Fluctuating hydrodynamics of electrolytes at electroneutral scales

Journal Article · Fri Apr 05 00:00:00 EDT 2019 · Physical Review Fluids

DOI:https://doi.org/10.1103/PhysRevFluids.4.043701· OSTI ID:1526544

Donev, Aleksandar ^[1]; Nonaka, Andrew J. ^[2]; Kim, Changho ^[3]; Garcia, Alejandro L. ^[4]; Bell, John B. ^[2]

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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

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.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
• Grant/Contract Number: SC0008271; AC02-05CH11231; CBET-1804940
• OSTI ID: 1526544
• Alternate ID(s): OSTI ID: 1505242
• Journal Information: Physical Review Fluids, Vol. 4, Issue 4; ISSN 2469-990X
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY