Fluctuating hydrodynamics of multispecies reactive mixtures

TL;DR

This paper develops a computational framework for fluctuating hydrodynamics in reactive multi-species mixtures, comparing stochastic chemistry models and validating results against theoretical predictions, highlighting the impact of chemical reactions on fluctuations.

Contribution

It introduces a numerical scheme for inhomogeneous reactive flows and compares two stochastic chemistry models, advancing the understanding of fluctuations in reactive mixtures.

Findings

Good agreement with theory validates the formulation.

Chemical reactions suppress long-range correlations.

Spontaneous fluctuations enhance pattern formation.

Abstract

We formulate and study computationally the fluctuating compressible Navier-Stokes equations for reactive multi-species fluid mixtures. We contrast two different expressions for the covariance of the stochastic chemical production rate in the Langevin formulation of stochastic chemistry, and compare both of them to predictions of the chemical Master Equation for homogeneous well-mixed systems close to and far from thermodynamic equilibrium. We develop a numerical scheme for inhomogeneous reactive flows, based on our previous methods for non-reactive mixtures [K. Balakrishnan, A. L. Garcia, A. Donev and J. B. Bell, Phys. Rev. E 89:013017, 2014]. We study the suppression of non-equilibrium long-ranged correlations of concentration fluctuations by chemical reactions, as well as the enhancement of pattern formation by spontaneous fluctuations. Good agreement with available theory demonstrates that the formulation is robust and a useful tool in the study of fluctuations in reactive multi-species fluids. At the same time, several problems with Langevin formulations of stochastic chemistry are identified, suggesting that future work should examine combining Langevin and Master Equation descriptions of hydrodynamic and chemical fluctuations.