projected area is nd2/4 and the volume is k d2, where k is a constant whose value depends on the shape of the particle. For a spherical particle, k is equal to tt/6. For rounded isometric particles, that is particles in which the dimension in three mutually perpendicular directions is approximately the same, k is about 0.5, and for angular particles k is about 0.4. For most minerals k lies between 0.2 and 0.5. 

Fig. 2.1 Methods of estimating d, the projected area diameter (a) image shearing method [after Heywood (H6)] (b) statistical intercept method [after Martin et al. (Ml)].

Martin s diameter and Feret s diameter of a particle depend on the particle orientation under which the measurement is made. Thus, obtaining a statistically significant measurement for these diameters requires a large number of randomly sampled particles which are measured in an arbitrarily fixed orientation. Since Martin s diameter, Feret s diameter, and projected area diameter are based on the two-dimensional image of the particles, they are generally used in optical and electron microscopy. The principles of microscopy as a sizing method are discussed in 1.2.2.2. 

Bo Magnetic flux density in a vacuum dA Projected area diameter... 

A fly ash sample from a fluidized bed coal combustor is analyzed to obtain particle size data. Table PI. 1 shows the distributions of the projected area equivalent diameter of the particle dA obtained by the image analysis and the volume diameter of the particle d obtained by the electrozone technique [Ghadiri et al., 1991]. 

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