Thermodynamically-consistent formulation of stochastic chemistry for modeling reactive gas dynamics at small scales

While the mean behavior of a fluid is well captured by deterministic fluid equations such as compressible Navier-Stokes equations down to micro and nanoscales, random molecular motions of fluid particles elicit thermal fluctuations at these small scales in the continuum description. In reactive fluid systems, these spontaneous fluctuations can grow beyond the microscale due to the interaction with the nonlinearity of chemical reactions, potentially impacting the macroscale behavior of the fluid. In this work, we develop a simulation method for reactive gas mixtures at small scales. To this end, we incorporate the chemical Langevin equation description of stochastic chemistry into the fluctuating hydrodynamics equations for the mesoscopic fluid description. We derive a thermodynamically-consistent stochastic chemistry formulation, where the temperature-dependence of the rate constants are correctly included. We validate our formulation and implementation by using an equilibrium gas mixture system undergoing a reversible dimerization reaction. We demonstrate that the correct temperature dependence of the rate constants is essential for achieving thermodynamic consistency even in a system with small temperature fluctuations.