(668b) Role of Stefan-Maxwell Fluxes in the Dynamics of Concentrated Electrolytes

Authors: 
Balu, B., Carnegie Mellon University
Khair, A. S., Carnegie Mellon University
This theoretical analysis investigates the effect of ambi-polar diffusion and coupled ionic fluxes on the dynamics of the charging 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 applied voltage is small compared to the thermal voltage, 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 linearized Poisson-Nernst-Planck equations, obtained by incorporating Stefan-Maxwell fluxes into the species balances, are formulated and solved analytically. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two separate time scales. A faster, RC time, τRC ~ κ-1L/De, where De is an effective diffusivity, characterizes the evolution of charge density at the electrode. The effective diffusivity, De, is a function of the ambi-polar diffusivity of the salt, Da, 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 τRC, the external current again decays exponentially on a slower, diffusive time scale, τD ~ L2 /Da . 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 demonstrate how these dynamics can be incorporated into an equivalent circuit model.