Thermodynamically consistent hydrodynamic models of multi-component compressible fluid flows

We present a systematic derivation of thermodynamically consistent hydrodynamic models for multi-component, compressible viscous fluid mixtures under isothermal conditions using the generalized Onsager principle and the one-fluid multi-component formulation. 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 that one compressible model reduces to the quasi-incompressible model via a Lagrange multiplier approach. Several different approaches to arriving at the quasi-incompressible model are discussed. Finally, we conduct a linear stability analysis on all the binary fluid models derived in the paper to show the differences of the models in near equilibrium dynamics.