### 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.

Original language | English (US) |
---|---|

Article number | 084113 |

Journal | Journal of Chemical Physics |

Volume | 149 |

Issue number | 8 |

DOIs | |

State | Published - Aug 28 2018 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*149*(8), [084113]. https://doi.org/10.1063/1.5043428

**Fluctuating hydrodynamics of reactive liquid mixtures.** / Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 149, no. 8, 084113. https://doi.org/10.1063/1.5043428

}

TY - JOUR

T1 - Fluctuating hydrodynamics of reactive liquid mixtures

AU - Kim, Changho

AU - Nonaka, Andy

AU - Bell, John B.

AU - Garcia, Alejandro L.

AU - Donev, Aleksandar

PY - 2018/8/28

Y1 - 2018/8/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85052842136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052842136&partnerID=8YFLogxK

U2 - 10.1063/1.5043428

DO - 10.1063/1.5043428

M3 - Article

VL - 149

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084113

ER -