Diffusion discrepancies

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. 

T he total or global solar radiation has a direct part (beam radiation) and a diffuse part (Fig. 11.31). In the simulation, solar radiation input values must be converted to radiation values for each surface of the building. For nonhorizontal surfaces, the diffuse radiation is composed of (a) the contribution from the diffuse sky and (b) reflections from the ground. The diffuse sky radiation is not uniform. It is composed of three parts, referred to as isotropic, circumsolar, and horizontal brightening. Several diffuse sky models are available. Depending on the model used, discrepancies for the boundary conditions may occur with the same basic set of solar radiation data, thus leading to differences in the simulation results. 

The scaling dependence of the diffusion coefficient on N and Cobs Iso poses a number of questions. While the original scaling predictions, based on reptation dynamics [26,38], oc N, have been verified by some measurements [91,98], significant discrepancies have been reported too [95,96]. Attempts to interpret existing data in terms of alternative models, e.g., by the so-called hydrodynamic scaling model [96], fail to describe observations [100,101]. 

The values for the lipid molecules compare well (althoughJgiey are still somewhat larger) with the experimental value of 1.5x10 cm /s as measured with the use of a nitroxide spin label. We note that the discrepancy of one order of magnitude, as found in the previous simulation with simplified head groups, is no longer observed. Hence we may safely conclude that the diffusion coefficient of the lipid molecules is determined by hydrodynamic interactions of the head groups with the aqueous layer rather than by the interactions within the lipid layer. The diffusion coefficient of water is about three times smaller than the value of the pure model water thus the water in the bilayer diffuses about three times slower than in the bulk. 

Nienhuis [189] has used a fitting procedure for the seven most sensitive elementary parameters (reactions SiH4 -t- SiH2 and Si2H6 -I- SiHi, dissociation branching ratio of SiH4, surface reaction coefficient and sticking probability of SiHa, and diffusion coefficients of SiH and H). In order to reduce the discrep-... 

Table VII should be 1.939 for the ratio k = 0.5. Part of the 17% discrepancy between the results of Lin et al. (L9) and Eq. (27) may be ascribed to the use of incorrect diffusivities. An estimate of the errors is possible for part of their experiments. The value of the product nD/T of K3Fe(CN)6 based on the electric mobility at infinite dilution as used by Lin et al. is 11% too high, according to more recent measurements of the effective ionic diffusivity of Fe(CN)(% by Gordon et al. (G5). Similarly, the mobility product of K4Fe(CN)6 is 16% too high, and that of 02 no less than 26% too high, compared with data of Davis et al. (D7) (see Table III). According to Eq. (27) the value of D would have to be 27% too high to account fully for a coefficient that is 17% too high consequently, the discrepancy cannot be attributed entirely to incorrect diffusivities.

The measured value of k Sg is 0.716 cm3/(sec-g catalyst) and the ratio of this value to k ltTueSg should be equal to our assumed value for the effectiveness factor, if our assumption was correct. The actual ratio is 0.175, which is at variance with the assumed value. Hence we pick a new value of rj and repeat the procedure until agreement is obtained. This iterative approach produces an effectiveness factor of 0.238, which corresponds to a differs from the experimental value (0.17) and that calculated by the cylindrical pore model (0.61). In the above calculations, an experimental value of eff was not available and this circumstance is largely responsible for the discrepancy. If the combined diffusivity determined in Illustration 12.1 is converted to an effective diffusivity using equation 12.2.9, the value used above corresponds to a tortuosity factor of 2.6. If we had employed Q)c from Illustration 12.1 and a tortuosity factor of unity to calculate eff, we would have determined that rj = 0.65, which is consistent with the value obtained from the straight cylindrical pore model in Illustration 12.2. 

Indeed, it is worth noting that by itself, a permeation rate proportional to p°50 could be consistent with any value whatever for the ratio of monatomic to diatomic species in the solid, if the diatomic species is very immobile. For in such case, the permeation flux would be carried entirely by the monatomic species, whose concentration always goes as p0 50. However, a sizable diatomic fraction would significantly modify the transient behavior of the permeation after a change in gas pressure. Although neither Van Wieringen and Warmholtz nor Frank and Thomas published details of the fit of their observed transients to the predictions of diffusion theory, it is unlikely that any large discrepancies would have escaped their attention. 

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