Abstract
Diffusion plays a central part in many unit operations. The Maxwell-Stefan model is the dominant model for both gaseous and liquid diffusion. However, it was developed from the kinetic theory of gases, raising the question of whether it can be extended to non-ideal liquid systems. The dynamic fluctuation model is an alternative model based on the Cussler theory and predicts a smaller thermodynamic influence relative to the linear influence of the Maxwell-Stefan model due to dynamic concentration fluctuations. Since the dynamic fluctuation model, which uses the scaling factor α, had improved performance relative to the Maxwell-Stefan model for a wide range of binary systems, it is postulated that this improved performance should also be observed for a ternary system. In this work, the dynamic molecular fluctuation model was extended to a highly non-ideal ternary system, using the same scaling factor α, through matrix manipulation. Using self-diffusion data measured by NMR, mutual diffusion predictions of the developed model and the Maxwell-Stefan model were compared to experimental mutual diffusion data of the partially miscible system ethanol/toluene/n-decane. It is demonstrated that the dynamic fluctuation model gives improved predictions relative to the Maxwell-Stefan approach, consistent with previous observations on binary systems, showing that the reduced thermodynamic influence of the dynamic fluctuation model is an improvement. In addition, we show that the use of local mole fractions, to account for molecular association, in both the dynamic fluctuation and Maxwell-Stefan models, results in improved diffusion predictions for the ternary system. The results confirm that the dynamic fluctuation model improves predictions of mutual diffusion in liquid mixtures, suggesting a non-linear correction to the thermodynamic correction factor. The results also suggest that that the key assumptions in the Maxwell-Stefan model and its derivation, rooted in the kinetic theory of gases, are not entirely accurate for highly non-ideal liquid systems. The optimum α for the ternary system studied here is approximately 0.45, similarly to the optimum α of 0.40 to 0.80 for a range of binary systems previously studied, suggesting that the use of the α scaling factor, which is grounded in scaling laws theory, is of general validity.
Highlights
Diffusion is an important natural phenomenon in chemical processes
In previous work using pulsed gradient stimulated echo nuclear magnetic resonance (PGSTE-NMR) of the nearly ideal ternary system of methanol/butan-1-ol/propan-1-ol,[18] we have shown that the multicomponent Darken model of Liu et al.[8] is more accurate than that of Krishna and van Baten.[7]
The dynamic fluctuation model, which uses the scaling factor a to reduce the non-ideal thermodynamic impact based on scaling theory, was extended to ternary systems
Summary
Diffusion is an important natural phenomenon in chemical processes. most industrial separations are influenced by liquid component diffusion, and in certain cases, diffusion may be the rate limiting process. The Maxwell–Stefan (MS) model is the dominant diffusion model for gaseous systems and it is applied to liquid systems due to its simple, linear dependence on the chemical potential gradient This model was developed using the kinetic theory of gases[5,6] and it has been extended unaltered to highly non-ideal liquid systems without rigorous experimental validation. Due to both a lack of experimental data, and the MS diffusion coefficients being impossible to measure directly, exhaustive molecular dynamic simulations have been pursued by some researchers.[7,8] These exhaustive calculations are impractical for general engineering purposes
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