Particle random packing

The PSD was calculated using the DFT method using the MiCTomeritics DFT applied to silica gel 200DF with model of cylindrical pores and another DFT version developed for the model of voids between spherical particles randomly packed in agglomerates (Gun ko 2007, Gnn ko et al. 2007f). 

Eor randomly packed spherical particles, the constants M and B have been deterrnined experimentally to be 150 and 1.75, respectively. Eor nonspherical particles, equivalent spherical diameters are employed and additional corrections for shape are introduced. 

FIGURE A.l A molecular representation of the three states of matter. In each case, the spheres represent particles that may be atoms, molecules, or ions, (a) In a solid, the particles are packed tightly together, but continue to oscillate, (b) In a liquid, the particles are in contact, but have enough energy to move past one another, (c) In a gas, the particles are far apart, move almost completely freely, and are in ceaseless random motion. 

Sintered metal fibers with filaments of uniform size (2-40 (tm), made of SS, Inconel, or Fecralloy , are fabricated in the form of panels. Gauzes based on thicker wires (100-250 tm) are made from SS, nickel, or copper. They have a low surface area of about 10 m g. Several procedures are used to increase the surface area, for example, leaching procedures, analogous to the production of Ra-Nickel, and electrophoretic deposition of particles or colloid suspensions. The porosity of structures formed from metal fibers range from 70 to 90%. The heat transfer coefficients are high, up to 2 times larger than for random packed beds [67]. 

Dixon and coworkers [25] have performed several CFD simulations of fixed beds with catalyst particles of different geometries (Figure 15.9). The vast number of surfaces and the problems with meshing the void fraction in a packed bed have made it necessary to limit the number of particles and use periodic boundary conditions to obtain a representative flow pattern. Hollow cylinders have a much higher contact area between the fluid and particles at the same pressure drop. However, with a random packing of the particles, there wiU be a large variation... 

An equivalent diameter de for flow through the bed can be defined as four times the cross-sectional flow area divided by the appropriate flow perimeter. For a random packing, this is equal to four times the volume occupied by the fluid divided by the surface area of particles in contact with the fluid. 

Figure 9.19 Typical dependence of the porosity, s, of a bidisperse PS with loose random packing of globules size of on partial volume of the larger particles X, and K=D ID2.

Figure 19.21 Dependence of porosity of a random packing of spherical particles in a cylinder container according to 1 [104], 2 [105], (3), (4) for loose and dense packings by [102], Solid lines correspond to calculations using Equation 9.42a through Equation 9.42c.

Unfortunately, the relations (9.61) and (9.62) do not allow establishment of an unequivocal interrelation between the coordination numbers of packings of particles ( ,) and pores (Zc) for corresponding V- and D-lattices, but, for undegenerated D-polyhedra of tetrahedron form Zc = 4. Typical values of nF for random packings and regular packings of monospheres are discussed in Section 9.7.3 and Section 9.7.2, respectively. 

We have assumed that a random packed structure is more likely at high rates with a distribution of floe sizes. The volume fraction of floes will depend upon the floe packing fraction, giving rise to a floe diameter 2af with particles per floe ... 

Fib er-Bed Scrubbers Fibrous-bed structures are sometimes used as gas-liquid contactors, with cocurrent flow of the gas and liquid streams. In such contactors, both scrubbing (particle deposition on droplets) and filtration (particle deposition on fibers) may take place. If only mists are to be collected, small fibers may be used, but if solid particles are present, the use of fiber beds is limited by the tendency of the beds to plug. For dust-collection service, the fiber bed must be composed of coarse fibers and have a high void fraction, so as to minimize the tendency to plug. The fiber bed may be made from metal or plastic fibers in the form of knitted structures, multiple layers of screens, or random-packed fibers. However, the bed must have sufficient dimensional stability so that it will not be compacted during operation. 

