Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Fluctuating hydrodynamics of reactive liquid mixtures

Abstract

Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.

Authors:
 [1];  [2];  [2];  [3];  [4]
+ Show Author Affiliations
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Univ. of California, Merced, CA (United States). Applied Mathematics
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
  3. San Jose State Univ., San Jose, CA (United States). Dept. of Physics and Astronomy
  4. New York Univ. (NYU), NY (United States). Courant Institute of Mathematical Sciences
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1526536
Alternate Identifier(s):
OSTI ID: 1467940
Grant/Contract Number:  
AC02-05CH11231; SC0008271
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 8; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Kim, Changho, Nonaka, Andy, Bell, John B., Garcia, Alejandro L., and Donev, Aleksandar. Fluctuating hydrodynamics of reactive liquid mixtures. United States: N. p., 2018. Web. doi:10.1063/1.5043428.
Copy to clipboard
Kim, Changho, Nonaka, Andy, Bell, John B., Garcia, Alejandro L., & Donev, Aleksandar. Fluctuating hydrodynamics of reactive liquid mixtures. United States. https://doi.org/10.1063/1.5043428
Copy to clipboard
Kim, Changho, Nonaka, Andy, Bell, John B., Garcia, Alejandro L., and Donev, Aleksandar. Tue . "Fluctuating hydrodynamics of reactive liquid mixtures". United States. https://doi.org/10.1063/1.5043428. https://www.osti.gov/servlets/purl/1526536.
Copy to clipboard
@article{osti_1526536,
title = {Fluctuating hydrodynamics of reactive liquid mixtures},
author = {Kim, Changho and Nonaka, Andy and Bell, John B. and Garcia, Alejandro L. and Donev, Aleksandar},
abstractNote = {Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.},
doi = {10.1063/1.5043428},
journal = {Journal of Chemical Physics},
number = 8,
volume = 149,
place = {United States},
year = {2018},
month = {8}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5043428
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Low Mach number fluctuating hydrodynamics for electrolytes
journal, November 2016

Reaction-diffusion master equation: A comparison with microscopic simulations
journal, December 1996

Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions
journal, September 2015

  • Ortiz de Zárate, J. M.; Kirkpatrick, T. R.; Sengers, J. V.
  • The European Physical Journal E, Vol. 38, Issue 9
  • DOI: 10.1140/epje/i2015-15099-x

A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws
journal, January 2011

  • Nonaka, A.; May, S.; Almgren, A. S.
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 4
  • DOI: 10.1137/100809520

Fluctuating hydrodynamics of multi-species reactive mixtures
journal, June 2015

  • Bhattacharjee, Amit Kumar; Balakrishnan, Kaushik; Garcia, Alejandro L.
  • The Journal of Chemical Physics, Vol. 142, Issue 22
  • DOI: 10.1063/1.4922308

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures
journal, March 2015

  • Donev, Aleksandar; Nonaka, Andy; Bhattacharjee, Amit Kumar
  • Physics of Fluids, Vol. 27, Issue 3
  • DOI: 10.1063/1.4913571

Rates of Spontaneous Cleavage of Glucose, Fructose, Sucrose, and Trehalose in Water, and the Catalytic Proficiencies of Invertase and Trehalas
journal, June 2008

  • Wolfenden, Richard; Yuan, Yang
  • Journal of the American Chemical Society, Vol. 130, Issue 24
  • DOI: 10.1021/ja802206s

Reaction-diffusion approach to prevertebrae formation: Effect of a local source of morphogen
journal, September 2013

  • Dziekan, P.; Signon, L.; Nowakowski, B.
  • The Journal of Chemical Physics, Vol. 139, Issue 11
  • DOI: 10.1063/1.4820952

Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions
journal, August 2009

Temporal integrators for fluctuating hydrodynamics
journal, March 2013

Microscopic simulation of chemical systems
journal, September 1992

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
journal, September 2011

  • Bedeaux, D.; Ortiz de Zárate, J. M.; Pagonabarraga, I.
  • The Journal of Chemical Physics, Vol. 135, Issue 12
  • DOI: 10.1063/1.3640010

Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front
journal, September 2013

Approximate accelerated stochastic simulation of chemically reacting systems
journal, July 2001

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 115, Issue 4
  • DOI: 10.1063/1.1378322

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems
journal, January 2013

  • Lemaigre, L.; Budroni, M. A.; Riolfo, L. A.
  • Physics of Fluids, Vol. 25, Issue 1
  • DOI: 10.1063/1.4774321

Pressure and temperature dependence of self-diffusion in water
journal, January 1978

  • Krynicki, Kazimierz; Green, Christopher D.; Sawyer, David W.
  • Faraday Discussions of the Chemical Society, Vol. 66
  • DOI: 10.1039/dc9786600199

Relations between mutual and intradiffusion coefficients in aqueous sucrose solutions
journal, July 1967

  • Tilley, J. F.; Mills, Reginald
  • The Journal of Physical Chemistry, Vol. 71, Issue 8
  • DOI: 10.1021/j100867a069

Electrophysiology
journal, October 2013

  • Griffith, Boyce E.; Peskin, Charles S.
  • Communications on Pure and Applied Mathematics, Vol. 66, Issue 12
  • DOI: 10.1002/cpa.21484

Phoretic Self-Propulsion
journal, January 2017

Fluctuating hydrodynamics of multispecies nonreactive mixtures
journal, January 2014

  • Balakrishnan, Kaushik; Garcia, Alejandro L.; Donev, Aleksandar
  • Physical Review E, Vol. 89, Issue 1
  • DOI: 10.1103/physreve.89.013017

Low Mach number fluctuating hydrodynamics of diffusively mixing fluids
journal, January 2014

  • Donev, Aleksandar; Nonaka, Andy; Sun, Yifei
  • Communications in Applied Mathematics and Computational Science, Vol. 9, Issue 1
  • DOI: 10.2140/camcos.2014.9.47

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
journal, March 2017

  • Kim, Changho; Nonaka, Andy; Bell, John B.
  • The Journal of Chemical Physics, Vol. 146, Issue 12
  • DOI: 10.1063/1.4978775

Concentration fluctuations in nonisothermal reaction-diffusion systems
journal, July 2007

  • Ortiz de Zárate, José M.; Sengers, Jan V.; Bedeaux, Dick
  • The Journal of Chemical Physics, Vol. 127, Issue 3
  • DOI: 10.1063/1.2746326

Fluctuations in the heterogeneous multiscale methods for fast–slow systems
journal, December 2017

Perspective: Stochastic algorithms for chemical kinetics
journal, May 2013

  • Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 138, Issue 17
  • DOI: 10.1063/1.4801941

An unsplit, higher order godunov method for scalar conservation laws in multiple dimensions
journal, January 1988

A weak trapezoidal method for a class of stochastic differential equations
journal, January 2011

  • Anderson, David F.; Mattingly, Jonathan C.
  • Communications in Mathematical Sciences, Vol. 9, Issue 1
  • DOI: 10.4310/cms.2011.v9.n1.a15

On the accuracy of finite-volume schemes for fluctuating hydrodynamics
journal, January 2010

  • Donev, Aleksandar; Vanden-Eijnden, Eric; Garcia, Alejandro
  • Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 2
  • DOI: 10.2140/camcos.2010.5.149

Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis
journal, June 2011

  • Moran, Jeffrey L.; Posner, Jonathan D.
  • Journal of Fluid Mechanics, Vol. 680
  • DOI: 10.1017/jfm.2011.132

Efficient reactive Brownian dynamics
journal, January 2018

  • Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho
  • The Journal of Chemical Physics, Vol. 148, Issue 3
  • DOI: 10.1063/1.5009464

