Document Type
Article
Publication Date
April 2019
Publication Title
Physical Review Fluids
Volume
4
Issue Number
4
DOI
10.1103/PhysRevFluids.4.043701
ISSN
2469-990X
Disciplines
Physical Sciences and Mathematics | Physics
Abstract
At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Péraud et al., Phys. Rev. Fluids 1, 074103 (2016)]. 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.
Recommended Citation
Aleksandar Donev, Andrew Nonaka, Changho Kim, Alejandro Garcia, and John Bell. "Fluctuating hydrodynamics of electrolytes at electroneutral scales" Physical Review Fluids (2019). https://doi.org/10.1103/PhysRevFluids.4.043701
Comments
This article was originally published in Physical Review Fluids, volume 4, issue 4, 2019. ©2016 American Physical Society.
This article is also available online at this link.