Coupled concentration-charge dynamics in 1:1 electrolytes with unequal diffusion coefficients: Local transient response and fluctuations

We investigate the coupled dynamics of concentration and charge in asymmetric 1:1 electrolytes, focusing on the interplay between diffusion asymmetry and external electric fields. Using Brownian dynamics simulations and linearized stochastic density functional theory (SDFT), we analyze the transient response of charge and number currents to inhomogeneous electric fields, as well as the steady-state spatio-temporal fluctuations under uniform fields. Our results reveal that asymmetry in ionic diffusion coefficients introduces a non-trivial coupling between charge and number transport, which modifies the two relaxation modes already present in symmetric electrolytes-a fast one associated with charge relaxation and a slow one linked to ambipolar diffusion. The dynamics are further modulated by the applied field, which enhances diffusion, alters screening lengths, and induces oscillatory behavior in the relaxation modes. The SDFT framework provides closed-form expressions for the intermediate scattering matrix, capturing the dynamics of density fluctuations and cross-correlations between number and charge. These predictions are validated by simulations, demonstrating excellent agreement across a wide range of wave vectors, both at equilibrium and under a finite electric field. Our findings highlight the critical role of diffusion asymmetry and external fields in tuning the transport properties of electrolytes, with implications for nanofluidic devices, energy harvesting, and iontronic circuits. This study bridges theoretical insights with practical applications, offering a robust framework for understanding and controlling electrolyte dynamics in asymmetric systems.