• Editors' Suggestion

Fluctuating hydrodynamics of electrolytes at electroneutral scales

Aleksandar Donev, Andrew J. Nonaka, Changho Kim, Alejandro L. Garcia, and John B. Bell
Phys. Rev. Fluids 4, 043701 – Published 5 April 2019

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 September 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.043701

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Aleksandar Donev1,*, Andrew J. Nonaka2, Changho Kim2,3, Alejandro L. Garcia4, and John B. Bell2

  • 1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
  • 2Center for Computational Science and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 3Department of Applied Mathematics, University of California, Merced, Merced, California 95343, USA
  • 4Department of Physics, San Jose State University, San Jose, California 95192, USA

  • *donev@courant.nyu.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 4, Iss. 4 — April 2019

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Fluids

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×