Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale

TL;DR

This paper develops a theoretical framework and simulations to understand electrokinetic fluctuations in electrolyte solutions at mesoscale, revealing different decorrelation processes and distribution behaviors across scales.

Contribution

It introduces a Landau-Lifshitz-based theory for fluctuation correlations and compares MD and cDPD simulations, highlighting scale-dependent fluctuation distributions and validating theoretical predictions.

Findings

Charge density follows Gamma distribution at sub-nanometer scales.

Fluctuation correlations agree with linearized hydrodynamics theory.

Gaussian approximation is valid above nanometer scales.

Abstract

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.