Equidimensional particle

Any equidimensional particle may commonly be specified by diameters . Nonequi-dimensional particles, or in other words, those which are longer in one direction than in others, are commonly characterized by the second longest major dimension. For needlelike particles, for instance, dp would represent the thickness of the particles, not length. 

Sphericity shape factor Circularity shape factor 1 W where a0 = shape factor for equidimensional particle and thus represents part of av which is due to geometric shape only av = volume shape coefficient m = flakiness ratio, or breadth/thickness n = elongation ratio, or length/breadth Sphericity = (surface area of sphere having same volume as particle) / (surface area of actual particle) Circularity = (perimeter of particle outline)2 / 4tr(cross-sectional or projection area of particle outline)... 

Xylitol occurs as a white, granular solid comprising crystalline, equidimensional particles having a mean diameter of about 0.4—0.6 mm. It is odorless, with a sweet taste that imparts a cooling sensation. Xylitol is also commercially available in powdered form and several granular, directly compressible forms. See also Section 17. 

When the elements of the disperse phase can be classified as equidimensional, namely they have nearly the same size or spread in multiple directions, and have constant material density, typically a single internal coordinate is used to identify the size of the elements. This could be particle mass (or volume), particle surface area or particle length. In fact, in the case of equidimensional particles these quantities are all related to each other. For example, in the trivial cases of spherical or cubic particles, particle volume and particle surface area can be easily written as Vp = k d and Ap = k d, or, in other words, as functions of a characteristic length, d (i.e. the diameter for the sphere and the edge for the cube), a volume shape factor, k, and a surface-area shape factor, k. For equidimensional objects the choice of the characteristic length is straightforward and the ratio between kp, and k is always equal to six. The approach can, however, be extended also to non-equidimensional objects. In this context, the extension turns out to be very useful only if... 

In the case of non-equidimensional particles, typically more than one internal coordinate is used to describe the shape, morphology, and size of the particles. To illustrate the issues related to phase-space advection due to mass transfer, let us analyze a simple example. We consider needle-like particles described as rectangular parallelepipeds with length and equal width and depth 2- Clearly the particle volume can easily be calculated from these two quantities (i.e. Vp = particle surface area... 

The parameter ke is obtained for equidimensional particles and is given in Table 1 7 along with the parameter c. The breadth m) to thickness n) parameters are also incorporated in the expression. Figure 1-5 shows the dimensions of n, m ) for the given object. With these values the shapes of irregular particles may be approximated to give values of the surface area and volume of the particles. 

Table 1-7 Shape coefficients for equidimensional particles (Heywood, 1963)...

An impactor, illustrated in Fig. 29.6, resembles a heavy-duty hammer mill except that it contains no grate or screen. Particles are broken by impact alone, without the rubbing action characteristic of a hammer mill. Impactors are often primary-reduction machines for rock and ore, processing up to 600 ton/h. They give particles that are more nearly equidimensional (more cubical ) than the slab-shaped particles from a jaw crusher or gyratory crusher. The rotor in an impactor, as in many hammer mills, may be run in either direction to prolong the life of the hammers,... 

Further elucidation of the reactivity of Pd colloids was reported by Bradley and Blackmond [13]. These authors prepared a series of well defined homopolymer-stabilised Pd colloids, varying the particle size, and used them in the Heck reaction between 4-bromobenzaldehyde and butyl acrylate. Interestingly, the authors found a correlation between initial rate and particle size the initial rate increases with decreasing particle size. No correlation was reported regarding the palladium specific surface area. Whereas the precise morphology of the Pd particles could not be defined, the authors found that they were quite equidimensional, allowing a representation as regular polyhedra to apply surface defect site statistics to char-... 

Granules are those particles having approximately equidimensional, nonspherical shapes. The term can also apply to small, coarse metal particles often formed by pouring molten metal through a screen into water and agitating violently as the metal solidifies. 

Granular (or powder) gran-y9-br (1794) adj. Particles having equidimensional non-spherical shapes. 

Permeability. Nonwoven fibrous media are also being extensively used in filtration and barrier applications. Several analytical approaches have been proposed for describing the dependence of their permeability on the shape and volume fraction of fibers (53-56). For simplicity, all these studies assumed that the fibrous media is made of a regular array of equidimensional cells, each consisting of a fiber segment surrounded by air. This is certainly not the case experimentally as fibrous media are made from a deposition process in which fibers are laid into a dense and compact mat. In one approach (57), the permeability of the sheet to diffusional flow is studied by a Monte-Carlo process. Here, the sheet is put in contact with a large external bath of small particles which diffuse through the... 

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