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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.01647 |
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| _version_ | 1866913199270395904 |
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| author | Boschman, Anne Espath, Luis van der Zee, Kris |
| author_facet | Boschman, Anne Espath, Luis van der Zee, Kris |
| contents | In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a bulk-surface dynamics, which is postulated on an arbitrary part $\mathcal{P}$ where the boundary $\partial\mathcal{P}$ may lose smoothness, that is, the normal field may be discontinuous at an edge $\partial^2\mathcal{P}$. The final set of equations somewhat resemble the Navier--Stokes--Cahn--Hilliard equation for the bulk and the surface. Aside from the systematical treatment based on a specialized version of the virtual power principle and free-energy imbalances for bulk-surface theories, we consider two additional ingredients: an explicit dependency of the apparent surface density on the surface thickness and mixed boundary conditions for the velocity, chemical potential, and microstructure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01647 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness Boschman, Anne Espath, Luis van der Zee, Kris Fluid Dynamics In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a bulk-surface dynamics, which is postulated on an arbitrary part $\mathcal{P}$ where the boundary $\partial\mathcal{P}$ may lose smoothness, that is, the normal field may be discontinuous at an edge $\partial^2\mathcal{P}$. The final set of equations somewhat resemble the Navier--Stokes--Cahn--Hilliard equation for the bulk and the surface. Aside from the systematical treatment based on a specialized version of the virtual power principle and free-energy imbalances for bulk-surface theories, we consider two additional ingredients: an explicit dependency of the apparent surface density on the surface thickness and mixed boundary conditions for the velocity, chemical potential, and microstructure. |
| title | A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2308.01647 |