We apply fluctuating hydrodynamics to strong electrolyte mixtures to compute the concentration corrections for chemical potential, diffusivity, and conductivity. We show these corrections to be in agreement with the limiting laws of Debye, Hückel, and Onsager. We compute explicit corrections for a symmetric ternary mixture and find that the co-ion Maxwell-Stefan diffusion coefficients can be negative, in agreement with experimental findings.Due to the long-range nature of Coulomb forces between ions it is well-known that electrolyte solutions have unique properties that distinguish them from ordinary mixtures [1]. Colligative properties, such as osmotic pressure, and transport properties, such as mobility, have corrections that scale with the square root of concentration [2,3,4,5]. This macroscopic effect has a mesoscopic origin, specifically, due to the competition of thermal and electrostatic energy at scales comparable to the Debye length.The traditional derivation of the thermodynamic corrections is by way of solving the Poisson-Boltzmann equation. For example, an approximate solution gives the Debye-Hückel limiting law for the activity coefficient [2,6]. The derivation of the transport properties, as developed by Onsager and co-workers [7,8,9], has a similar starting point but is much more complicated. Here, we present an alternative approach using fluctuating hydrodynamics (FHD) [10].This paper generalizes our previous derivation for binary electrolytes [11] to arbitrary solute mixtures, and, as an illustrative example, calculates transport properties for a ternary electrolyte. It should be noted that our FHD approach extends closely-related density functional Email address: donev@courant.nyu.edu (Aleksandar Donev) theory calculations of relaxation corrections to the conductivity [12] of binary electrolytes to account for advection, which enables us to also compute the electrophoretic corrections [2].First formulated by Landau and Lifshitz to predict light scattering spectra [13,14], more recently FHD has been applied to study various mesoscopic phenomena in fluid dynamics [10,15,16,17]. The current popularity of fluctuating hydrodynamics is due, in part, to the availability of efficient and accurate numerical schemes for solving the FHD equations [18,19,20,21,22,23,24,25,26]. While in this work we give analytical results for dilute electrolytes under simplifying assumptions, numerical techniques can in principle be used to compute the transport coefficients for moderately dilute solutions.From the work of Onsager et al. [7,8,9] we can obtain the Fickian diffusion matrix for sufficiently dilute electrolytes. For neutral multispecies mixtures, especially non-dilute ones, using binary Maxwell-Stefan (MS) diffusion coefficients (inverse friction coefficients) [27,28] is preferred because generally they are positive and depend weakly on concentration. In this paper we use our FHD formulation to calculate the effective macroscopic (renormalized) co-ion and counter-ion MS coefficients for binary and symmetric ter...

In this letter we analyze the effects of an externally applied electric field on thermal fluctuations for a fluid containing charged species. We show in particular that the fluctuating Poisson-Nernst-Planck equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation, result in enhanced charge transport. Although this transport is advective in nature, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity. We calculate the renormalized electric conductivity by deriving and integrating the structure factor coefficients of the fluctuating quantities and show that the renormalized electric conductivity and diffusion coefficients are consistent although they originate from different noise terms. In addition, the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, and provides a quantitative theory that predicts a non-zero cross-diffusion MaxwellStefan coefficient that agrees well with experimental measurements. Finally, we show that strong applied electric fields result in anisotropically enhanced velocity fluctuations and reduced fluctuations of salt concentrations.