### 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 language | English (US) |
---|---|

Pages (from-to) | 10829-10833 |

Number of pages | 5 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 114 |

Issue number | 41 |

DOIs | |

State | Published - Oct 10 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of the National Academy of Sciences of the United States of America*,

*114*(41), 10829-10833. https://doi.org/10.1073/pnas.1714464114

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

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 114, no. 41, pp. 10829-10833. https://doi.org/10.1073/pnas.1714464114

}

TY - JOUR

T1 - Fluctuation-enhanced electric conductivity in electrolyte solutions

AU - Péraud, Jean Philippe

AU - Nonaka, Andrew J.

AU - Bell, John B.

AU - Donev, Aleksandar

AU - Garcia, Alejandro L.

PY - 2017/10/10

Y1 - 2017/10/10

N2 - 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.

AB - 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.

KW - Electrohydrodynamics

KW - Fluctuating hydrodynamics

KW - Multicomponent diffusion

KW - Navier–Stokes equations

KW - Nernst–Plank equations

UR - http://www.scopus.com/inward/record.url?scp=85030780751&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030780751&partnerID=8YFLogxK

U2 - 10.1073/pnas.1714464114

DO - 10.1073/pnas.1714464114

M3 - Article

VL - 114

SP - 10829

EP - 10833

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 41

ER -