Diffusion of mixtures

Studies of the diffusivities of mixtures of sorbates can be simply carried out and chemical reaction kinetics on porous materials can also be measured using a flow FR system [25]. A flow system is, again, more complex to operate and more expensive to construct than a batch system. 

Fig. 11 Self-diffusivities of mixture components in silicalite as a function of the 2-methyl-pentane fraction in the gas phase (left) and as a function of the 2-methylpentane loading (total hydrocarbon pressure 6.6 kPa, 433 K)...

Fig. 14 Self-diffusivities of mixture components in both MFI-type zeolites as a function of 2-methylpentane loading, 433 K...

Finally, just as thermophoresis has as a limit thermal diffusion- in dilute gas mixtures, so one would expect a thermophoretic effect on particles suspended in dense gases and liquids, whose limit would be thermal diffusion of mixtures in these media. The photophoretic effect may have been observed by BARKAS [2.145] in aqueous solutions of colloids. More recently, McNAB and MEISEN [2.146] have reported experimental evidence of thermophoresis in liquids for 1.011 and 0.79 ym spheres in water and n-hexane. They report that their data for the thermophoretic velocity are described by an empirical equation... 

Fuller s equation, applied for the estimation of the coefficient of diffusion of a binary gas mixture, at a pressure greater than 10 bar, predicts values that are too high. As a first approximation, the value of the coefficient of diffusion can be corrected by multiplying it by the compressibility of the gas /... 

When a mixture of gases replaces the pure gas, but there is no relative diffusion of the separate species, the total flux is given by equation (2.22), The flux of each species separately is then given by -X B p... 

The conclusion of all these thermodynamic studies is the existence of thiazole-solvent and thiazole-thiazole associations. The most probable mode of association is of the n-rr type from the lone pair of the nitrogen of one molecule to the various other atoms of the other. These associations are confirmed by the results of viscosimetnc studies on thiazole and binary mixtures of thiazole and CCU or QHij. In the case of CCU, there is association of two thiazole molecules with one solvent molecule, whereas cyclohexane seems to destroy some thiazole self-associations (aggregates) existing in the pure liquid (312-314). The same conclusions are drawn from the study of the self-diffusion of thiazole (labeled with C) in thiazole-cyclohexane solutions (114). 

Diffusivities of various elements ate determined experimentally. Dopant profiles can be determined. The junction depth can be measured by chemically staining an angle-lapped sample with an HE/HNO mixture. The -type region of the junction stains darker than the n-ty e region. The sheet resistivity can also be measured using a four-point probe measurement. These two techniques ate used for process monitoring. 

Selective Toluene Disproportionation. Toluene disproportionates over ZSM-5 to benzene and a mixture of xylenes. Unlike this reaction over amorphous sihca—alumina catalyst, ZSM-5 produces a xylene mixture with increased -isomer content compared with the thermodynamic equihbtium. Chemical modification of the zeohte causing the pore diameter to be reduced produces catalysts that achieve almost 100% selectivity to -xylene. This favorable result is explained by the greatly reduced diffusivity of 0- and / -xylene compared with that of the less bulky -isomer. For the same reason, large crystals (3 llm) of ZSM-5 produce a higher ratio of -xyleneitotal xylenes than smaller crystahites (28,57). 

For prediction of the gas diffusivity of binary air-hydrocarbon or nonhydrocarbon gas mixtures at low pressures, the method of Fuller et al. given by Eq. (2-152) is recommended. 

The diffusivity of solute 1 in the mixture is related to the binary infinite dilution diffiisivities for each of the other components calculated from Eq. (2-155) or the Umesi method. The viscosities are calculated by the methods in the previous section. Errors are not quantifiable, as little experimental data exist, although these errors would be related to those assumed for the binaiy pairs. 

TABLE 5-17 Relationships for Diffusivities of Multicomponent Gas Mixtures at Low Pressure... 

TABLE 5-18 Correlations for Diffusivities of Dilute/ Binary Mixtures of Nonelectrolytes in Liquids... 

Dilute Binary Mixtures of a Nonelectrolyte in Water The correlations that were suggested previously for general mixtures, unless specified otherwise, may also be applied to diffusion of miscellaneous solutes in water. The following correlations are restricted to the present case, however. 

Matthews-Akgerman The free-volume approach of Hildebrand was shown to be valid for binary, dilute liquid paraffin mixtures (as well as self-diffusion), consisting of solutes from Cg to Cig and solvents of Cg and C o- The term they referred to as the diffusion volume was simply correlated with the critical volume, as = 0.308 V. We can infer from Table 5-15 that this is approximately related to the volume at the melting point as = 0.945 V, . Their correlation was vahd for diffusion of linear alkanes at temperatures up to 300°C and pressures up to 3.45 MPa. Matthews et al. and Erkey and Akger-man completea similar studies of diffusion of alkanes, restricted to /1-hexadecane and /i-octane, respectively, as the solvents. 

One particular case of multicomponent diffusion that has been examined is the dilute diffusion of a solute in a homogeneous mixture (e.g., of A in B -h C). Umesi and Danner compared the three equations given below for 49 ternaiy systems. All three equations were equivalent, giving average absolute deviations of 25 percent. 

C. In their first series of experiments, six data sets were obtained for (H) and (u), employing six solvent mixtures, each exhibiting different diffusivities for the two solutes. This served two purposes as not only were there six different data sets with which the dispersion equations could be tested, but the coefficients in those equations supported by the data sets could be subsequently correlated with solute diffusivity. The solvents employed were approximately 5%v/v ethyl acetate in n-pentane, n-hexane, n-heptane, -octane, -nonane and n-decane. The solutes used were benzyl acetate and hexamethylbenzene. The diffusivity of each solute in each solvent mixture was determined in the manner of Katz et al. [3] and the values obtained are included... 

Diffusion theory involves the interdiffusion of macromolecules between the adhesive and the substrate across the interface. The original interface becomes an interphase composed of mixtures of the two polymer materials. The chemical composition of the interphase becomes complex due to the development of concentration gradients. Such a macromolecular interdiffusion process is only... 

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