Fluctuating hydrodynamics of multispecies nonreactive mixtures

Balakrishnan, Kaushik; Garcia, Alejandro L.; Donev, Aleksandar; Bell, John B.

doi:10.1103/PhysRevE.89.013017

Fluctuating hydrodynamics of multispecies nonreactive mixtures

Journal Article · Tue Jan 21 23:00:00 EST 2014 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.89.013017· OSTI ID:1407226

Balakrishnan, Kaushik ^[1]; Garcia, Alejandro L. ^[2]; Donev, Aleksandar ^[3]; Bell, John B. ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
San Jose State Univ., CA (United States). Dept. of Physics and Astronomy
New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences

In this study we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive 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 nonequilibrium 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. Finally, 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 multispecies fluids.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); National Science Foundation (NSF) (United States)

Grant/Contract Number:: AC02-05CH11231; SC0008271

OSTI ID:: 1407226

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Journal Issue: 1 Vol. 89; ISSN 1539-3755

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (48)

An experimental study of three component gas diffusion Duncan, J. B.; Toor, H. L. AIChE Journal, Vol. 8, Issue 1 https://doi.org/10.1002/aic.690080112	journal	March 1962
Multicomponent Flow Modeling Giovangigli, Vincent Modeling and Simulation in Science, Engineering and Technology book series https://doi.org/10.1007/978-1-4612-1580-6	book	January 1999
Numerical integration of the fluctuating hydrodynamic equations Garcia, Alejandro L.; Mansour, M. Malek; Lie, George C. Journal of Statistical Physics, Vol. 47, Issue 1-2 https://doi.org/10.1007/BF01009043	journal	April 1987
Multicomponent flow modeling Giovangigli, Vincent Science China Mathematics, Vol. 55, Issue 2 https://doi.org/10.1007/s11425-011-4346-y	journal	December 2011
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions Gillespie, Daniel T. Journal of Computational Physics, Vol. 22, Issue 4 https://doi.org/10.1016/0021-9991(76)90041-3	journal	December 1976
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
Thermal diffusion in ternary mixtures Van der Valk, F. Physica, Vol. 30, Issue 4 https://doi.org/10.1016/0031-8914(64)90118-1	journal	April 1964
Thermal diffusion in ternary mixtures Van Der Valk, F. Physica, Vol. 29, Issue 5 https://doi.org/10.1016/S0031-8914(63)80153-6	journal	May 1963
Stochastic differential equations for non-linear hydrodynamics Español, Pep Physica A: Statistical Mechanics and its Applications, Vol. 248, Issue 1-2 https://doi.org/10.1016/S0378-4371(97)00461-5	journal	January 1998
Fluctuating hydrodynamics and concentration fluctuations in ternary mixtures Ortiz de Zárate, José M.; Hita, Jorge Luis; Sengers, Jan V. Comptes Rendus Mécanique, Vol. 341, Issue 4-5 https://doi.org/10.1016/j.crme.2013.01.018	journal	April 2013
Hybrid continuum-particle method for fluctuating lipid bilayer membranes with diffusing protein inclusions Sigurdsson, Jon K.; Brown, Frank L. H.; Atzberger, Paul J. Journal of Computational Physics, Vol. 252 https://doi.org/10.1016/j.jcp.2013.06.016	journal	November 2013
Fluctuating hydrodynamics for a rarefied gas based on extended thermodynamics Ikoma, Akiyuki; Arima, Takashi; Taniguchi, Shigeru Physics Letters A, Vol. 375, Issue 27 https://doi.org/10.1016/j.physleta.2011.05.057	journal	July 2011
Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells Trevelyan, P. M. J.; Almarcha, C.; De Wit, A. Journal of Fluid Mechanics, Vol. 670 https://doi.org/10.1017/S0022112010005008	journal	January 2011
Giant fluctuations in a free diffusion process Vailati, Alberto; Giglio, Marzio Nature, Vol. 390, Issue 6657 https://doi.org/10.1038/36803	journal	November 1997
Fractal fronts of diffusion in microgravity Vailati, Alberto; Cerbino, Roberto; Mazzoni, Stefano Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1290	journal	April 2011
Computational fluctuating fluid dynamics Bell, John B.; Garcia, Alejandro L.; Williams, Sarah A. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44, Issue 5 https://doi.org/10.1051/m2an/2010053	journal	August 2010
Contributions to Nonequilibrium Thermodynamics. II. Fluctuation Theory for the Boltzmann Equation Fox, Ronald Forrest Physics of Fluids, Vol. 13, Issue 12 https://doi.org/10.1063/1.1692878	journal	January 1970
Contributions to Non-Equilibrium Thermodynamics. I. Theory of Hydrodynamical Fluctuations Fox, Ronald Forrest Physics of Fluids, Vol. 13, Issue 8 https://doi.org/10.1063/1.1693183	journal	January 1970
Constraints in nonequilibrium thermodynamics: General framework and application to multicomponent diffusion Öttinger, Hans Christian The Journal of Chemical Physics, Vol. 130, Issue 11 https://doi.org/10.1063/1.3088847	journal	March 2009
A light scattering study of non equilibrium fluctuations in liquid mixtures to measure the Soret and mass diffusion coefficient Croccolo, F.; Bataller, H.; Scheffold, F. The Journal of Chemical Physics, Vol. 137, Issue 23 https://doi.org/10.1063/1.4771872	journal	December 2012
Perspective: Stochastic algorithms for chemical kinetics Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R. The Journal of Chemical Physics, Vol. 138, Issue 17 https://doi.org/10.1063/1.4801941	journal	May 2013
