### Abstract

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Péraud, Phys. Rev. Fluids 1, 074103 (2016)2469-990X10.1103/PhysRevFluids.1.074103]. 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 nonideality 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.

Original language | English (US) |
---|---|

Article number | 043701 |

Journal | Physical Review Fluids |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2019 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Modeling and Simulation
- Fluid Flow and Transfer Processes

### Cite this

*Physical Review Fluids*,

*4*(4), [043701]. https://doi.org/10.1103/PhysRevFluids.4.043701

**Fluctuating hydrodynamics of electrolytes at electroneutral scales.** / Donev, Aleksandar; Nonaka, Andrew J.; Kim, Changho; Garcia, Alejandro L.; Bell, John B.

Research output: Contribution to journal › Article

*Physical Review Fluids*, vol. 4, no. 4, 043701. https://doi.org/10.1103/PhysRevFluids.4.043701

}

TY - JOUR

T1 - Fluctuating hydrodynamics of electrolytes at electroneutral scales

AU - Donev, Aleksandar

AU - Nonaka, Andrew J.

AU - Kim, Changho

AU - Garcia, Alejandro L.

AU - Bell, John B.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Péraud, Phys. Rev. Fluids 1, 074103 (2016)2469-990X10.1103/PhysRevFluids.1.074103]. 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 nonideality 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.

AB - At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Péraud, Phys. Rev. Fluids 1, 074103 (2016)2469-990X10.1103/PhysRevFluids.1.074103]. 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 nonideality 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.

UR - http://www.scopus.com/inward/record.url?scp=85065045569&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevFluids.4.043701

DO - 10.1103/PhysRevFluids.4.043701

M3 - Article

AN - SCOPUS:85065045569

VL - 4

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 4

M1 - 043701

ER -