Low Mach number fluctuating hydrodynamics for electrolytes

Journal Article · Fri Nov 18 00:00:00 EST 2016 · Physical Review Fluids

DOI:https://doi.org/10.1103/PhysRevFluids.1.074103· OSTI ID:1379816

Péraud, Jean-Philippe ^[1]; Nonaka, Andy ^[1]; Chaudhri, Anuj ^[2]; Bell, John B. ^[1]; Donev, Aleksandar ^[3]; Garcia, Alejandro L. ^[4]

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1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
2. Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore (India). Engineering Mechanics Unit
3. New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences
4. San Jose State Univ., CA (United States). Dept. of Physics and Astronomy

Here, we formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are also interested in studying transport in mixtures of charged species at the mesoscale, down to scales below the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids (A. Donev, et al., Physics of Fluids, 27, 3, 2015), we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the mass and momentum equations. Our low Mach number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. Furthermore, we demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second-order in the deterministic setting, and for length scales much greater than the Debye length gives results consistent with an electroneutral/ambipolar approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1379816
• Alternate ID(s): OSTI ID: 1332778
• Journal Information: Physical Review Fluids, Vol. 1, Issue 7; ISSN 2469-990X
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
fluctuating hydrodynamics
computational fluid dynamics
Navier-Stokes equations
low Mach number methods
multicomponent diffusion
electrohydrodynamics