Fluctuating hydrodynamics of reactive liquid mixtures

• Published in: The Journal of chemical physics Vol. 149; no. 8; pp. 084113 - 84131
• Main Authors: Kim, Changho, Nonaka, Andy, Bell, John B., Garcia, Alejandro L., Donev, Aleksandar
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 28.08.2018
• Subjects: Acid-base neutralization; Chemical reactions; Computational fluid dynamics; Computer simulation; Computing time; Coupling (molecular); Dilution; Fluid flow; Fluid mechanics; Gravitational instability; Hydrodynamics; Incompressible flow; Mathematical models; Nonequilibrium thermodynamics; Numerical analysis; Organic chemistry; Physics; Poisson density functions; Statistical analysis; Statistical mechanics; Variation
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.5043428

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.