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Title: Fluctuating hydrodynamics of electrolytes at electroneutral scales

Abstract

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral, and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit, and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross-diffusion and non-ideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species, and cannot treat the acid,more » base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales.« less

Authors:
 [1];  [2];  [3];  [4];  [2]
  1. New York Univ., NY (United States). Courant Institute of Mathematical Sciences
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Computational Science and Engineering (CCSE)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Computational Science and Engineering (CCSE); Univ. of California, Merced, CA (United States). Dept. of Applied Mathematics
  4. San Jose Univ., CA (United States). Dept. of Physics
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
OSTI Identifier:
1526544
Alternate Identifier(s):
OSTI ID: 1505242
Grant/Contract Number:  
SC0008271; AC02-05CH11231; CBET-1804940
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Fluids
Additional Journal Information:
Journal Volume: 4; Journal Issue: 4; Journal ID: ISSN 2469-990X
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Donev, Aleksandar, Nonaka, Andrew J., Kim, Changho, Garcia, Alejandro L., and Bell, John B. Fluctuating hydrodynamics of electrolytes at electroneutral scales. United States: N. p., 2019. Web. doi:10.1103/PhysRevFluids.4.043701.
Donev, Aleksandar, Nonaka, Andrew J., Kim, Changho, Garcia, Alejandro L., & Bell, John B. Fluctuating hydrodynamics of electrolytes at electroneutral scales. United States. https://doi.org/10.1103/PhysRevFluids.4.043701
Donev, Aleksandar, Nonaka, Andrew J., Kim, Changho, Garcia, Alejandro L., and Bell, John B. Fri . "Fluctuating hydrodynamics of electrolytes at electroneutral scales". United States. https://doi.org/10.1103/PhysRevFluids.4.043701. https://www.osti.gov/servlets/purl/1526544.
@article{osti_1526544,
title = {Fluctuating hydrodynamics of electrolytes at electroneutral scales},
author = {Donev, Aleksandar and Nonaka, Andrew J. and Kim, Changho and Garcia, Alejandro L. and Bell, John B.},
abstractNote = {At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral, and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit, and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross-diffusion and non-ideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species, and cannot treat the acid, base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales.},
doi = {10.1103/PhysRevFluids.4.043701},
journal = {Physical Review Fluids},
number = 4,
volume = 4,
place = {United States},
year = {Fri Apr 05 00:00:00 EDT 2019},
month = {Fri Apr 05 00:00:00 EDT 2019}
}

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Cited by: 13 works
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Works referenced in this record:

Induced-charge electro-osmosis beyond weak fields
journal, December 2012


Fluctuation-enhanced electric conductivity in electrolyte solutions
journal, September 2017

  • Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 41
  • DOI: 10.1073/pnas.1714464114

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures
journal, March 2015

  • Donev, Aleksandar; Nonaka, Andy; Bhattacharjee, Amit Kumar
  • Physics of Fluids, Vol. 27, Issue 3
  • DOI: 10.1063/1.4913571

Fluctuating Hydrodynamics and Debye-Hückel-Onsager Theory for Electrolytes
journal, February 2019

  • Donev, Aleksandar; Garcia, Alejandro L.; Péraud, Jean-Philippe
  • Current Opinion in Electrochemistry, Vol. 13
  • DOI: 10.1016/j.coelec.2018.09.004

Buoyancy-driven instabilities around miscible A + B C reaction fronts: A general classification
journal, February 2015


Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction
journal, August 2012


Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems
journal, January 2013

  • Lemaigre, L.; Budroni, M. A.; Riolfo, L. A.
  • Physics of Fluids, Vol. 25, Issue 1
  • DOI: 10.1063/1.4774321

Fractal fronts of diffusion in microgravity
journal, April 2011

  • Vailati, Alberto; Cerbino, Roberto; Mazzoni, Stefano
  • Nature Communications, Vol. 2, Issue 1
  • DOI: 10.1038/ncomms1290

Excess wing in glass-forming glycerol and LiCl-glycerol mixtures detected by neutron scattering
journal, January 2015


Nonequilibrium fluctuations in time-dependent diffusion processes
journal, October 1998


Electrophysiology
journal, October 2013

  • Griffith, Boyce E.; Peskin, Charles S.
  • Communications on Pure and Applied Mathematics, Vol. 66, Issue 12
  • DOI: 10.1002/cpa.21484

Electrokinetic self-propulsion by inhomogeneous surface kinetics
journal, December 2010

  • Yariv, Ehud
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 467, Issue 2130
  • DOI: 10.1098/rspa.2010.0503

Low Mach number fluctuating hydrodynamics of diffusively mixing fluids
journal, January 2014

  • Donev, Aleksandar; Nonaka, Andy; Sun, Yifei
  • Communications in Applied Mathematics and Computational Science, Vol. 9, Issue 1
  • DOI: 10.2140/camcos.2014.9.47

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
journal, March 2017

  • Kim, Changho; Nonaka, Andy; Bell, John B.
  • The Journal of Chemical Physics, Vol. 146, Issue 12
  • DOI: 10.1063/1.4978775

An unsplit, higher order godunov method for scalar conservation laws in multiple dimensions
journal, January 1988


On the accuracy of finite-volume schemes for fluctuating hydrodynamics
journal, January 2010

  • Donev, Aleksandar; Vanden-Eijnden, Eric; Garcia, Alejandro
  • Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 2
  • DOI: 10.2140/camcos.2010.5.149

Multi-ion diffusiophoresis
journal, June 2014


Staggered Schemes for Fluctuating Hydrodynamics
journal, January 2012

  • Balboa, Florencio; Bell, John B.; Delgado-Buscalioni, Rafael
  • Multiscale Modeling & Simulation, Vol. 10, Issue 4
  • DOI: 10.1137/120864520

An Asymptotic Derivation of the Thin-Debye-Layer Limit for Electrokinetic Phenomena
journal, October 2009


Fluctuating hydrodynamics of reactive liquid mixtures
journal, August 2018

  • Kim, Changho; Nonaka, Andy; Bell, John B.
  • The Journal of Chemical Physics, Vol. 149, Issue 8
  • DOI: 10.1063/1.5043428

Key parameters controlling the performance of catalytic motors
journal, March 2016

  • Esplandiu, Maria J.; Afshar Farniya, Ali; Reguera, David
  • The Journal of Chemical Physics, Vol. 144, Issue 12
  • DOI: 10.1063/1.4944319

Exploring the Maxwell-Stefan description of ion exchange
journal, April 1995

  • Wesselingh, J. A.; Vonk, P.; Kraaijeveld, G.
  • The Chemical Engineering Journal and the Biochemical Engineering Journal, Vol. 57, Issue 2
  • DOI: 10.1016/0923-0467(94)02932-6

Low Mach number fluctuating hydrodynamics of binary liquid mixtures
journal, January 2015

  • Nonaka, Andrew; Sun, Yifei; Bell, John
  • Communications in Applied Mathematics and Computational Science, Vol. 10, Issue 2
  • DOI: 10.2140/camcos.2015.10.163

Works referencing / citing this record:

Diffusion of multiple electrolytes cannot be treated independently: model predictions with experimental validation
journal, January 2019

  • Gupta, Ankur; Shim, Suin; Issah, Luqman
  • Soft Matter, Vol. 15, Issue 48
  • DOI: 10.1039/c9sm01780a