Arguments, tortuosity

Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls (see Eq. 5-236). The tortuosity T that expresses this hindrance has been estimated from geometric arguments. Unfortunately, measured values are often an order of magnitude greater than those estimates. Thus, the effective diffusivity D f (and hence t) is normally determined by comparing a diffusion model to experimental measurements. The normal range of tortuosities for sihca gel, alumina, and other porous solids is 2 < T < 6, but for activated carbon, 5 < T < 65. 

Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls (see Eq. 5-249). The tortuosity x that expresses this hindrance has been estimated from geometric arguments. Unfortunately,... 

Here,/is the water vapor flux, C is the saturated water vapor concentration, De is the water vapor diffusion coefficient in air, T is the temperature, and z is a position in the sample. In this study, it was assumed that the water vapor in the snow sample was saturated. Although there were some arguments about water vapor diffusion coefficient in snow and tortuosity dependence, we did not use those values because we have no data on how those values change during dry snow metamorphism. In reality, we think those values probably affect the water vapor flux. 

When considering an isotropic porous medium, Liu et al. (32) argued that the tortuous passage bears a two-dimensional property. With the argument that either direction should have the same void space ratio for an isotropic porous medium and the porosity is a product of the two directions, the tortuosity can be determined as... 

In practice, intercalation is relatively easy to achieve, while something close to true exfoliation is much more difficult. It is worth noting that enhancement of properties may be seen in both cases. While mechanical properties are most improved through exfoliation, improved thermal, fire, and barrier properties and decreased thermal expansion coefficients may be expected without complete exfoliation based solely on arguments of silicate layer properties and increased tortuosity with respect to the path of diffusing species. 

In any case, dispersion obtained via in-situ polymerization may improve the barrier and thermal properties based on a tortuosity argument alone but may or may not improve the mechanical performance, depending on the level of polymer/silicate interactions. Without thermodynamic compatibility, the silicate layers may even collapse to form multilayer stacks if the nanocomposite is heated. Finally, all of these techniques become somewhat complicated by any changes the silicate layers cause in terms of the polymer s molecular weight distribution as compared to silicate-free controls. 

The arrangement of the layers themselves also has an impact. The self-extinguishing properties of these materials, for instance, have been described qualitatively. A protective char layer forms and acts as a diffusion barrier to further combustion. Likewise, before the advents of nanocomposites, models of the barrier properties of glass-ribbon reinforced composites foreshadowed the increased tortuosity arguments often heard with regard to nanocomposite barrier properties. Improvements on these first approximations of bar-... 

Similar to the Nielsen model, the Bharadwaj model is based strictly on tortuosity arguments. The main difference is the consideration of the orientation and... 

The foregoing arguments regarding tortuosity call for the same substitutions, eqn (3.17) with T given by eqn (3.19), in the conventional inertial regime relation, eqn (3.13). This time, however, a further effect of bed expansion has to be taken into account. 

One of the principal assumptions of the Nielsen model is that the plates are oriented parallel to the polymer surface. In literature some results where the plates are randomly oriented along the film thickness are reported. In order to overcome this problem, Bharadwaj proposed an extension of the Nielsen model able to describe the effects of the sheet orientation on the relative permeability. The new study addressed both of these issues by modifying a simple model developed to describe permeability in filled polymers on the basis of tortuosity arguments. The tortuosity factor is modified to include the orientational order, and the relative permeability is given by Equation (11.5) ... 

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