Fluctuating Hydrodynamics of Reactive Liquid Mixtures

TL;DR

This paper develops a fluctuating hydrodynamics framework for reactive liquid mixtures, combining stochastic chemistry and multispecies diffusion, enabling efficient and accurate simulations of nonequilibrium phenomena.

Contribution

It introduces a thermodynamically consistent FHD formulation for reactive mixtures with stochastic chemistry, using Maxwell-Stefan diffusion and stochastic Navier-Stokes equations.

Findings

Efficient simulation of reactive mixtures with large molecule numbers.

Accurate modeling of fluctuations even with few reactive molecules.

Validation on equilibrium and nonequilibrium problems, including gravitational instability.

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 dominate the initial growth of the instability.