Low Mach Number Fluctuating Hydrodynamics for Electrolytes

TL;DR

This paper develops a computational low Mach number fluctuating hydrodynamics model for electrolyte solutions, capturing thermal fluctuations and electric effects at mesoscale, improving efficiency and accuracy over fully compressible models.

Contribution

It introduces a low Mach number formulation for electrolyte hydrodynamics that includes electric charge effects, enabling efficient simulation of mesoscale transport phenomena with fluctuations.

Findings

Model accurately simulates saltwater equilibrium and nonequilibrium fluctuations.

Results are consistent with electroneutral approximation at large scales.

Identifies and models an instability during diffusive mixing under electric fields.

Abstract

We formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are 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. 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.