2025/03/31 by Marco F. P. ten Eikelder, Eikelder, M. F. P. ten, E. H. van Brummelen +3 · 3 citations
Engineering · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2503.24225
openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 modeling 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.