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We present a systematic derivation of thermodynamically consistenthydrodynamic phase field models for compressible viscous fluid mixtures usingthe generalized Onsager principle. By maintaining momentum conservation whileenforcing mass conservation at different levels, we obtain two compressiblemodels. When the fluid components in the mixture are incompressible, we showthe compressible model reduces to the quasi-incompressible model via a Lagrangemultiplier approach. Several equivalent approaches to arrive at thequasi-incompressible model are discussed. Finally, we conduct a linearstability analysis on all binary models and show the differences of the modelsin near equilibrium dynamics.

Thermodynamically Consistent Hydrodynamic Models of Multi-Component Fluid Flows