Nonuniform porosity

The porosity is important for high permeability and also for providing a reservoir of electrolyte in the cell. Higher and more uniform porosity is desirable for unhindered ionic current flow. Nonuniform porosity leads to nonuniform current density, and can lead further to reduced activity of the electrodes. Cell failure can result because during discharge in some areas of the electrodes works harder than others. 

Two-phase pressure drop in micropacked beds is very large, particularly, for particles with small diameter, and is significantly influenced by capillary forces, especially at higher reactor-to-partide diameter ratios [94]. The two-phase flow in micro packed bed reactors with radially nonuniform porosity distribution was simulated by solving a two-dimensional hydrodynamic model based on the volume-averaged mass and momentum conservation equations. 

A convential laboratory hydraulic press and suitable punches and dies can be readily used to produce disks, short cylinders, or other shapes of uniform cross section. However, cylinders that have heights approaching or exceeding their diameters will exhibit nonuniform porosity if produced in this way because the compaction pressure is not uniform under these cases. 

Heterogeneity, nonuniformity and anisotropy are terms which are defined in the volume-average sense. They may be defined at the level of Darcy s law in terms of permeability. Permeability, however, is more sensitive to conductance, mixing and capillary pressure than to porosity. 

To determine the average porosity of a homogeneous but nonuniform medium, the correct mean of the distribution of porosity must be evaluated. The porosities of natural and artificial media usually are normally distributed. The average porosity of a heterogeneous nonuniform medium is the volume-weighted average of the number average ... 

The influence of the crystallite size of catalysts upon such reactions as hydrogenation or dehydrogenation over platinum or nickel has been investigated by Rubinshtein and others (376). Roginskil s school has applied mathematical statistics to systems formed by primary monocrystals of a catalyst the cracks and pores of varying dimensions created by these crystals predetermine the nature of the resulting porosity. The application of the statistical method to the theory of adsorption and catalysis was recently described by V. I. Levin (200) and an equation for adsorption on nonuniform surfaces derived by Ya. Zel dovich and S. Z. 

The benefits of nonuniform activity distributions (site density) or diffusive properties (porosity, tortuosity) within pellets on the rate of catalytic reactions were first suggested theoretically by Kasaoka and Sakata (Ml). This proposal followed the pioneering experimental work of Maatman and Prater (142). Models of nonuniform catalyst pellets were later extended to more general pellet geometries and activity profiles (143), and applied to specific catalytic reactions, such as SO2 and naphthalene oxidation (144-146). Previous experimental and theoretical studies were recently discussed in an excellent review by Lee and Aris (147). Proposed applications in Fischer-Tropsch synthesis catalysis have also been recently reported (50-55,148), but the general concepts have been widely discussed and broadly applied in automotive exhaust and selective hydrogenation catalysis (142,147,149). 

It must be emphasized that the mathematical simplicity of equations (13.1) and (13.2) is the consequence of a specific time-constant distribution. As shown in this chapter, time-constant distributions can result from nonuniform mass transfer, geometry-induced nonuniform current and potential distributions, electrode porosity, and distributed properties of oxides. At first glance, the associated impedance responses may appear to have a CPE behavior, but the frequency dependence of the phase angle shows that the time-constant distribution differs from that presented in equation (13.7). 

FIGURE 3-17 Dispersion of a pulse of a tracer substance in a sand column experiment. Note the parallel between this and the corresponding dispersion of a tracer in a flowing river (Fig. 2-4). The same equation, with a correction factor for porosity in the case of the sand column, describes both situations. However, the physical processes responsible for the Fickian transport differ mechanical dispersion dominates in the sand column, while turbulent diffusion and the dispersion associated with a nonuniform velocity profile dominate in the river. 

The washing of filter cake is carried out to remove liquid impurities from the valuable solid filter cake or to increase the recovery of valuable filtrate. Wakeman (1990) has shown that the axial dispersion flow model, as developed in Sec. 4.3.6, provides a fundamental description of cake washing and can take into account the influence of many phenomena. These include nonuniformities in the liquid flow pattern, non-uniform porosity distributions, the initial spread of washing liquid onto the topmost surface of the filter cake and the desorption of solute from the solid surfaces. 

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