# Fluctuation-enhanced electric conductivity in electrolyte solutions

## Abstract

In this work, 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 ofmore »

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
- New York Univ. (NYU), NY (United States). Department of Mathematics, Courant Institute of Mathematical Sciences
- San Jose State University, CA (United States). Department of Physics and Astronomy

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1396062

- Alternate Identifier(s):
- OSTI ID: 1426738

- Grant/Contract Number:
- AC02-05CH11231; SC0008271

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America

- Additional Journal Information:
- Journal Volume: 114; Journal Issue: 41; Related Information: © 2017, National Academy of Sciences. All rights reserved.; Journal ID: ISSN 0027-8424

- Publisher:
- National Academy of Sciences, Washington, DC (United States)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; fluctuating hydrodynamics; electrohydrodynamics; Navier–Stokes equations; multicomponent diffusion; Nernst–Plank equations

### Citation Formats

```
Péraud, Jean-Philippe, Nonaka, Andrew J., Bell, John B., Donev, Aleksandar, and Garcia, Alejandro L.
```*Fluctuation-enhanced electric conductivity in electrolyte solutions*. United States: N. p., 2017.
Web. doi:10.1073/pnas.1714464114.

```
Péraud, Jean-Philippe, Nonaka, Andrew J., Bell, John B., Donev, Aleksandar, & Garcia, Alejandro L.
```*Fluctuation-enhanced electric conductivity in electrolyte solutions*. United States. doi:10.1073/pnas.1714464114.

```
Péraud, Jean-Philippe, Nonaka, Andrew J., Bell, John B., Donev, Aleksandar, and Garcia, Alejandro L. Tue .
"Fluctuation-enhanced electric conductivity in electrolyte solutions". United States.
doi:10.1073/pnas.1714464114.
```

```
@article{osti_1396062,
```

title = {Fluctuation-enhanced electric conductivity in electrolyte solutions},

author = {Péraud, Jean-Philippe and Nonaka, Andrew J. and Bell, John B. and Donev, Aleksandar and Garcia, Alejandro L.},

abstractNote = {In this work, 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. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.},

doi = {10.1073/pnas.1714464114},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

number = 41,

volume = 114,

place = {United States},

year = {Tue Sep 26 00:00:00 EDT 2017},

month = {Tue Sep 26 00:00:00 EDT 2017}

}