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Fluctuation-enhanced electric conductivity in electrolyte solutions

  1. Alejandro L. Garciac
  1. aComputational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94703;
  2. bDepartment of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;
  3. cDepartment of Physics and Astronomy, San Jose State University, San Jose, CA 95192
  1. Contributed by John B. Bell, August 31, 2017 (sent for review August 16, 2017; reviewed by Florence Suzy Baras and Annie Lemarchand)


Using fluctuating hydrodynamics, we demonstrate that thermal fluctuations contribute to charge transport in binary electrolyte solutions. We show the existence of an enhancement, or renormalization, of the electric conductivity due to the coupling between fluctuations of charge and fluid velocity. This coupling results in nontrivial corrections to the classical Poisson–Nernst–Planck equations, which are of the order of the square root of the salt concentration and therefore significant even for dilute solutions. Our calculations predict a cation–anion cross-diffusion coefficient that is in quantitative agreement with experimental measurements. Our findings have important implications for the fields of both mesoscale hydrodynamics and electrolyte transport.


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.


  • ?1To whom correspondence should be addressed. Email: JBBell{at}lbl.gov.
  • Author contributions: J.-P.P., J.B.B., A.D., and A.L.G. designed research; J.-P.P., A.J.N., A.D., and A.L.G. performed research; and J.-P.P., J.B.B., A.D., and A.L.G. wrote the paper.

  • Reviewers: F.S.B., Laboratory Interdisciplinaire Carnot de Bourgogne; and A.L., CNRS, Université Pierre et Marie Curie.

  • The authors declare no conflict of interest.

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