Estimation of Diffusion Coefficients

The coefficient of interdiffusion of two liquids must be considered as depending on all the physical properties of the mixture according to laws which must be ascertained only by experiment. 

Thus far we have introduced two different constitutive relations along with their respective diffusion coefficients, the Maxwell-Stefan and the Fick D. Here we show how these coefficients are related to each other and present a sample of values of these coefficients determined experimentally. 

For process engineering calculations it is almost inevitable that experimental values of D or f), even if available in the literature, will not cover the entire range of temperature, pressure, and concentration that is of interest in any particular application. It is, therefore, important that we be able to predict these coefficients from fundamental physical and chemical data, such as molecular weights, critical properties, and so on. Estimation of gaseous diffusion coefficients at low pressures is the subject of Section 4.1.1, the correlation and prediction of binary diffusion coefficients in liquid mixtures is covered in Sections 4.1.3-4.1.5. We do not intend to provide a comprehensive review of prediction methods since such are available elsewhere (Reid et al., 1987 Ertl et al., 1974 Danner and Daubert, 1983) rather, it is our purpose to present a selection of methods that may be useful in engineering calculations. 

While the thermodynamic treatments of diffusion in Sections 2.3 and 3.3 provide some useful information on the multicomponent diffusion coefficients, it does not solve our most important problem, how do we predict these coefficients Multicomponent diffusivity data is not an item that we have in abundance and there are no correlations of multicomponent diffusivity data that we might use. It is the Maxwell-Stefan Eqs. 2.1.24 for ideal gases or Eq. 

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Although there are a lot of data in the literature regarding diffusion coefficients in liquids or then calculation from molecular properties (Appendix I, Section 1.2), it is not the case for diffusion coefficients in solids, where the phenomena appearing are more complex. In solids, the molecule may be forced to follow a longer and tortuous path due to the blocking of the cross-sectional area, and thus the diffusion is somehow impaired. Several models have been developed to take into consideration this effect in the estimation of diffusion coefficients, leading, however, to a variety of results. 

The use of isotopic models in the literature—practical limits of usage As mentioned above, simplified solutions are employed in ion exchange for the estimation of diffusion coefficients. For example, the equations of Vermeulen and Patterson, derived from isotopic exchange systems, have been successfully used, even in processes that are not isotopic. Inglezakis and Grigoropoulou (2001) conducted an extended review of the literature on the use of isotopic models for ion-exchange systems. 

This permits the estimation of diffusion coefficients from measurements of conductivity. 

The second mode of diffusion allows estimation of diffusion coefficients for different substances by using the value of a diffusion coefficient for a single substance, taken as a standard (17). 

In contrast to the situation for gases, there are no satisfactory theoretical methods for predicting diffusivities in liquid systems. Different approaches are needed, depending on whether the solutions are electrolytic or nonelectrolytic. Most studies have been devoted to the estimation of diffusion coefficients in very dilute solutions. However, some papers report substantial variations with increasing concentrations of the diffusing solute. The theories and the experimental methods available for estimating diffusivities in liquids are well reviewed by Kamal and Caqjar (Kl), Nienow (N8), Bretsznajder (B24), Tyn (T12), Dullien et al. (E4, G6), and Simons and Ponter (S29). 

So far, several estimates of diffusion coefficients have been proposed, as given by the stochastic pump or three-resonance model and their extensions [12,17,18]. These studies, however, assume only the diffusion along the resonances, while our results, in contrast, exhibit the importance of resonance overlap to the global diffusion along resonances. 

Estimation of Diffusion Coefficients in Dilute Liquid Mixtures... 

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