Diffusion apparent

On the other hand, the more rigorous Maxwell-Stefan equations and the dusty gas model are seldom used in industrial reaction engineering applications. Nevertheless, the dusty gas model [64] represents a modern attempt to provide a more realistic description of the combined bulk and Knudsen diffusion mechanisms based on the multicomponent Maxwell-Stefan model formulation. Similar extensions of the Maxwell-Stefan model have also been suggested for the surface diffusion of adsorbed molecular pseudo-species, as well as the combined bulk, Knudsen and surface diffusion apparently with limited success [48] [49]. 

Fig. 6. In situ conversion reaction in brain slices on glass slides (Bessen et al., 1997). A distinct autoradiographic image is seen with scrapie-infected, but not uninfected control, brains. If the brain slices are solubilized after the conversion reaction and analyzed by SDS-PAGE/autoradiography, then PK-resistant S-PrP conversion products similar to those produced in cell-free conversion reactions (see Fig. 5) are observed. Higher magnification images (bottom panels) show that the pattern of in situ conversion product closely matches that of immunohistochemical staining for PrP-res in regions known to contain either amyloid plaques or diffuse apparently nonamyloid deposits.

If the phenomenon of internal convection flow is ignored, the effective diffusivity "apparent" effective diffusivity) increases along with external fluid flow, and even more so as the permeability coefficient grows larger. 

Fructose both enters and leaves absorptive epithelial cells by facilitated diffusion, apparently via transport proteins that are part of the GLUT family. The transporter on the luminal side has been identified as GLUT 5. Although this transporter can transport glucose, it has a much higher activity with fructose (see Fig. 27.12). Other fructose transport proteins also may be present. For reasons as yet unknown, fructose is absorbed at a much more rapid rate when it is ingested as sucrose than when it is ingested as a monosaccharide. 

The third solution is porosity diffusion. In this solution the fluid is unable to compress because the motions are too slow, therefore it releases the stresses imparted on it by the matrix through fluid motions observed as pressure and porosity diffusion. Apparently, the compressible-incompressible transition comes at about a frequency of strain excitation of 10 to 10° Hz for the common range of liquids and phase compressibilities. Above this transition frequency, the fluid will compress (strain) in response to excitation. 

Damkholer number (=k(T ) /k ) axial dispersion effective diffusivity apparent effective diffusivity particle diameter... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

In a solution of molecules of uniform molecular weight, all particles settle with the same value of v. If diffusion is ignored, a sharp boundary forms between the top portion of the cell, which has been swept free of solute, and the bottom, which still contains solute. Figure 9.13a shows schematically how the concentration profile varies with time under these conditions. It is apparent that the Schlieren optical system described in the last section is ideally suited for measuring the displacement of this boundary with time. Since the velocity of the boundary and that of the particles are the same, the sedimentation coefficient is readily measured. 

The time constant R /D, and hence the diffusivity, may thus be found dkecdy from the uptake curve. However, it is important to confirm by experiment that the basic assumptions of the model are fulfilled, since intmsions of thermal effects or extraparticle resistance to mass transfer may easily occur, leading to erroneously low apparent diffusivity values. 

As a result of these difficulties the reported diffusivity data show many apparent anomaUes and inconsistencies, particularly for 2eohtes and other microporous adsorbents. Discrepancies of several orders of magnitude in the diffusivity values reported for a given system under apparendy similar conditions are not uncommon (18). Since most of the intmsive effects lead to erroneously low values, the higher values are probably the more rehable. 

In principle, the catalytic converter is a fixed-bed reactor operating at 500—620°C to which is fed 200—3500 Hters per minute of auto engine exhaust containing relatively low concentrations of hydrocarbons, carbon monoxide, and nitrogen oxides that must be reduced significantly. Because the auto emission catalyst must operate in an environment with profound diffusion or mass-transfer limitations (51), it is apparent that only a small fraction of the catalyst s surface area can be used and that a system with the highest possible surface area is required. 

For adsorbent materials, experimental tortuosity factors generally fall in the range 2-6 and generally decrease as the particle porosity is increased. Higher apparent values may be obtained when the experimental measurements are affected by other resistances, while v ues much lower than 2 generally indicate that surface or solid diffusion occurs in parallel to pore diffusion. 

For mixtures of unlike ions (the usual case), the apparent diffusivity will be intermediate between these values because of the elec tric coupling effect. For a system with two counterions A and B, with charge z-a and z-b, Eqs. (16-73) and (16-74) reduce to ... 

Thus, a plot of the apparent diffusivity versus the linear adsorption equilibrium constant should be linear so long as Dp and D,i remain constant. 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

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