Nanohydrodynamics simulations: An atomistic view of the Rayleigh-Taylor instability Kadau, K.; Germann, T. C.; Hadjiconstantinou, N. G. Proceedings of the National Academy of Sciences, Vol. 101, Issue 16 https://doi.org/10.1073/pnas.0401228101	journal	April 2004
The importance of fluctuations in fluid mixing Kadau, K.; Rosenblatt, C.; Barber, J. L. Proceedings of the National Academy of Sciences, Vol. 104, Issue 19 https://doi.org/10.1073/pnas.0702871104	journal	April 2007
Hydrodynamic Correlation Functions for Binary Mixtures Cohen, Claude; Sutherland, J. W. H.; Deutch, J. M. Physics and Chemistry of Liquids, Vol. 2, Issue 4 https://doi.org/10.1080/00319107108083815	journal	January 1971
Fluctuation-induced and Nonequilibrium-induced Bifurcations in a Thermochemical System Lemarchand, A.; Nowakowski, B. Molecular Simulation, Vol. 30, Issue 11-12 https://doi.org/10.1080/0892702042000270151	journal	September 2004
Enhancement of diffusive transport by non-equilibrium thermal fluctuations Donev, Aleksandar; Bell, John B.; de la Fuente, Anton Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011, Issue 06 https://doi.org/10.1088/1742-5468/2011/06/P06014	journal	June 2011
Noncritical liquid mixtures far from equilibrium: The Rayleigh line Law, B. M.; Nieuwoudt, J. C. Physical Review A, Vol. 40, Issue 7 https://doi.org/10.1103/PhysRevA.40.3880	journal	October 1989
Theory of light scattering by a nonequilibrium binary mixture Nieuwoudt, J. C.; Law, B. M. Physical Review A, Vol. 42, Issue 4 https://doi.org/10.1103/PhysRevA.42.2003	journal	August 1990
Nonequilibrium fluctuations in time-dependent diffusion processes Vailati, Alberto; Giglio, Marzio Physical Review E, Vol. 58, Issue 4 https://doi.org/10.1103/PhysRevE.58.4361	journal	October 1998
Universal behavior of nonequilibrium fluctuations in free diffusion processes Brogioli, Doriano; Vailati, Alberto; Giglio, Marzio Physical Review E, Vol. 61, Issue 1 https://doi.org/10.1103/PhysRevE.61.R1	journal	January 2000
Sensitivity of explosion to departure from partial equilibrium Nowakowski, B.; Lemarchand, A. Physical Review E, Vol. 68, Issue 3 https://doi.org/10.1103/PhysRevE.68.031105	journal	September 2003
Long-wavelength nonequilibrium concentration fluctuations induced by the Soret effect Ortiz de Zárate, José María; Fornés, José Antonio; Sengers, Jan V. Physical Review E, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevE.74.046305	journal	October 2006
Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations Bell, John B.; Garcia, Alejandro L.; Williams, Sarah A. Physical Review E, Vol. 76, Issue 1 https://doi.org/10.1103/PhysRevE.76.016708	journal	July 2007
Extent of validity of the hydrodynamic description of ions in dense plasmas Mithen, James P.; Daligault, Jérôme; Gregori, Gianluca Physical Review E, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevE.83.015401	journal	January 2011
Temporal integrators for fluctuating hydrodynamics Delong, Steven; Griffith, Boyce E.; Vanden-Eijnden, Eric Physical Review E, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevE.87.033302	journal	March 2013
Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: Fluctuating hydrodynamics thermostat Wang, Yaohong; Sigurdsson, Jon Karl; Brandt, Erik Physical Review E, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevE.88.023301	journal	August 2013
Diffusive Transport by Thermal Velocity Fluctuations Donev, Aleksandar; Bell, John B.; de la Fuente, Anton Physical Review Letters, Vol. 106, Issue 20 https://doi.org/10.1103/PhysRevLett.106.204501	journal	May 2011
Fluctuating hydrodynamics in a dilute gas Mansour, M. Malek; Garcia, Alejandro L.; Lie, George C. Physical Review Letters, Vol. 58, Issue 9 https://doi.org/10.1103/PhysRevLett.58.874	journal	March 1987
Dynamics of Liquid Nanojets Eggers, Jens Physical Review Letters, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevLett.89.084502	journal	August 2002
High-Resolution EM of Colloidal Nanocrystal Growth Using Graphene Liquid Cells Yuk, Jong Min; Park, Jungwon; Ercius, Peter Science, Vol. 336, Issue 6077 https://doi.org/10.1126/science.1217654	journal	April 2012
Formation, Stability, and Breakup of Nanojets Moseler, M. Science, Vol. 289, Issue 5482 https://doi.org/10.1126/science.289.5482.1165	journal	August 2000
Staggered Schemes for Fluctuating Hydrodynamics Balboa, Florencio; Bell, John B.; Delgado-Buscalioni, Rafael Multiscale Modeling & Simulation, Vol. 10, Issue 4 https://doi.org/10.1137/120864520	journal	January 2012
Computational fluctuating fluid dynamics B., Bell, John; A., Williams, Sarah; L., Garcia, Alejandro The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/h52y-eq56	text	January 2010
On the accuracy of finite-volume schemes for fluctuating hydrodynamics Donev, Aleksandar; Vanden-Eijnden, Eric; Garcia, Alejandro Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 2 https://doi.org/10.2140/camcos.2010.5.149	journal	January 2010
On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics Donev, A.; Vanden-Eijnden, E.; Garcia, A. L. arXiv https://doi.org/10.48550/arxiv.0906.2425	preprint	January 2009
Enhancement of Diffusive Transport by Nonequilibrium Thermal Fluctuations Donev, A.; de la Fuente, A.; Bell, J. B. arXiv https://doi.org/10.48550/arxiv.1103.5244	text	January 2011
Staggered Schemes for Fluctuating Hydrodynamics Balboa, F. B.; BelL, J. B.; Delgado-Buscalioni, R. arXiv https://doi.org/10.48550/arxiv.1108.5188	preprint	January 2011
Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations Bell, John B.; Garcia, Alejandro L.; Williams, Sarah A. arXiv https://doi.org/10.48550/arxiv.math/0612324	text	January 2006

