Shapes of particles

Abrasion, a serious problem in some appHcations, requires the addition of hard-surfacing materials to points exposed to abrasive wear (12). The severity of wear depends on the nature, size, hardness, and shape of particles as well as the frequency of contact, the force exerted against the wearing parts, and sohds loading as related to feed rate and soflds concentration. 

Material and uses Shape"of particles Size range, U.S. standard mesh f Internal porosity, % Bulk dry density, kg/L Average pore diameter, nm Surface area, kmVkg Sorptive capacity, kg/kg (dry)... 

Material Shape" of particles Bulk wet density (drained), kg/L Moisture content (drained), % by weight Swelhng due to exchange, % Maximum operating temperature, Operating pH range Exchange capacity ... 

The EPMA technique is developed for individual particles of fine-dispersed zeolite powder of various trademarks ZSM-5, ZSM-12, MOR, BEA. The phase and chemical composition of zeolite powder, the surface, shape of particles, stmcture and their distribution in terms of the size were studied using Superprobe-733 device. 

Wood structure before pressing, size and shape of particles... 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

The value of A decreases linearly with increasing filler content for a fixed filler content it increases from a filler with the spherical shape of particle to scales and further to fibers. For /J the observed behavior was reversed. 

Analytical solutions of equation 9.44 in the form of infinite series are available for some simple regular shapes of particles, such as rectangular slabs, long cylinders and spheres, for conditions where there is heat transfer by conduction or convection to or from the surrounding fluid. These solutions tend to be quite complex, even for simple shapes. The heat transfer process may be characterised by the value of the Biot number Bi where ... 

The relationship between effectiveness factor p and Thiele modulus < >l may be calculated for several other regular shapes of particles, where again the characteristic dimension of the particle is defined as the ratio of its volume to its surface area. It is found that... 

Silicone rubber-hydrogel composite is a two-phase system that is capable of swelling in water. The hydrogels prepared have different chemical compositions, size and shape of particles, and correspondingly different specific surfaces. It was found that the mechanical properties of silicone rubber-hydrogel composites depend mostly on the magnitude of the contact surface of both phases. ... 

More recently, many workers have concentrated on controlling the size and shape of particles, with an eye on industrial applications, where such features must be well defined and controllable. Many shapes have been made, including fibres, spheres, plates, as well as membranes cast on... 

Table 2.1 Some terms used to describe the shape of particles (qualitative definition).

Fig. 3.1a shows the different sizes and shapes of particles that have been used as stationary phases in hplc. The particles are usually silica, although in ion exchange and exclusion chromatography polymeric gels or resins are common. 

The procedure described in Example 8-4 may be used to obtain analytical solutions for concentration profiles and tj for other shapes of particles, such as spherical and cylindrical shapes indicated in Figure 8.9. Spherical shape is explored in problem 8-13. The solution for a cylinder is more cumbersome, requiring a series solution in terms of certain Bessel junctions, details of which we omit here. The results for the dimensionless... 

The method is only approximate because it is assumed that k completely defines the shape of the particle, whereas there are many different shapes of particle for which the value of k is the same. Further, it assumes that the diameter dp is the same as the mean projected diameter d. This is very nearly so in regions (b) and (c), although in region (a) the particle tends to settle so that the longest face is parallel to the direction of motion and some error may therefore be introduced in the calculation, as indicated by Hiass and Coull(28). ... 

Some values of S and e for different beds of particles are listed in Table 4.1. Values of e much higher than those shown in Table 4.1, sometimes up to about 0.95, are possible in beds of fibres 3 1 and some ring packings. For a given shape of particle, S increases as the particle size is reduced, as shown in Table 4.1. 

Extraction by supercritical fluids, in particular carbon dioxide and propane, is currently being investigated as a means of controlling the size and shape of particles for inhalation. Supercritical fluids are liquids above their critical pressure and temperature [28]. Under these conditions the molecules exhibit the flow, polarity, and solvency properties common of liquids but have the diffusivities and reactivities characteristic of gases. 

Table 25.1 Conversion-Time Expressions for Various Shapes of Particles, Shrinking-Core Model...

Figure 5.20. Real-time in situ ETEM image of the role of gas environments on Cn-Pd/C (a) H2 gas, (b) CO. The natnre and shape of particles are different. (After Gai et al 1990.)...

In the second stage, cross-link formation triggers phase separation, and further cross-link fixes the unevenly localized and deformed shape of particle. Thus, the red-cell-like particles are prepared during polymerization and not formed during isooctane evaporation. The red-cell-like particles find practically use for controlling rheological and optical characteristics in the coating and paint industry. 

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