(10i) Prediction of Multicomponent Diffusion Coefficients in Liquids

The physical phenomenon of diffusion is omnipresent in every natural as well industrial process involving mass transfer. In many cases, diffusion plays an important role as the rate limiting mechanism. Therefore, the determination of diffusion coefficients in liquids is of great interest for the calculation and simulation of mass transfer processes.

There are two well established theories describing diffusion. The older and more commonly used one is Fick's Law. This theory was developed in the 19th century in analogy to Fourier's description of heat transfer. Later, Maxwell and Stefan developed a physically more consistent alternative theory for diffusion. Contrary to Fick's Law, the multicomponent Maxwell-Stefan diffusion coefficients can be related to the binary case.

Therefore, Maxwell-Stefan diffusion coefficients are more suitable for prediction. Subsequently, Fick diffusion coefficients can be calculated from the predicted Maxwell-Stefan diffusion coefficients using the thermodynamic factor. This correction factor is computed from available excess energy models such as Wilson, Uniquac, or NRTL. The relevant parameters are determined by standard VLE-experiments.

Most studies about diffusion coefficients focus on measuring and predicting diffusion coefficients in binary mixtures. Research on this topic is advanced, also due to a fair database of experimentally determined binary diffusivities. However, real processes mostly deal with mixtures involving more than two components. In this case, both the experimental and theoretical investigations of diffusion are much more complex. Prediction of multicomponent diffusion coefficients is still in its very beginning due to the lack of ternary diffusion data. To overcome this limitation, multicomponent diffusion coefficients were measured by holographic interferometry within the whole concentration space of several non-ideal ternary systems. Experimental Fickian diffusivities are transformed into Maxwell-Stefan diffusivities. Existing prediction models as well as a newly developed one are tested against four ternary systems including more than 100 ternary data points.

The results prove the great importance of an accurate thermodynamic description of the system for transformation between Fickian and Maxwell-Stefan diffusion coefficients in both directions. However, there is a lack of proven rules for the selection of appropriate thermodynamic data sets needed for the calculation. The influence of different thermodynamic data sets on this calculation is shown, and criteria for the selection of appropriate parameters are given.