Stefan-Maxwell diffusivities in concentrated multi-species transport, and the Onsager's regression hypothesis.

Stefan-Maxwell diffusivities play an important role in continuum models of multi-species transport because they describe drag between different species, as well as the entropy production rate. We investigate a lesser-known computational method for determining Stefan-Maxwell diffusivities that is better suited to the concentrated-solution regime. The method is based on Onsager's regression hypothesis, which in Casimir's interpretation states that autocorrelation functions of fluctuating quantities satisfy, in the linearized approximation, corresponding continuum model equations. We test this conjecture by comparing analytic computations of Stefan-Maxwell diffusivities for mixtures of Lennard-Jones gases, based on high-order expansions of the Enskog type, with molecular dynamics simulations that extract the same diffusivities from autocorrelation functions of Fourier-transformed species densities. We also compare the results with molecular dynamics diffusivity measurements by the familiar Green-Kubo approach. Analytic and molecular dynamics simulations of diffusivities match reasonably well, despite the fact that not all the assumptions of the regression-based continuum theory can be reproduced–or easily reproduced–in molecular dynamics simulations. We extend our study by testing the diffusivity measurement technique on complex liquids, implementing molecular dynamics simulation of Stefan-Maxwell diffusivities of liquid electrolytic solutions, which play an important role in battery modeling, and where robust computational methods covering a broad variety of salts and solvents compositions is much desired. For the electrolytes, analytic predictions are no longer available, but for the LiPF6 salts and a variety of solvents they have been measured experimentally in our group.