Tortuous path

Filler materials render barrier properties to composite systems by forcing the gas molecules to travel around the filler particles, thus making the permeation path tortuous compared to a monolithic polymer. For thin, plate-Uke fillers for example, inorganic clay platelets, GO sheets, and so on, the path can be depicted as shown in Figure 8.8 (Nielsen, 1967). 

Barrier Phenomenon. In red cell filtration, the blood first comes into contact with a screen filter. This screen filter, generally a 7—10-) m filter, does not allow micro aggregate debris through. As the blood product passes through the deeper layer of the filter, the barrier phenomenon continues as the fiber density increases. As the path becomes more and more tortuous the cells are more likely to be trapped in the filter. 

Two basic flow schemes are used tortuous path flow and sheet flow (Fig. 22-59). Tortuous path spacers are cut to provide a long path between inlet and outlet, providing a relatively long residence bme and high velocity past the membrane. The flow channel is open. Sheet flow units have a net spacer separating the membranes. Mass transfer is enhanced either by the spacer or by higher velocity. 

FIG. 22-59 Schematic of two ways to pass solution across an ED membrane. Tortuous flow (left) uses a special spacer to force the solution through a narrow, winding path, raising its velocity, mass transfer, and pressure drop. Sheet feed (right) passes the solution across the plate uniformly, with lower pressure drop and mass transfer. Coutiesy Elsevier.)... 

In a packed column the individual solute molecules will describe a tortuous path through the interstices between the particles and some will randomly travel shorter routes than the average and some longer. The multi-path effect is diagramatically depicted in Figure 5. 

Now, consider a packed GC column due to the turbulence resulting from the rapid changes in direction of the gas velocity as it winds its tortuous path between the... 

Depth filter A filter medium consisting of randomly distributed particles or fibers resulting in openings with a non-uniform and tortuous path. 

Depth filters on the other hand are composed of layers of fabric or fibers, which provide many tortuous paths for the fluid to flow through. The pores or passages must be larger than the rated size of the filter if particles are to be retained in the depth of the media rather than on the surface. 

Sprayed coatings have structures in which fine pores thread tortuous paths through the deposit, and it is necessary to apply a coating thickness of about 350 ftm if all these paths are to be closed. Scratch-brushing of the deposit, however, makes it possible to consolidate the surface and to achieve adequate continuity in thinner deposits, e.g. 200 m. 

Tye [38] explained that separator tortuosity is a key property determining the transient response of a separator (and batteries are used in a non steady-state mode) steady-state electrical measurements do not reflect the influence of tortuosity. He recommended that the distribution of tortuosity in separators be considered some pores may have less tortuous paths than others. He showed mathematically that separators with identical average tortuosities and porosities can be distinguished by their unsteady-state behavior if they have different distributions of tortuosity. 

The residence time or contact time discussed in the preceding section is a simple average. Hyman (H21) pointed out that the residence time of any one gas molecule could vary widely from the mean because of the tortuous paths followed by the gas bubbles from the gas inlet to the surface. Knowledge of gas residence time is important for design purposes and is necessary for an understanding of the behavior of gas-liquid dispersions (W5). Relatively little experimental effort has been devoted to this area. 

The internal structure of the catalyst particle is often of a complex labyrinth-like nature, with interconnected pores of a multiplicity of shapes and sizes, In some cases, the pore size may be less than the mean free path of the molecules, and both molecular and Knudsen diffusion may occur simultaneously. Furthermore, the average length of the diffusion path will be extended as a result of the tortuousity of the channels. In view of the difficulty of precisely defining the pore structure, the particle is assumed to be pseudo-homogeneous in composition, and the diffusion process is characterised by an effective diffusivity D, (equation 10.8). 

One must be very careful in reviewing the older, and some more recent, literature in consideration of the tortuosity and constriction factors some work has attempted to separate these two factors however, more modem developments show that they cannot be strictly decoupled. This aspect will be particularly important when reviewing the barrier and tortuous-path theories of electrophoresis, as discussed later. 

The tortuous-path and barrier theories consider the effects of the media on the electrophoretic mobility in a way similar to the effect of media on diffusion coefficients discussed in a previous section of this chapter. The tortuons-path theory seeks to determine the effect of increased path length on electrophoretic mobility. The barrier theory considers the effects of the barrier or media conductivity on the electrophoretic mobility. 

Interestingly, the permeability coefficients of mannitol in the two cell types are identical, most probably for different reasons, since the physical dimensions of the Caco-2 and MDCK monolayers (Table 8) are markedly different. Compared to the MDCK cell monolayer, the Caco-2 cell monolayer has a taller cell height, a shorter length in tight junctions, longer tortuous path lengths, and smaller slit width in lateral space. One recognizes that... 

Because they do not obey the octet rule, hypervalent molecules have often been thought to involve some type of bonding that is not found in period 2 molecules. Ideas concerning the nature of this bonding have developed along a somewhat tortuous path that it is interesting and instructive to follow. We will in the end conclude that the nature of the bonding in these molecules is not different in type from that in related period 2 molecules and that there is therefore little justification for the continued use of this concept. 

The geometry of the pore structure makes it impossible to determine accurately the effective length of the diffusion path. Interconnections within the pore structure, the tortuous character of individual pores, and variations in cross-sectional area along the pore length all contribute to the difficulty of the task. 

Because the fluid in a porous medium follows a tortuous path through channels of varying size and shape, one method of describing the flow... 

Note that Eq. (8.1) is remarkably independent of electron velocity. The stopping power -dE Idx = v-1(-dE /dt) does depend on velocity, but Frohlich and Platzman preferred not to use the stopping power due to a lack of knowledge of the actual tortuous path. Taking s = 80, ir = 5, d = 3.3A, and x = 10-11 s for water at 20°, they computed -dE /dt 1013 s-1, which is about three orders of magnitude less than that for excitation and ionization at higher energies. 

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