As e is increased, flow through the bed becomes easier and so the permeability coefficient B increases a relation between B, e, and S is developed in a later section of this chapter. If the particles are randomly packed, then e should be approximately constant throughout the bed and the resistance to flow the same in all directions. Often near containing walls, e is higher, and corrections for this should be made if the particle size is a significant fraction of the size of the containing vessel. This correction is discussed in more detail later. 

Carman found that when R jpu was plotted against Re using logarithmic coordinates, his data for the flow through randomly packed beds of solid particles could be correlated approximately by a single curve (curve A, Figure 4.1), whose general equation is ... 

Drying without the occurrence of large capillary stresses was obtained with supercritical drying in an autoclave. In this case a mean pore size was obtained which was twice that obtained under normal drying conditions and with a broad pore size distribution in accordance with the expectation for a noncompressed, random packing of particles. 

The total exclusion chromatogram provides the means to obtain the e values and this was found to be 0.423. It is interesting to compare this value with that reported ( ) for the interstitial volume of randomly packed rigid spheres which is 0.364. We assume that our value deviates from the hard sphere value primarily because of the inefficient packing of particles in the case of the column used in this work varied substantially in size (35 -75 p). 

Porous inkjet papers are in general created from colloidal dispersions. The eventual random packing of the colloid particles in the coated and dried film creates an open porous structure. It is this open structure that gives photographic-quality inkjet paper its apparently dr/ quality as it comes off the printer. Both the pore structure and pore wettability control the liquid invasion of the coated layer and therefore the final destination of dyes. Dispersion and stability of the colloidal system may require dispersant chemistries specific to the particle and solution composition. In many colloidal systems particle-particle interactions lead to flocculation which in turn leads to an increase in viscosity of the system. The viscosity directly influences the coating process, through the inverse relation between viscosity and maximum coating speed. 

Packing surface area per unit volume increases. Elficiency increases as the particle size decreases (random packing, Fig. 14-59) or as the channel size narrows (structured packing, Fig. 14-60). 

Experiments were also performed to compare the holdup and flow distribution in a bed, randomly packed with 3 mm spherical alumina particle, under the same flow conditions as was done for structured packing. However, it was evident that the successful operating conditions for structured packing were too severe for random packed bed, due to very high pressure drop. For very low liquid velocity ( 1 mm/s) and no gas flow, when the experiment was possible, the liquid distribution was poor as indicated by a low uniformity factor ( 40%). However, this information is insufficient to compare the distribution characteristics of structured and random packings. 

Fig. 4.20 DEM-simulated packing density under gravity for a two-dimensional spherical particulate assembly 50 pm in diameter, with f =fw = 0.364 and with van der Waals forces, showing the formation of clusters, which decrease the packing density by more than 10%. [Reprinted by permission from Y. F. Cheng, S. J. Guo, and H. Y. Li, DEM Simulation of Random Packing of Spherical Particles, Powder Technol., 107, 123-130 (2000).]...

Therefore, in this example, the number of particles was reduced to a reasonable value and, in the first instance, instead of the random packing shown in the previous section, a regular arrangement consisting of spherical particles was assumed. Similar to the arrangement of atoms in ideal crystals, two densest particle beds were chosen. For the body-centered cubic (bcc) arrangement of catalyst particles, the void fraction is equal to 32%, for the face-centered cubic (fee) arrangement, it is 26%. 

In this study, we have shown how gas-liquid flow through a random packing may be represented by a percolation process. The main concepts of percolation theory allow us to account for the random nature of the packing and to derive a theoretical expression of the liquid flow distribution at the bed scale. This flow distribution allows us to establish an averaging formula between the particle and bed scales. Using this formula, we propose the bed scale modelling of some transport processes previously modelled at the particle scale. 

Flow through packed beds (eddy or multipath diffusion). In chromatography, component zones are carried through a bed of randomly packed particles. The streamlines in such flow veer back and forth to find passage between the particles (see Figure 5.4) and fluctuate in velocity... 

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