Modeling Multi-phase Flow using Fluctuating Hydrodynamics

TL;DR

This paper develops a numerical model for multiphase fluid flow near the critical point using fluctuating hydrodynamics, incorporating thermal fluctuations and interfacial effects, validated through theoretical comparisons and non-equilibrium simulations.

Contribution

It introduces an extended numerical algorithm for fluctuating hydrodynamics of multiphase flows with interfacial tension near the critical point, validated against theoretical predictions.

Findings

Thermal fluctuations influence domain size and growth during spinodal decomposition.

The algorithm accurately reproduces equilibrium structure factors and capillary wave spectra.

Fluctuations significantly affect non-equilibrium phenomena like the piston effect.

Abstract

Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single component, multiphase flow in the neighborhood of the critical point. The system is modeled using a compressible flow formulation with a van der Waals equation of state, incorporating a Korteweg stress term to treat interfacial tension. We present a numerical algorithm for modeling this system based on an extension of algorithms developed for fluctuating hydrodynamics for ideal fluids. The scheme is validated by comparison of measured structure factors and capillary wave spectra with equilibrium theory. We also present several non-equilibrium examples to illustrate the capability of the algorithm to model multi-phase fluid phenomena in a neighborhood of the critical point. These examples include a study of the impact of fluctuations on the spinodal decomposition following a rapid quench, as well as the piston effect in a cavity with supercooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches.