Nernst–Planck laws, distilled from Onsager–Stefan–Maxwell theory

Abstract

Here, we generalize Newman’s concentrated solution theory, establish a framework to underpin experimental parameterizations of multicomponent electrolytic solutions, and prove thermodynamic consistency of the Nernst–Planck–Poisson model of dilute-ion transport. Our proposed constitutive model, based on Onsager–Stefan–Maxwell flux laws from irreversible thermodynamics, describes coupled material and charge transfer in isobaric, isothermal, single-phase electrolytes containing any number of components, accounting for excluded-volume effects, thermodynamic nonideality, cross-diffusion, and local electroneutrality violations. Key results from the mass-transport and electrochemical literature are combined and extended. We contextualize prior electrolyte-transport theories within the general framework and establish minimal composition-dependent parameter sets for targeting by future characterization initiatives. A thermodynamically consistent version of Nernst–Planck theory emerges after applying several foundational idealizations and simplifications within the non-neutral Onsager–Stefan–Maxwell electrolyte-transport model.