Thermodynamically Consistent Hydrodynamic Models of Multi-Component Fluid Flows

TL;DR

This paper systematically derives thermodynamically consistent hydrodynamic models for multi-component fluid flows, including compressible and quasi-incompressible cases, and analyzes their stability and dynamic differences.

Contribution

It introduces a unified derivation framework for compressible and quasi-incompressible fluid mixture models using the generalized Onsager principle.

Findings

Derived two compressible models maintaining momentum and mass conservation.

Reduced the compressible model to a quasi-incompressible model using a Lagrange multiplier.

Performed linear stability analysis revealing differences in near equilibrium dynamics.

Abstract

We present a systematic derivation of thermodynamically consistent hydrodynamic phase field models for compressible viscous fluid mixtures using the generalized Onsager principle. By maintaining momentum conservation while enforcing mass conservation at different levels, we obtain two compressible models. When the fluid components in the mixture are incompressible, we show the compressible model reduces to the quasi-incompressible model via a Lagrange multiplier approach. Several equivalent approaches to arrive at the quasi-incompressible model are discussed. Finally, we conduct a linear stability analysis on all binary models and show the differences of the models in near equilibrium dynamics.