Sphere-shaped particles

Particle shape is also important. Disk-shaped as well as cylindrical-shaped conductors have a high response because large induced current loops are formed. Small randomly shaped conductors, such as those present in cmshed slag, also respond favorably. Sphere-shaped particles generate small-current loops, however, and do not have a high response. Multiple-current loops occur in conductors that have irregular bends, producing counteractive forces that tend to nullify each other. 

The pore shape is determined by the particle shape. Plate-shaped particles lead to plate-shaped pores in the case of regular packing. Sphere-shaped particles favor cylindrical or sometimes ink-bottle-type pores. 

Hollow Disc and Sphere-Shaped Particles from Red Blood Cell Templates... 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Irregular-shaped particles exhibit greater surface area than regular-shapea cubes and spheres, the amount of this increase being possibly 25 percent. The effect of particle size and size distribution on effective surface, in a shaft employed for calcination of limestone, is shown in... 

This form is particularly simple, since /(r) is independent of the type of species i. It behaves as if each particle excluded a volume equal to the smallest cube into which its effective hard sphere shape could be placed. The alternative form... 

Recently, Rumpf (R5) has considered the forces of attraction between a plate and a sphere and between irregular shape particles. His conclusions are that the capillary bonds are relatively insensitive to the particle shape, but the van der Waals force of attraction is extremely sensitive. Although weaker in magnitude than the two aforementioned bonds, the electrostatic bonds may persist over long separation distances. 

It should be emphasized that this equation holds only for a sphere. When it is applied to irregularly shaped particles, significant errors can result. Photon correlation spectroscopy is best suited for narrow distributions of particles, although various mathematical treatments have been developed for analyzing broad distributions [46], Photon correlation spectroscopy is applicable for... 

The results from Fig. 14.1 show the developing turbulent flame zone. The nonsymmetries of the reaction rate field are due to inhomogeneity of the polydis-persed mixture, i.e., nonsymmetrical distribution of model particles and their velocities. The reaction front is under formation oxygen and partially the volatiles in the center are burnt out, but the reaction front is not sphere-shaped yet. The nonuniformity of the model particles distribution was induced initially due to the stochastic modeling of the particulate phase. 

For spheres sufficiently small that Rayleigh theory (Chapter 5) is applicable, or for arbitrarily shaped particles that satisfy the requirements of the Rayleigh-Gans approximation (Chapter 6), incident light with electric field components parallel and perpendicular to the scattering plane may be scattered with different amplitudes however, there is no phase shift between the two components. Hence, the amplitude scattering matrix has the form... 

Bottiger, J. R., E. S. Fry, and R. C. Thompson, 1980. Phase matrix measurements for electromagnetic scattering by sphere aggregates, in Light Scattering by Irregularly Shaped Particles, D. Schuerman (Ed.), Plenum, New York, pp. 283-290. 

The concept of specific area defined by Equation (1) is important because this is a quantity that can be measured experimentally for finely divided solids without any assumptions as to the shape or uniformity of the particles. We discuss the use of gas adsorption to measure Asp in Chapter 9. If the particles are known to be uniform spheres, this measured quantity may be interpreted in terms of Equation (2) to yield a value of Rs. If the actual system consists of nonuniform spheres, an average value of the radius may be evaluated by Equation (2). Finally, even if the particles are nonspherical, a quantity known as the radius of an equivalent sphere may be extracted from experimental values. This often proves to be a valuable way of characterizing an array of irregularly shaped particles. We have a good deal more to say about average dimensions in this chapter and about equivalent spheres in Chapter 2. 

Aerodynamic diameter Particles suspended in gases typically have irregular shapes. The aerodynamic behavior of an irregularly shaped particle may be modeled with an idealized sphere of uniform composition. The diameter of the sphere is the aerodynamic diameter (compare with mass median aerodynamic diameter). 

A better picture of the crystallization phenomena was obtained from the microscope examination of the crystals at different stages of their development. The first crystals of zeolite omega appeared as spheres with diameters around 0.5-1 pm (Fig.2). With the appearance of (001) faces, this form evolved into barrel-shaped particles (Fig.3). At a later stage of the syntheses, the habit evolved to euhedral hexagonal with the development of (100) faces (Fig.4). 

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