Vignes correlation

These data were shown in Figure 4.1 and used as the basis for Example 4.1.3. Carry out your own check of the accuracy of the Vignes correlation using the NRTL model for the activity coefficients and the parameters in Example 4.1.3. Repeat the calculations using the Van Laar model with parameters 12 = 1.5922 and 21 = 0.9836. 

Dullien, F. A. L., Statistical Test of Vignes Correlation of Liquid Phase Diffusion Coefficients, Ind. Eng. Chem. Fundam., 10, 41-49 (1971). 

The corrected diffusivities (Dqa, Dqb) can be obtained from singlecomponent measurements but the mutual diffusivity is not amenable to direct measurement. Krishna has suggested that it may be estimated from the Vignes correlation [52], which was originally suggested for diffusion in liquid systems ... 

Fig. 14 Separation of C2H6/CH4 mixtures by permeation through a silicalite membrane, a Flux b selectivity. Continuous lines show the predictions of the Maxwell-Stefan model (Eq. 44) based on single-component diffusivities (Dqa> F>ob) with Dab from the Vignes correlation (Eq. 46). Dotted lines show predictions from the simplified Habgood model in which mutual diffusion effects are ignored (Eq. 45). From van de Graaf et al. [53] with permission...

Vignes correlated the composition dependence of binaiy diffiision coefficients in terms of their inflnite-dilution values and this thermodynamic correction factor. 

A single experimental measurement of the average diflbsivity over the whole composition range gave a value of 7.4 X 10 " m /s. These solutions do form neatly ideal liquid mixtures so the diffiisivity of a 50/50 mixture could be estimated from Vignes correlation ... 

The model of the ideal dilute solution is applicable, if the concentration of the solute does not exceed 5-10%. To apply the model to the general case of arbitrary concentrations, the Vignes correlation [94] can be used... 

There is one experimental value available for Dj, which is almost met by accident. For the actual concentrations, the Vignes correlation [94] yields... 

Vigne.s empirically correlated mixture diffusivity data for 12 binary mixtures. Later Ertl et al. evaluated 122 binary systems, which showed an average absolute deviation of only 7 percent. None of the latter systems, however, was veiy nonideal. 

Bosse [48] proposed a new model to predict binary Maxwell-Stefan diffusion coefficients Dij, based on Eyrings absolute reaction rate theory [49]. A correlation from Vignes [50] which was shown to be valid only for ideal systems of similar-sized molecules without energy interactions [51] was extended with a Gibbs-excess energy term... 

In nonideal mixtures, the thermodynamic nonideality of the mixture has to be considered. We still need to predict the concentration dependence of the mutual diffusion coefficient Dt] of a binary pair of nonelectrolytes. The concentration dependency of l)u in liquid mixtures may be calculated by using the Vignes equation or the Leffler and Cullinan equation. Besides these, we may also use a correlation suggested by Dullien and Asfour (1985), given by... 

The thermodynamic equilibrium is based on the UNIQUAC model [100], The liquid-phase binary diffusivities are determined using the method of Tyn and Calus (see [94]) for the diluted mixtures corrected by the Vignes equation [42] to account for finite concentrations. The vapor-phase diffusion coefficients are assumed constant. The reaction kinetics parameters are taken from [101]. The vapor and liquid binary mass-transfer correlations were calculated for the inert packing and the catalytic rings with the correlation of Onda et al. [102]. 

In metal alloys fomung solid solutions over significant composition ranges, the binary diffiisivity varies wiffi composition. Figure 2.3-6 shows some typical data lor difliision in the Fe-Ni stem at 1185 C. Vignes arid Birchenall have presented a correlation for the concentmtion dependence in binary aih s similar to Eq. (2.3-18) for liquids but they requited an additional factor involvirig the melting temperature of ttie alloy to obtain a satisfoctoiy correlation. 

A molecular dynamics approach can also be used to predict mixed gas diffusivities in microporous materials, at the expense of computation cost (e.g., Qureshi and Wei, 1990 Chitra and Yashonath, 1995 Trout et al., 1997 Snurr and Karger, 1997). The empirical correlation of Vignes (1966) for binary diffusivities in liquid solutions and also metallic alloys has been used extensively for calculating binary diffusivities, using the Maxwell-Stefan formalism for flux equations (e.g., Krishna, 1990). 

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