Staggered Schemes for Fluctuating Hydrodynamics
journal, January 2012

  • Balboa, Florencio; Bell, John B.; Delgado-Buscalioni, Rafael
  • Multiscale Modeling & Simulation, Vol. 10, Issue 4
  • DOI: 10.1137/120864520

Confinement effects on electroconvective instability: General
journal, December 2016

  • Andersen, Mathias B.; Wang, Karen M.; Schiffbauer, Jarrod
  • ELECTROPHORESIS, Vol. 38, Issue 5
  • DOI: 10.1002/elps.201600391

Multiscale temporal integrators for fluctuating hydrodynamics
journal, December 2014

Key parameters controlling the performance of catalytic motors
journal, March 2016

  • Esplandiu, Maria J.; Afshar Farniya, Ali; Reguera, David
  • The Journal of Chemical Physics, Vol. 144, Issue 12
  • DOI: 10.1063/1.4944319

Low Mach number fluctuating hydrodynamics of binary liquid mixtures
journal, January 2015

  • Nonaka, Andrew; Sun, Yifei; Bell, John
  • Communications in Applied Mathematics and Computational Science, Vol. 10, Issue 2
  • DOI: 10.2140/camcos.2015.10.163

Multicomponent Maxwell−Stefan Diffusivities at Infinite Dilution
journal, April 2011

  • Liu, Xin; Bardow, André; Vlugt, Thijs J. H.
  • Industrial & Engineering Chemistry Research, Vol. 50, Issue 8
  • DOI: 10.1021/ie102515w

Mesoscopic non-equilibrium thermodynamics of non-isothermal reaction-diffusion
journal, January 2010

  • Bedeaux, D.; Pagonabarraga, I.; Ortiz de Zárate, J. M.
  • Physical Chemistry Chemical Physics, Vol. 12, Issue 39
  • DOI: 10.1039/c0cp00289e

Fluctuating hydrodynamics approach to chemical reactions
journal, March 1997

  • Pagonabarraga, I.; Pérez-Madrid, A.; Rubí, J. M.
  • Physica A: Statistical Mechanics and its Applications, Vol. 237, Issue 1-2
  • DOI: 10.1016/s0378-4371(96)00377-9

Efficient Variable-Coefficient Finite-Volume Stokes Solvers
journal, November 2014

  • Cai, Mingchao; Nonaka, Andy; Bell, John B.
  • Communications in Computational Physics, Vol. 16, Issue 5
  • DOI: 10.4208/cicp.070114.170614a

A weak second order tau-leaping method for chemical kinetic systems
journal, July 2011

  • Hu, Yucheng; Li, Tiejun; Min, Bin
  • The Journal of Chemical Physics, Vol. 135, Issue 2
  • DOI: 10.1063/1.3609119

Giant fluctuations in a free diffusion process
journal, November 1997

  • Vailati, Alberto; Giglio, Marzio
  • Nature, Vol. 390, Issue 6657
  • DOI: 10.1038/36803

Rates of Spontaneous Cleavage of Glucose, Fructose, Sucrose, and Trehalose in Water, and the Catalytic Proficiencies of Invertase and Trehalas
text, January 2008

  • Richard, Wolfenden,; Yang, Yuan,
  • The University of North Carolina at Chapel Hill University Libraries
  • DOI: 10.17615/q9xb-qw88

Multiscale temporal integrators for fluctuating hydrodynamics
text, January 2014

  • Eric, Vanden-Eijnden,; Steven, Delong,; Aleksandar, Donev,
  • The University of North Carolina at Chapel Hill University Libraries
  • DOI: 10.17615/tqvv-e430

On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics
preprint, January 2009

A weak trapezoidal method for a class of stochastic differential equations
preprint, January 2009

Staggered Schemes for Fluctuating Hydrodynamics
preprint, January 2011

Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids
text, January 2012

Efficient Variable-Coefficient Finite-Volume Stokes Solvers
text, January 2013

Low Mach Number Fluctuating Hydrodynamics of Multispecies Liquid Mixtures
text, January 2014

Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions
text, January 2015

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: