Diffusion coefficients, effects

Molecular bulk diffusion coefficient Effective diffusivity... 

D.C. Stone, J.F. Tyson, Flow cell and diffusion coefficient effects in flow injection analysis, Anal. Chim. Acta 179 (1986) 432. 

FWS surface per volume of water c Concentration of solute c Concentration at inlet Cp Concentration in matrix pore water D Apparent diffusion coefficient Effective diffusion coefficient Dl Dispersion coefficient Dp Diffusion coefficient in pore water D , Diffusion coefficient in free water i Hydraulic gradient K Volume based sorption coefficient Kg Hydraulic conductivity L Length of flowpath M Mass of solute injected in a stream... 

Reactant concentration on the outer catalyst surface Reference tracer concentration Diameter of the channel (tube), hydraulic diameter Molecular diffusion coefficient Effective diffusion coefficient Diameter of particle... 

Mampallil, D., Mathwig, K., Kang, S., and Lemay, S. G. 2013. Redox couples with unequal diffusion coefficients Effect on redox cycling. A a/. Chem. 85 6053-6058. 

Although the model provides a mechanism to measure the total activity of enzyme immobilized on an electrode, it also allows estimation of the combined mass transfer parameter (A/nad+) for the diffusing substrate (in this case, NAD" ). This value, however, is limited somewhat by the fact that the term is cumulative for several variables that may individually contribute to overall electrode mass transfer combined contributions of the molecular diffusion coefficient, effective surface area, diffusion length, pore structure, and mass transfer through the film. Unfortunately, this approach will remain limited unless additional modeling is incorporated that can specifically differentiate these parameters. If more parameters are to be added to the... 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

However, we would expect the binary pair diffusion coefficients to be replaced by effective diffusion coefficients in the mediuTn, so that... 

The solute species therefore diffuse independently, rather as in Knudsen diffusion, but with effective diffusion coefficients D, where... 

The limiting cases of greatest interest correspond to conditions in which the mean free path lengths are large and small, respectively, compared with the pore diameters. Recall from the discussion in Chapter 3 that the effective Knudsen diffusion coefficients are proportional to pore diameter and independent of pressure, while the effective bulk diffusion coefficients are independent of pore diameter and inversely proportional to pressure. 

It may seem curious that Knudsen diffusion coefficients still appear in equations (5.18) and (5.19), which supposedly give the flux relations at the limit of bulk diffusion control. However, inspection reveals that only ratios of these coefficients are effectively present, and from equation (2,11) it follows that... 

The second case follows from a suggestion of Bird [27] to Che effect that binary pair bulk diffusion coefficients might be approximated by expressions of the form... 

Note that the effective diffusion coefficient relating N and dc /dz in... 

These must supplement the minimal set of experiments needed to determine the available parameters in the model-It should be emphasized here, and will be re-emphasized later, Chat it is important Co direct experiments of type (i) to determining Che available parameters of some specific model of Che porous medium. Much confusion has arisen in the past frcjci results reported simply as "effective diffusion coefficients", which cannot be extrapolated with any certainty to predict... 

The size of the error which can be introduced by imprecise interpretation of the data in terms of an "effective diffusion coefficient" can easily be estimated. Denoting by flux of substance 1 in the... 

Here L is the thickness of the porous septum and jS the length of each dead-end micropore, the effective binary bulk diffusion coefficient... 

In contrast to the cell experiments of Gibilaro et al., it is now seen from equation (10.45) that measurement of the delay time gives no information about diffusion within the pellets this can be obtained only through equation (10.46) from measurements of the second moment. As in the case of the cell experiment, the results can also be Interpreted in terms of an "effective diffusion coefficient" associated with a Fick equation for the... 

Hence, from equation (10.48), the effective diffusion coefficient determined by "chromatographic" testing is given by... 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

Effective diffusion coefficient, in porous medium at bulk diffusion limit, 14... 

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