Fluctuating hydrodynamics of reactive liquid mixtures

Area of Science:

• Computational physics and chemistry
• Statistical mechanics and thermodynamics
• Fluid dynamics and reaction kinetics

Background:

• Microscopic fluctuations are crucial in systems governed by statistical mechanics and nonequilibrium thermodynamics.
• Existing methods for modeling reactive mixtures struggle with computational efficiency and accuracy at low molecule counts.

Purpose of the Study:

• To develop a fluctuating hydrodynamics (FHD) formulation for isothermal, reactive, incompressible liquid mixtures with stochastic chemistry.
• To enable efficient and accurate simulation of complex fluid dynamics coupled with chemical reactions at the mesoscopic level.

Main Methods:

• Formulated fluctuating multispecies mass diffusion using a Maxwell-Stefan description for non-dilute solutions.
• Employed a stochastic Navier-Stokes equation for fluid velocity and a thermodynamically consistent law of mass action within the chemical master equation (CME) for reactions.
• Developed and validated a numerical algorithm for solving coupled FHD and CME equations.

Main Results:

• The FHD approach demonstrates significant computational efficiency compared to traditional reaction-diffusion master equation methods, especially for large numbers of reactive molecules.
• The method maintains accuracy even with as few as ten reactive molecules per hydrodynamic cell.
• Simulations of a diffusively driven gravitational instability with an acid-base reaction showed that coupled velocity and concentration fluctuations dominate initial instability growth.

Conclusions:

• The developed FHD formulation offers a powerful and efficient framework for simulating reactive fluid systems with stochastic chemistry.
• This approach bridges the gap between microscopic fluctuations and macroscopic behavior in complex chemical and physical systems.
• The findings highlight the critical role of coupled fluctuations in the dynamics of reactive instabilities.