  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
dominate the initial growth of the instability.
