Compressible N-phase fluid mixture models
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912301841383424 |
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| author | Eikelder, M. F. P. ten van Brummelen, E. H. Schillinger, D. |
| author_facet | Eikelder, M. F. P. ten van Brummelen, E. H. Schillinger, D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compressible N-phase fluid mixture models Eikelder, M. F. P. ten van Brummelen, E. H. Schillinger, D. Fluid Dynamics Mathematical Physics Analysis of PDEs 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. |
| title | Compressible N-phase fluid mixture models |
| topic | Fluid Dynamics Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2503.24225 |