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 = κL/D, where κ is the Debye length, L is the length of the half-cell, and D is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, D, is a function of the ambi-polar diffusivity of the salt, D, as well as a cross-diffusivity, D, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τ, the external current again decays exponentially on a slower, diffusive time scale, τ∼L/D, where D 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.

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“…The channel wall is impenetrable to the solute and the colloid. The steady hydrodynamic flow v(r) is directed along the axial direction z and may vary in the radial direction r. The colloid C(r, z, t) and solute S(r, z, t) concentration fields are symmetrically distributed about the channel centreline, and may vary in the radial and axial directions, and in time t. For C S, which is common for colloidal or bacterial suspensions containing molecular solutes, the influence of the evolution of C on S is negligible (Lapidus & Schiller 1976;Rivero-Hudec & Lauffenburger 1986;Staffeld & Quinn 1989;Ford & Cummings 1992;Marx & Aitken 2000;Abecassis et al 2008;Tindall et al 2008;Palacci et al 2010Palacci et al , 2012Kar et al 2015;Banerjee et al 2016;Shi et al 2016;Shin et al 2016;Ault et al 2017Ault et al , 2018Peraud et al 2017;Shin et al 2017;Balu & Khair 2018;Raynal et al 2018;Raynal & Volk 2019;Shim et al 2019;Chu et al 2020a). The advection-diffusion transport of the solute is governed by…”

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