[Paper Review] Fluctuation-enhanced electric conductivity in electrolyte solutions

Jean-Philippe Péraud, Andrew J. Nonaka+3 more|arXiv (Cornell University)|Jun 20, 2017

Spectroscopy and Quantum Chemical Studies24 references35 citations

TL;DR

This paper proposes that thermal fluctuations in electrolyte solutions, when coupled with an external electric field, enhance net charge transport through a fluctuation-induced electroconvection mechanism. Using fluctuating hydrodynamics and linearized stochastic PNP-Navier-Stokes equations, the authors derive a renormalized electric conductivity that accounts for advective fluxes from velocity-charge correlations and predicts a non-zero Maxwell-Stefan cross-diffusion coefficient consistent with experiments.

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.

Motivation & Objective

• To understand how thermal fluctuations in charged fluids couple with an external electric field to enhance charge transport.
• To develop a theoretical framework that explains macroscopic conductivity enhancement beyond classical Nernst-Einstein theory.
• To reconcile fluctuating hydrodynamics with the Debye-Hückel-Onsager theory and quantify corrections to conductivity and diffusion.
• To predict and explain the existence of a non-zero Maxwell-Stefan cross-diffusion coefficient from fluctuation-induced couplings.
• To analyze the anisotropic enhancement of velocity fluctuations and suppression of concentration fluctuations under strong electric fields.

Proposed method

• Formulates the fluctuating Poisson-Nernst-Planck (PNP) and Landau-Lifshitz Navier-Stokes equations for a dilute electrolyte with charged species.
• Applies linearized fluctuating hydrodynamics to derive the Ornstein-Uhlenbeck process for fluctuations in mass fraction, charge density, and velocity.
• Computes structure factors via the steady-state solution of the matrix Lyapunov equation MS + SM* = -NN*.
• Uses Fourier-space analysis to compute correlations between velocity and charge density fluctuations (⟨vδc⟩) and between electric field and concentration fluctuations (⟨δEδn⟩).
• Derives the renormalized electric conductivity from the linear response of the charge flux to the applied field, including advective and relaxation contributions.
• Validates consistency with Onsager's reciprocal relations by showing that the Maxwell-Stefan cross-diffusion coefficient emerges naturally from the fluctuation coupling.

Experimental results

Research questions

• RQ1 How do thermal fluctuations in a charged fluid couple with an externally applied electric field to enhance charge transport?
• RQ2 Can the fluctuating hydrodynamics framework reproduce the electrophoretic and relaxation corrections from Debye-Hückel-Onsager theory?
• RQ3 What is the origin and magnitude of the non-zero Maxwell-Stefan cross-diffusion coefficient in electrolyte solutions?
• RQ4 How does the applied electric field affect the anisotropy of velocity and concentration fluctuations?
• RQ5 Is the renormalized electric conductivity consistent with Onsager's reciprocal relations when cross-diffusion is included?

Key findings

• The fluctuation-induced electroconvection mechanism leads to a renormalized electric conductivity that exceeds the classical Nernst-Einstein prediction due to advective fluxes from velocity-charge correlations.
• The renormalized conductivity is consistent with Onsager's reciprocal relations only when a non-zero Maxwell-Stefan cross-diffusion coefficient is included, which is confirmed by experimental measurements.
• The theory predicts a non-zero cross-diffusion coefficient between cations and anions, with a magnitude that agrees well with experimental data.
• Under strong electric fields, velocity fluctuations are anisotropically enhanced as the square of the field strength, while salt concentration fluctuations are suppressed.
• The structure factor calculations show that the ⟨vδc⟩ correlation is the dominant contribution to the enhanced charge flux, with a linear dependence on the applied field.
• The framework recovers the electrophoretic and relaxation corrections from Debye-Hückel-Onsager theory as limiting cases, validating its consistency with established electrokinetic theory.