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.

N1 - Funding Information:
We thank Jean-Philippe Péraud for help with comparisons between charged-fluid and electroneutral formulations. We would like to thank Anne De Wit for helpful discussions regarding gravitational instabilities in the presence of neutralization reactions and Ehud Yariv for generously sharing his knowledge about the electroneutral limit. We also acknowledge informative discussions with Charles Peskin. This material was based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics Program under Award No. DE-SC0008271 and under Contract No. DE-AC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. A.D. was supported in part by the Division of Chemical, Bioengineering, Environmental and Transport Systems of the National Science Foundation under Award No. CBET-1804940.
Publisher Copyright:
© 2019 American Physical Society..

PY - 2019/4

Y1 - 2019/4

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.

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U2 - 10.1103/PhysRevFluids.4.043701

DO - 10.1103/PhysRevFluids.4.043701

M3 - Article

AN - SCOPUS:85065045569

SN - 2469-990X

VL - 4

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 4

M1 - 043701

ER -