Data for diffusion

Table 6.2 Data for diffusion coefficients in pure metals...

The diffusion coefficient as defined by Fick s law, Eqn. (3.4-3), is a molecular parameter and is usually reported as an infinite-dilution, binary-diffusion coefficient. In mass-transfer work, it appears in the Schmidt- and in the Sherwood numbers. These two quantities, Sc and Sh, are strongly affected by pressure and whether the conditions are near the critical state of the solvent or not. As we saw before, the Schmidt and Prandtl numbers theoretically take large values as the critical point of the solvent is approached. Mass-transfer in high-pressure operations is done by extraction or leaching with a dense gas, neat or modified with an entrainer. In dense-gas extraction, the fluid of choice is carbon dioxide, hence many diffusional data relate to carbon dioxide at conditions above its critical point (73.8 bar, 31°C) In general, the order of magnitude of the diffusivity depends on the type of solvent in which diffusion occurs. Middleman [18] reports some of the following data for diffusion. 

The quantity ( D) is the average effective diffusivity, which describes the overall diffusion in the system. The diffusion in the system therefore behaves macroscopically as if bulk diffusion were occurring in a homogeneous material possessing a uniform diffusivity given by Eq. 9.4. The situation is illustrated schematically in Fig. 9.4a, and experimental data for diffusion of this type are shown in Fig. 9.5. This diffusion regime is called the multiple-boundary diffusion regime since the diffusion field... 

Diffusion-Controlled Reactions. The specific rates of many of the reactions of elq exceed 10 Af-1 sec.-1, and it has been shown that many of these rates are diffusion controlled (92, 113). The parameters used in these calculations, which were carried out according to Debye s theory (41), were a diffusion coefficient of 10-4 sec.-1 (78, 113) and an effective radius of 2.5-3.0 A. (77). The energies of activation observed in e aq reactions are also of the order encountered in diffusion-controlled processes (121). A very recent experimental determination of the diffusion coefficient of e aq by electrical conductivity yielded the value 4.7 0.7 X 10 -5 cm.2 sec.-1 (65). This new value would imply a larger effective cross-section for e aq and would increase the number of diffusion-controlled reactions. A quantitative examination of the rate data for diffusion-controlled processes (47) compared with that of eaq reactions reveals however that most of the latter reactions with specific rates of < 1010 Af-1 sec.-1 are not diffusion controlled. 

Japan published in March 2003 its first PRTR report for 2001 data on 354 chemicals based on a legislative framework. The report includes release and transfer data submitted by industry for 35 000 facilities and estimated release data for diffuse sources. Information is available in English, also for 2002. 

With this in mind, it seems to be a reasonable compromise to consider a FEM implementation of the modelling of stress-assisted diffusion over the previously (or simultaneously) performed stress analysis taking the nodal values of stresses, obtained with a post-processing technique, as the entry data for diffusion, i.e., constructing a finite-element approximation of the stress field with the aid of the same finite-element shape functions used in the mechanical analysis to approximate the displacement fields. 

The theoretical expression (3.25) is in good agreement with data for diffusion in aqueous solutions over the high Pe range of interest in aerosol deposition. Recalling that Pe = Sc-Re, (3.25) can be rearranged to give... 

Based on experimental data for diffusion controlled electrochemical reactions in aqueous solution, the following expression was proposed by Lin et al. (1953) for the eddy diffusion coefficient in the viscous sublayer... 

There is no systematic correlation between the preexponential factor Dqi and more direct measures of the size of a penetrant, such as its molar volume at OK. [5] In the absence of such a correlation, and of suitable experimental data for diffusion in PVDC, Dqi was treated as a single adjustable parameter. Equations (1) and (6) were used to fit ln[D(V D,d)] to ln[D(P D,d)], at 298.15K, for the idealized completely amorphous PVDC system. The results of this fit are shown in Figure 6. Unlike D(P D,d), D(V D,d) has the expected slightly convex shape, allowing it to fall off increasingly rapidly with increasing d. 

Need t and k. There being no data for diffusivity (Schmidt number) D and hence Pe, cannot be obtained using tubular flow correlations. 

Fig. 11 Arrhenius-plot relating the parabolic rate constant for the growth ofAl203 scales and data for diffusion in AI2O3, (the scale for the grain boundary diffusion data at the right has been adjusted, so that if 5 = 1 nm, the grain boundary diffusion coefficient corresponds to the bulk diffusion scale) [51].

Notice that the crystals in these two examples both have the fluorite structure, but the diffusion mechanism that operates is very different because the point defects involved are different. Experimental data for diffusion in several oxides are plotted in Figure 11.12. 

For systems in which the diffusivity ratio is smaller a more gradual variation in diffusivity and diffusional activation energy with ion exchange is predicted. The theoretical curve calculated from this model provides a good representation of the experimental data for diffusion of butane in Na-Ca zeolite A, as may be seen from Figure 5.13b. 

Permeability equations for diffusion in solids. In many cases the experimental data for diffusion of gases in solids are not given as diffusivities and solubilities but. as permeabilities, Pm, in m of solute gas A at STP (0°C and 1 atm press) diffusing per second per m cross-sectional area through a solid 1 m thick under a pressure difference of 1 atm pressure. This can be related to Pick s equation (6.5-2) as follows. 

Experimental diffusivities, solubilities, and permeabilities. Accurate prediction of diffusivities in solids is generally not possible because of the lack of knowledge of the theory of the solid state. Hence, experimental values are needed. Some experimental data for diffusivities, solubilities, and permeabilities are given in Table 6.5-1 for gases diffusing in solids and solids diffusing in solids. 

Data for diffusion in a fluid in streamline flow inside a pipe filled circles, vaporization data of Gilliland and Sherwood open circles, dissolving-solids data of Linton and Sherwood. From W. H. Linton and T. K. Sherwood, Chem. Eng. Progr., 46, 258 (1950). With permission. ]... 

A method was presented for the determination of the diffiisivities of donors in p-type semiconductors at relatively low temperatures. The method was based upon capacitance transient measurements. The law which described the capacitance transient was determined, and this then permitted the determination of the diffusion coefficient. It was found that the data for diffusion in CdTe could be described by ... 

We have collected in Table 2 some data for diffusion coefficient (D) obtained in the literature for some couples of stimulant/PP determined by different experimental techniques. The diffusivity ranges from lO to lO depending on the temperature and the couple stimulant/PP. 

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