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We theoretically investigate an electric-field-driven system of chargedspheres as a primitive model of concentrated electrolytes under an appliedelectric field. First, we provide a unified formulation for the stochasticcharge and density dynamics of the electric-field-driven primitive model usingthe stochastic density functional theory (DFT). The stochastic DFT integratesvarious frameworks of the equilibrium and dynamic DFTs, the liquid statetheory, and the field-theoretic approach, which allows us to justify in aunified manner various modifications previously made for thePoisson-Nernst-Planck model. Next, we consider stationary density-density andcharge-charge correlation functions of the primitive model with a staticelectric field. We focus on an electric-field-induced synchronization betweenthe emergence of density and charge oscillations, or the crossover frommonotonic to oscillatory decay of density-density and charge-chargecorrelations. The correlation function analysis demonstrates the appearance ofstripe states formed by segregation bands perpendicular to the external field.We also predict the following: (i) the electric-field-induced crossover occursprior to the conventional Kirkwood crossover without an applied electric field,and (ii) the ion concentration dependence of the decay lengths at theelectric-field-induced crossovers bears a similarity to the underscreeningbehavior found by simulation and theoretical studies on the oscillatory decaylength in equilibrium.

Electric-field-induced oscillations in ionic fluids: a unified  formulation of modified Poisson-Nernst-Planck models and its relevance to  correlation function analysis