Fluctuation-enhanced electric conductivity in electrolyte solutions

Jean Philippe Péraud, Andrew J. Nonaka, John B. Bell, Aleksandar Donev, Alejandro L. Garcia

Research output: Contribution to journalArticle

Abstract

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.

Original languageEnglish (US)
Pages (from-to)10829-10833
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Volume114
Issue number41
DOIs
StatePublished - Oct 10 2017

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electrolytes
conductivity
diffusion coefficient
macroscopic equations
salts
electric fields
hydrodynamic equations
fluids
coefficients
advection
hydrodynamics
momentum
augmentation
predictions

Keywords

  • Electrohydrodynamics
  • Fluctuating hydrodynamics
  • Multicomponent diffusion
  • Navier–Stokes equations
  • Nernst–Plank equations

ASJC Scopus subject areas

  • General

Cite this

Fluctuation-enhanced electric conductivity in electrolyte solutions. / Péraud, Jean Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 114, No. 41, 10.10.2017, p. 10829-10833.

Research output: Contribution to journalArticle

Péraud, Jean Philippe ; Nonaka, Andrew J. ; Bell, John B. ; Donev, Aleksandar ; Garcia, Alejandro L. / Fluctuation-enhanced electric conductivity in electrolyte solutions. In: Proceedings of the National Academy of Sciences of the United States of America. 2017 ; Vol. 114, No. 41. pp. 10829-10833.
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