Predictive Darken Equation for Maxwell-Stefan Diffusivities in Multicomponent Mixtures

Abstract

This Article presents the derivation and validation of a rigorous model for the prediction of multicomponent Maxwell-Stefan (MS) diffusion coefficients. The MS theory provides a sound framework for modeling mass transport in gases and liquids. Unfortunately, MS diffusivities are concentration dependent, and this needs to be taken into account in practical applications. There is therefore a considerable interest in models describing the concentration dependence of MS diffusivities. While current practice employs empirical models for this purpose, recent work on molecular simulations favor the physically based Darken equation. The Darken equation, however, is limited to binary mixtures and is not predictive. In this study, a multicomponent Darken model for MS diffusivities is derived from linear response theory and the Onsager relations. In addition, a predictive model for the required self-diffusivities in the mixture is proposed, leading to the predictive Darken-LBV model. We compare our novel model to the existing generalized Vignes equation and the generalized Darken equation using molecular dynamics (MD) simulation. Two systems are considered: (1) ternary and quaternary systems in which particles are interacting using the Weeks-Chandler-Andersen (WCA) potential; (2) the ternary system n-hexane-cyclohexane-toluene. Our results show that, in all studied systems, the novel predictive Darken-LBV equation describes the concentration dependence better than the existing models. The physically based Darken-LBV model provides a sound and robust framework for prediction of MS diffusion coefficients in multicomponent mixtures.