Cylindrical-shaped particle

Figure 8.28 shows the pore size distributions for the PS formed on highly doped / -Si at different current densities." For the PS formed on heavily doped silicon, the pores at a given HF concentration have a narrower distribution at lower current at a given current density, the distribution is narrower at lower HF concentrations. A bimodal distribution of pore diameter is gena-ally associated with two-layer PS on lowly doped / -Si and iUmninated n-Si. The PS formed on p-Si has also been found to have a bimodal distribution of particles sizes small spherically shaped particles with a diameter of a few nanometers and large cylindrically shaped particles oriented with their axis perpendicular to the surface.The distribution of pore size with multiple peaks may be attributed to the fact that PS may have a surface micropore layer and smaller branched pores. Due to the hierarchical structure of the branched pores, the distribution of pore diameters for highly branched PS is found to be fractal-like. ° ... 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

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. 

A considerable amount of information has been reported regarding mass transfer between a single fluid phase and solid particles (such as those of spherical and cylindrical shape) forming a fixed bed. A recent review has been presented by Norman (N2). The applicability of such data to calculations regarding trickle-flow processes is, however, questionable, due to the fundamental difference between the liquid flow pattern of a fixed bed with trickle flow and that of a fixed bed in which the entire void volume is occupied by one fluid. 

Schluter AD (2005) A Covalent Chemistry Approach to Giant Macromolecules with Cylindrical Shape and an Engineerable Interior and Surface. 245 151-191 Schmitt V, Leal-Calderon F, Bibette J (2003) Preparation of Monodisperse Particles and Emulsions by Controlled Shear. 227 195-215... 

Figure 31 (Liu, Liu, Li and Kwauk, 1986) shows a cylindrically shaped shallow fluid bed tubular heat exchanger. Solid particles are fluidized with a small stream of activating gas Ga, so as to insure maximal heat transfer between the particles and the exchanger tube wall. The waste gas Gw, from which heat is to be extracted, passes through the solid...

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 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. 

Wheeler [16] proposed that the mean radius, r, and length, L, of pores in a catalyst pellet (of, for that matter, a porous solid reactant) are determined in such a way that the sum of the surface areas of all the pores constituting the honeycomb of pores is equal to the BET (Brunauer, Emmett and Teller [17]) surface area and that the sum of the pore volume is equed to the experimental pore volume. If represents the external surface area of the porous particle (e.g. as determined for cracking catalysts be sedimentation [18]) and there are n pores per unit external area, the pore volume contained by nSx cylindrically shaped pores is nSx nr L. The total extent of the experimentally measured pore volume will be equal to the product of the pellet volume, Vp, the pellet density, Pp, and the specific pore volume, v. Equating the experimental pore volume to the pore volume of the model... 

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

An essential precondition for the establishment of the above mentioned profiles is that the catalyst particle is uniformly exposed over its entire surface to a flow with uniform temperature and concentration. This is, of course, never the case in random packings. Figure 5 gives an image of the local mass transfer distribution around cylindrical or ring shaped particles in a random packing. A test reaction producing dark deposits has been used. The intensity of the dark coloration is thus directly proportional to the local reaction rate of the surface reaction. Since the test reaction is mass transfer controlled, the coloration is also proportional to the local mass transfer, and if the mass transfer and heat transfer are equivalent, also to the local heat transfer [6]. 

Figure 4.21 Liquid hold-up state for a MWPB operated with air and water. Packing particles of cylindrical shape with dp = 0.012 m, pp = 430 kg/m, Hg = 0.18 m.

Consider two parallel similar toms-shaped particles at separation R between their centers (Fig. 19.14) [9]. A toms can be constmcted by joining the ends of a cylindrical tube. We denote the radius of the tube by a and the distance from the center of the tube to the center of the toms by b. The length of the cylindrical tube is thus 2iib and the closest distance H between the surfaces of these tori is H=R 2 a. Let N be the number of molecules contained within the particles. The interaction energy V R) between two parallel tori can be calculated with the help of Eqs. (19.1) and (19.54) (Fig. 19.15), namely. 

R (outer) radius of a cylindrical or ring-shaped particle... 

Victorian coals contain significant quantities of cylindrical rod-shaped particles, 1 xm in diameter and 6-8 xm long, which are high in carbon and hydrogen. 

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