Role of Stefan–Maxwell fluxes in the dynamics of concentrated electrolytes

Abstract

This theoretical analysis quantifies the effect of coupled ionic fluxes on the charging dynamics of an electrochemical cell. We consider a model cell consisting of a concentrated, binary electrolyte between parallel, blocking electrodes, under a suddenly applied DC voltage. It is assumed that the magnitude of the applied voltage is small compared to the thermal voltage scale, RT/F, where R is the universal gas constant, T is the temperature and F is the Faraday's constant. We employ the Stefan–Maxwell equations to describe the hydrodynamic coupling of ionic fluxes that arise in concentrated electrolytes. These equations inherently account for asymmetry in the mobilities of the ions in the electrolyte. A modified set of Poisson–Nernst–Planck equations, obtained by incorporating Stefan–Maxwell fluxes into the species balances, are formulated and solved in the limit of weak applied voltages. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two distinct time scales. The first is a faster “RC” time, τ_RC = κ⁻¹L/_E, where κ⁻¹ is the Debye length, L is the length of the half-cell, and _E is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, _E, is a function of the ambi-polar diffusivity of the salt, _a, as well as a cross-diffusivity, ₊₋, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τ_RC, the external current again decays exponentially on a slower, diffusive time scale, τ_D ∼ L²/_a, where _a is the ambi-polar diffusivity of the salt. This diffusive time scale is due to the unequal ion mobilities that result in a non-uniform bulk concentration of the salt during the charging process. Finally, we propose an approach by which our theory may be used to measure the cross-diffusivity in concentrated electrolytes.