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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.15712 |
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| _version_ | 1866916911446491136 |
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| author | Lai, Jun |
| author_facet | Lai, Jun |
| contents | Static droplets serve as fundamental benchmarks for interface-resolved simulations of two-phase flows. However, their accurate representation in phase-field models remains elusive due to persistent numerical artifacts. This work rigorously proves that static droplets cannot exist in phase-field models governed by the Cahn-Hilliard-Navier-Stokes equations. Through equilibrium analysis of the governing equations, we demonstrate that equilibrium necessitates uniform chemical potential, which nullifies the interfacial force, enforcing a uniform pressure field. This directly contradicts the pressure jump required by Laplace's law for a curved interface, proving mechanical equilibrium is impossible. The results reveal an intrinsic incompatibility between non-flat equilibrium interfaces and the Cahn-Hilliard-Navier-Stokes system, provides a fundamental theoretical explanation for long-standing paradoxes such as droplet shrinkage and parasitic currents. This fundamental limitation applies universally to droplets/bubbles and necessitates re-evaluation of phase-field models for multiphase systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic Incompatibility: Why Static Droplets Cannot Exist in Cahn-Hilliard-Navier-Stokes Systems Lai, Jun Fluid Dynamics Static droplets serve as fundamental benchmarks for interface-resolved simulations of two-phase flows. However, their accurate representation in phase-field models remains elusive due to persistent numerical artifacts. This work rigorously proves that static droplets cannot exist in phase-field models governed by the Cahn-Hilliard-Navier-Stokes equations. Through equilibrium analysis of the governing equations, we demonstrate that equilibrium necessitates uniform chemical potential, which nullifies the interfacial force, enforcing a uniform pressure field. This directly contradicts the pressure jump required by Laplace's law for a curved interface, proving mechanical equilibrium is impossible. The results reveal an intrinsic incompatibility between non-flat equilibrium interfaces and the Cahn-Hilliard-Navier-Stokes system, provides a fundamental theoretical explanation for long-standing paradoxes such as droplet shrinkage and parasitic currents. This fundamental limitation applies universally to droplets/bubbles and necessitates re-evaluation of phase-field models for multiphase systems. |
| title | Intrinsic Incompatibility: Why Static Droplets Cannot Exist in Cahn-Hilliard-Navier-Stokes Systems |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2508.15712 |