Diffusivities pure, single diffusion process

Systems Involving a Pure, Single Diffusion Process. 252... 

The diffusivities can be readily derived from the FR data if only a pure, single diffusion process occurs in a microporous material system where the in-phase and the out-of-phase characteristic curves merge asymptotically at high frequencies as shown in Fig. 3b. 

For p-xylene, the sorbed molecules diffuse down the direction of both the straight and sinusoidal channels in silicahte-1 at loadings < 4 m./u.c. and low temperatures. At high temperatures, however, only a pure, single diffusion process can be detected. Surprisingly, the sorbed p-xylene molecules diffuse faster down the straight channel direction than benzene, a smaller molecule than p-xylene. The diffusivities of the four aromatics illustrated in Fig. 15 show a decrease in the order of p-xylene > toluene > benzene > ethylbenzene. 

In transient diffusion, the concentration of a species varies, as we have seen, with both time and distance. The underlying process of diffusion may take place in isolahon or it may be accompanied by a chemical reaction, by flow, or by both reaction and flow. These more complex cases are not taken up here, and we limit ourselves instead to the consideration of purely diffusive processes. Furthermore, with one or two exceptions, the treatment is confined to a single spatial coordinate represented by the Cartesian x- (or z-) axis or by the radial variable r. The last is used in formulating diffusion in a sphere, or in the radial direction of a cylinder. Pick s equation for these three cases can be deduced from the general conservation equation (Equation 2.24a) and Table 2.3. They are as follows ... 

The proper definition of these two correlators is the fundamental issue. Very often the slow correlator is addressed to the orientational self-correlation of the single rigid molecule, see (2.33), which according to the Debye-Stokes-Einstein model (DSE) can be described as a pure Brownian diffusive process [19,42]. Hence the slow correlator becomes... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

For any pure chemical species, there exists a critical temperature (Tc) and pressure (Pc) immediately below which an equilibrium exists between the liquid and vapor phases (1). Above these critical points a two-phase system coalesces into a single phase referred to as a supercritical fluid. Supercritical fluids have received a great deal of attention in a number of important scientific fields. Interest is primarily a result of the ease with which the chemical potential of a supercritical fluid can be varied simply by adjustment of the system pressure. That is, one can cover an enormous range of, for example, diffusivities, viscosities, and dielectric constants while maintaining simultaneously the inherent chemical structure of the solvent (1-6). As a consequence of their unique solvating character, supercritical fluids have been used extensively for extractions, chromatographic separations, chemical reaction processes, and enhanced oil recovery (2-6). 

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