# Fluctuation-enhanced electric conductivity in electrolyte solutions

## TL;DR

This paper demonstrates how external electric fields enhance charge transport in electrolyte solutions through fluctuating hydrodynamics, leading to renormalized conductivity and agreement with classical theories and experiments.

## Contribution

It introduces a fluctuating hydrodynamics framework that predicts enhanced electric conductivity and recovers classical electrophoretic effects in electrolyte solutions.

## Key findings

- Renormalized electric conductivity derived from fluctuations.
- Agreement with Debye-Huckel-Onsager theory.
- Electric fields cause anisotropic fluctuation enhancements.

## Abstract

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 Maxwell-Stefan 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.