Maxwell-Stefan Diffusivities and Velocity Cross-Correlations in Dilute Ternary Systems

Abstract

The Maxwell-Stefan (MS) approach is commonly used for describing mass transport by diffusion in gases and liquids since it correctly accounts for the chemical potential gradient as driving force. It is well known that MS diffusivities are concentration dependent which should be taken into account in practical applications. Unfortunately, it is difficult to obtain MS diffusivities both from experiments and molecular simulations. Therefore, there is a considerable interest in predictive models describing the concentration dependence of MS diffusivities. MS diffusivities can be expressed as functions of (1) easily obtainable self- diffusivities, and (2) the integrals of velocity cross-correlations. By assuming that the latter terms are small, we recently derived the multicomponent Darken equation. The objectives of the present study are twofold: First, we present a validation of the multicomponent Darken equation in ternary systems. Second, we investigate the dependence of velocity crosscorrelations on concentration and system size. A linear relation between the velocity cross-correlations and 1/N is found (“N” being the total number of molecules in the system). Two types of systems are studied: (1) Weeks-Chandler-Andersen (WCA) fluids in which only repulsive interactions are considered; (2) the ternary system water-DMSO-methanol in which atoms are interacting using both Lennard-Jones and electrostatic potentials.