1,278 research outputs found
Low Mach Number Fluctuating Hydrodynamics for Electrolytes
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.Comment: 37 pages, 5 figure
A Staggered Scheme for the Compressible Fluctuating Hydrodynamics of Multispecies Fluid Mixtures
We present a numerical formulation for the solution of non-isothermal,
compressible, Navier-Stokes equations with thermal fluctuations to describe
mesoscale transport phenomena in multispecies fluid mixtures. The novelty of
our numerical method is the use of staggered grid momenta along with a finite
volume discretization of the thermodynamic variables to solve the resulting
stochastic partial differential equations. The key advantages of the numerical
scheme are significantly simplified and compact discretization of the diffusive
and stochastic momentum fluxes, and an unambiguous prescription of boundary
conditions involving pressure. The staggered grid scheme more accurately
reproduces the equilibrium static structure factor of hydrodynamic fluctuations
in gas mixtures compared to a collocated scheme described previously in
Balakrishnan et al., Phys. Rev. E 89:013017, 2014. The numerical method is
tested for ideal noble gases mixtures under various nonequilibrium conditions,
such as applied thermal and concentration gradients, to assess the role of
cross-diffusion effects, such as Soret and Dufour, on the long-ranged
correlations of hydrodynamic fluctuations, which are also more accurately
reproduced compared to the collocated scheme. We numerically study giant
nonequilibrium fluctuations driven by concentration gradients, and
fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever
applicable, excellent agreement is observed with theory and measurements from
the direct simulation Monte Carlo (DSMC) method.Comment: 20 pages, 9 figures, 9 pages supplementary materia
Fluctuating hydrodynamics of multi-species, non-reactive mixtures
In this paper we discuss the formulation of the fuctuating Navier-Stokes
(FNS) equations for multi-species, non-reactive fluids. In particular, we
establish a form suitable for numerical solution of the resulting stochastic
partial differential equations. An accurate and efficient numerical scheme,
based on our previous methods for single species and binary mixtures, is
presented and tested at equilibrium as well as for a variety of non-equilibrium
problems. These include the study of giant nonequilibrium concentration
fluctuations in a ternary mixture in the presence of a diffusion barrier, the
triggering of a Rayleigh-Taylor instability by diffusion in a four-species
mixture, as well as reverse diffusion in a ternary mixture. Good agreement with
theory and experiment demonstrates that the formulation is robust and can serve
as a useful tool in the study of thermal fluctuations for multi-species fluids.
The extension to include chemical reactions will be treated in a sequel paper
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