Maxwell–Stefan diffusion coefficient estimation for ternary systems: an ideal ternary alcohol system

The Maxwell–Stefan model is a popular diffusion model originally developed to model diffusion of gases, which can be considered thermodynamically ideal mixtures, although its application has been extended to model diffusion in non-ideal liquid mixtures as well. A drawback of the model is that it requires the Maxwell–Stefan diffusion coefficients, which are not based on measurable quantities but they have to be estimated. As a result, numerous estimation methods, such as the Darken model, have been proposed to estimate these diffusion coefficients. However, the Darken model was derived, and is only well defined, for binary systems. This model has been extended to ternary systems according to two proposed forms, one by R. Krishna and J. M. van Baten, Ind. Eng. Chem. Res., 2005, 44, 6939–6947 and the other by X. Liu, T. J. H. Vlugt and A. Bardow, Ind. Eng. Chem. Res., 2011, 50, 10350–10358. In this paper, the two forms have been analysed against the ideal ternary system of methanol/butan-1-ol/propan-1-ol and using experimental values of self-diffusion coefficients. In particular, using pulsed gradient stimulated echo nuclear magnetic resonance (PGSTE-NMR) we have measured the self-diffusion coefficients in various methanol/butan-1-ol/propan-1-ol mixtures. The experimental values of self-diffusion coefficients were then used as the input data required for the Darken model. The predictions of the two proposed multicomponent forms of this model were then compared to experimental values of mutual diffusion coefficients for the ideal alcohol ternary system. This experimental-based approach showed that the Liu's model gives better predictions compared to that of Krishna and van Baten, although it was only accurate to within 26%. Nonetheless, the multicomponent Darken model in conjunction with self-diffusion measurements from PGSTE-NMR represents an attractive method for a rapid estimation of mutual diffusion in multicomponent systems, especially when compared to exhaustive MD simulations.