On a phase field model for binary mixtures of micropolar fluids with non-matched densities and moving contact lines
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918005186756608 |
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| author | Chan, Kin Shing Hao, Baoli Lam, Kei Fong Stinner, Björn |
| author_facet | Chan, Kin Shing Hao, Baoli Lam, Kei Fong Stinner, Björn |
| contents | We introduce a new phase field model for binary mixtures of incompressible micropolar fluids, which are among the simplest categories of fluids exhibiting internal rotations. The model fulfils local and global dissipation inequalities so that thermodynamic consistency is guaranteed. Our model consists of a Navier--Stokes--Cahn--Hilliard system for the fluid velocity, pressure, phase field variable and chemical potential, coupled to an additional system of Navier--Stokes type for the micro-rotation. Our model accounts for non-matched densities as well as moving contact line dynamics, and serve as a generalisation to earlier models for binary fluid flows based on a volume averaged velocity formulation. We also establish the existence of global weak solutions in three spatial dimensions for the model equipped with singular logarithmic and double obstacle potentials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_21258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a phase field model for binary mixtures of micropolar fluids with non-matched densities and moving contact lines Chan, Kin Shing Hao, Baoli Lam, Kei Fong Stinner, Björn Analysis of PDEs 35A01, 35K35, 35Q30, 35Q35, 76D03, 76D45, 76T06 We introduce a new phase field model for binary mixtures of incompressible micropolar fluids, which are among the simplest categories of fluids exhibiting internal rotations. The model fulfils local and global dissipation inequalities so that thermodynamic consistency is guaranteed. Our model consists of a Navier--Stokes--Cahn--Hilliard system for the fluid velocity, pressure, phase field variable and chemical potential, coupled to an additional system of Navier--Stokes type for the micro-rotation. Our model accounts for non-matched densities as well as moving contact line dynamics, and serve as a generalisation to earlier models for binary fluid flows based on a volume averaged velocity formulation. We also establish the existence of global weak solutions in three spatial dimensions for the model equipped with singular logarithmic and double obstacle potentials. |
| title | On a phase field model for binary mixtures of micropolar fluids with non-matched densities and moving contact lines |
| topic | Analysis of PDEs 35A01, 35K35, 35Q30, 35Q35, 76D03, 76D45, 76T06 |
| url | https://arxiv.org/abs/2504.21258 |