Fluid mixture models are essential for describing a wide range of physical phenomena, including wave dynamics and spinodal decomposition. However, there is a lack of consensus in the modelling of compressible mixtures, with limited connections between different classes of models. On the one hand, existing compressible two-phase flow models accurately describe wave dynamics, but do not incorporate phase separation mechanisms. On the other hand, phase-field technology in fluid dynamics consists of models incorporating spinodal decomposition; however, a general phase-field theory for compressible mixtures remains largely undeveloped. In this paper we take an initial step toward bridging the gap between compressible two-phase flow models and phase-field models by developing a theory for compressible, isothermal N-phase mixtures. Our theory establishes a system of reduced complexity by formulating N mass balance laws alongside a single momentum balance law, thereby naturally extending the Navier–Stokes Korteweg model to N phases and providing the Navier–Stokes Cahn–Hilliard/Allen–Cahn model for compressible mixtures. Key aspects of the framework include its grounding in continuum mixture theory and its preservation of thermodynamic consistency despite its reduced complexity.
Eikelder et al. (Mon,) studied this question.