The use of the Stefan-Maxwell Equations in Modelling Ion Transport in Concentrated Electrolytes

This work has two primary objectives: (i) to give a clear mathematical explanation of how the Stefan-Maxwell equations can be used to derive a one-dimensional drift-diffusion model for ion transport in concentrated multi-species electrolytes; and (ii) to systematically derive a multi-dimensional mixed drift-diffusion-flow model of ion transport, in a concentrated electrolyte, from a generalisation of the Stefan-Maxwell equations. We begin by analysing a Stefan-Maxwell type model for a generic concentrated electrolyte in one-dimension (applicable, e.g., to molten salts or ionic liquids). It is shown that the Stefan-Maxwell equations admit a solution only under the condition of electroneutrality and require an additional constitutive relation for uniqueness. Following previous works, we employ an excluded volume constraint for this purpose. In higher dimensions (2D and 3D), the inclusion of a fluid momentum equation becomes necessary. A physically motivated drift-diffusion-flow model is first proposed on an ad-hoc basis and then derived systematically from generalised Stefan-Maxwell equations, which incorporate both inertia and viscous stresses. The analysis is specialised to moderately concentrated electrolytes, where salt concentrations remain small relative to that of the solvent, but ion-ion interactions are still significant, before specialising further to the dilute limit, in which the classical Nernst-Planck equations are recovered.