Diffusional time constant

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

Diffusional time constants and diffusivities for C02 4A calculated from uptake curves for crystals of different size. 34pra, o 21.5pm, A 7.3pm . Values calculated for 7.3pm crystals from non-isothermal model . (Reproduced with permission from Ref. 9. Copyright 1980, J. Colloid Sci.)... 

In the chromatographic method a pulse or step change in sor-bate concentration is introduced into the carrier stream at the inlet of a packed adsorption column and the diffusional time constant is determined from the dispersion of the response signal at the column outlet. Since heat transfer in a packed bed is much faster than in a closed system the chromatographic method may, in principle, be used to follow somewhat faster sorption processes. 

In the adsorption rates of all the components on the CMS, the difiusional time constants showed strong dependence of pressure. Reid and Thomas (1999) suggest that the reason for these increases in the adsorption rate with surface coverage is probably related to the sur ce diffiision. These exponential increases of the effective diffusional time constant might be explained by above Darken-based models. 

As shown in Figures 3 and 4, the large deviations between experimental and predicted results by Darken-based models (Eqs. (6) (9)) were observed in Ae experimental range of pressure. At each case, the experimental diffusional time constant showed much stronger pressure dependence than the results predicted by the Daiken-based models. 

Fig. 21 Variation of diffusional time constant (Dq/R ), dimensionless Henry constant (iC), and the product KDq with temperature. (From data of Chen et al. [127].) The value of Dq/R calculated from reaction rate measurements at 698 K is also shown. Corrected dif-fusivities are calculated from the reported integral diffusivities according to the analysis of Garg and Ruthven [126]. From Ruthven [98]...

Fig. 9 Effect of sample quantity and nature of purge gas on ZLC response curves for benzene in 50- jim crystals of NaX zeolite at 250 °C. a Desorption curves. Note that when the sample is sufficiently small, desorption is rapid and the curves for He and N2 purge coincide, but for a larger sample we see slower desorption with a significant difference between the curves for He and N2, indicating the intrusion of external diffusional resistance. b Apparent diffusional time constants showing the variation with sample mass. Filled symbols denote He purge, open symbols denote N2 purge. Note that when the sample mass is sufficiently small, the time constants for He and N2 become coincident and independent of sample mass, showing the absence of external diffusional resistance. From Brandani et al. [55]...

Even if the intrusion of heat transfer or bed diffusional resistance cannot be entirely eliminated, it may still be possible to derive values for the diffusional time constant by using the appropriate solution of the diffusion equation. Some relevant solutions to the coupled heat and mass transfer equations for such systems are given in Section 6.3. 

As an alternative to conventional sorption rate measurements it is also possible to derive diffusional time constants from the dynamic response of a packed column to a change in sorbate concentration. In a chromatographic system the broadening of the response peak results from the combined effects of axial dispersion and mass transfer resistance. By making measurements over a range of gas velocities it is possible to separate the dispersion and mass transfer effects and so to determine the effective overall mass transfer coefficient or the diffusional time constant. Further details are given in Section 8.5. 

FIGURE 5.9. Variation of diffusional time constant with sorbate pressure for (a) /7-butane in 55- m (X) and 27.5-/im (O) crystals of 5A zeolite (i) CO2 in 34- im (o), 2I.5-/im (A), and 7,3- m ( ) crystals of 4A zeolite. Values for CO2 in the 73-fim crystals derived from the nonisothermal model are shown by filled squares (see Figure 6.13). For the other systems diffusion is slow enough for heat effects to be neglected. (From refs. 2 and 49, with permission.)... 

FIGURE 5 1. Concenlralion dependence of diffusional time constant for Nj in molecular sieve carbon. (From ref. 82. with permission.)... 

In the long time region a plot of ln(l - mjm versus t should be linear with slope -v D fr] and intercept ln(6/ir ), as illustrated in Figure 6.2. Such a plot provides, in principle, a simple meUiod of both checking the conformity of an experimental uptake curve with the diffusion equation and determining the diffusional time constant. 

The variation of the heat transfer time coristant ha/C,) and the bed diffusional time constant D/l with pressure is shown, for several different... 

The ease with which the individual mass transfer parameters and the axial dispersion coefficient can be determined depends on the relative magnitude of the various resistances. If mass transfer is rapid the dispersion of the chro matogram will be caused mainly by axial dispersion, jand under these conditions it is not possible to derive any information coiicerning the diffusional time constants. In the low Reynolds number regime Sh = D , w2.0 so... 

The general model described in the theory section reduces to the surface barrier control limit if the diffusional time constant is small compared to that of the surface barrier, i.e. 5 1. In order to have a qualitative understanding of the effect of a partial loading experiment we will consider Lo = 20 and vary Tpl and A and fix 5 = 0.1. 

The dispersion model with particle diffusion always assumes complete external contacting of particles by liquid which may not be the case in trickle flow. This means that the effective diffusional time constant is increased in trickle flow resulting in a reduced apparent effective diffusivity which is based on the total external surface area. Using this diffusivity in the expression for the Thiele modulus, and equating it to the modulus defined for trickle-bed operation by Dudukovic (130) results in the following estimate of the external catalyst contacting efficiency, UcE ... 

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