  Electrolyte solutions play an important role in energy storage devices, whose
performance highly relies on the electrokinetic processes at sub-micron
scales.\ Although fluctuations and stochastic features become more critical at
small scales, the long-range Coulomb interactions pose a particular challenge
for both theoretical analysis and simulation of fluid systems with fluctuating
hydrodynamic and electrostatic interactions. Here, we present a theoretical
framework based on the Landau-Lifshitz theory to derive closed-form expressions
of fluctuation correlations in electrolyte solutions, indicating significantly
different decorrelation processes of ionic concentration fluctuations from
hydrodynamic fluctuations, which provides insights for understanding transport
phenomena of coupled fluctuating hydrodynamics and electrokinetics.
Furthermore, we simulate fluctuating electrokinetic systems using both
molecular dynamics (MD) with explicit ions and mesoscopic charged dissipative
particle dynamics (cDPD) with semi-implicit ions, from which we identify that
the spatial probability density functions of local charge density follow Gamma
distribution at sub-nanometer scale (i.e., 0.3 nm) and converge to Gaussian
distribution above nanometer scales (i.e., 1.55 nm), indicating the existence
of a lower limit of length scale for mesoscale models using Gaussian
fluctuations. The temporal correlation functions of both hydrodynamic and
electrokinetic fluctuations are computed from all-atom MD and mesoscale cDPD
simulations, showing a good agreement with the theoretical predictions based on
the linearized fluctuating hydrodynamics theory.