Cited By (10)

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures Donev, Aleksandar; Nonaka, Andy; Bhattacharjee, Amit Kumar Physics of Fluids, Vol. 27, Issue 3 https://doi.org/10.1063/1.4913571	journal	March 2015
Modeling nanoscale hydrodynamics by smoothed dissipative particle dynamics Lei, Huan; Mundy, Christopher J.; Schenter, Gregory K. The Journal of Chemical Physics, Vol. 142, Issue 19 https://doi.org/10.1063/1.4921222	journal	May 2015
Fluctuating hydrodynamics of multi-species reactive mixtures Bhattacharjee, Amit Kumar; Balakrishnan, Kaushik; Garcia, Alejandro L. The Journal of Chemical Physics, Vol. 142, Issue 22 https://doi.org/10.1063/1.4922308	journal	June 2015
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach Kim, Changho; Nonaka, Andy; Bell, John B. The Journal of Chemical Physics, Vol. 146, Issue 12 https://doi.org/10.1063/1.4978775	journal	March 2017
Fluctuating hydrodynamics of reactive liquid mixtures Kim, Changho; Nonaka, Andy; Bell, John B. The Journal of Chemical Physics, Vol. 149, Issue 8 https://doi.org/10.1063/1.5043428	journal	August 2018
On the suppression and distortion of non-equilibrium fluctuations by transpiration Ladiges, Daniel R.; Nonaka, Andrew J.; Bell, John B. Physics of Fluids, Vol. 31, Issue 5 https://doi.org/10.1063/1.5093922	journal	May 2019
Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions Ortiz de Zárate, J. M.; Kirkpatrick, T. R.; Sengers, J. V. The European Physical Journal E, Vol. 38, Issue 9 https://doi.org/10.1140/epje/i2015-15099-x	journal	September 2015
Low Mach Number Fluctuating Hydrodynamics of Multispecies Liquid Mixtures Donev, A.; Nonaka, A. J.; Bhattacharjee, A. K. arXiv https://doi.org/10.48550/arxiv.1412.6503	text	January 2014
Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions de Zarate, J. M. Ortiz; Kirkpatrick, T. R.; Sengers, J. V. arXiv https://doi.org/10.48550/arxiv.1505.01355	text	January 2015
On the Suppression and Distortion of Non-Equilibrium Fluctuations by Transpiration Ladiges, Daniel R.; Nonaka, Andrew J.; Bell, John B. arXiv https://doi.org/10.48550/arxiv.1902.10598	text	January 2019

Similar Records

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures

Journal Article · Sun Mar 15 00:00:00 EDT 2015 · Physics of Fluids (1994) · OSTI ID:22403221

Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures

Journal Article · Mon Jan 23 23:00:00 EST 2023 · Physical Review. E · OSTI ID:2242456

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
fluctuating Navier-Stokes equations
fluctuating hydrodynamics
multi-species
thermal fluctuations

Fluctuating hydrodynamics of multispecies nonreactive mixtures

Citation Formats

References (48)

Cited By (10)

Similar Records

Related Subjects