Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics
We present a constructive paradigm to derive thermodynamically consistent models coupling the bulk and surface dynamics hierarchically following the generalized Onsager principle. In the model, the bulk and surface thermodynamical variables are allowed to be different and the free energy of the mode...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Online Access: | https://www.mdpi.com/1099-4300/24/11/1683 |
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| author | Xiaobo Jing Qi Wang |
| author_facet | Xiaobo Jing Qi Wang |
| author_sort | Xiaobo Jing |
| collection | DOAJ |
| description | We present a constructive paradigm to derive thermodynamically consistent models coupling the bulk and surface dynamics hierarchically following the generalized Onsager principle. In the model, the bulk and surface thermodynamical variables are allowed to be different and the free energy of the model comprises the bulk, surface, and coupling energy, which can be weakly or strongly non-local. We illustrate the paradigm using a phase field model for binary materials and show that the model includes the existing thermodynamically consistent ones for the binary material system in the literature as special cases. In addition, we present a set of such phase field models for a few selected mobility operators and free energies to show how boundary dynamics impart changes to bulk dynamics and vice verse. As an example, we show numerically how reactive transport on the boundary impacts the dynamics in the bulk using a reactive transport model for binary reactive fluids by adopting a structure-preserving algorithm to solve the model equations in a rectangular domain. |
| first_indexed | 2024-03-09T18:20:59Z |
| format | Article |
| id | doaj.art-c85548860e65476d9aa53106ddf57fdd |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T18:20:59Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c85548860e65476d9aa53106ddf57fdd2023-11-24T08:19:09ZengMDPI AGEntropy1099-43002022-11-012411168310.3390/e24111683Thermodynamically Consistent Models for Coupled Bulk and Surface DynamicsXiaobo Jing0Qi Wang1Beijing Computational Science Research Center, Beijing 100193, ChinaDepartment of Mathematics, University of South Carolina, Columbia, SC 29028, USAWe present a constructive paradigm to derive thermodynamically consistent models coupling the bulk and surface dynamics hierarchically following the generalized Onsager principle. In the model, the bulk and surface thermodynamical variables are allowed to be different and the free energy of the model comprises the bulk, surface, and coupling energy, which can be weakly or strongly non-local. We illustrate the paradigm using a phase field model for binary materials and show that the model includes the existing thermodynamically consistent ones for the binary material system in the literature as special cases. In addition, we present a set of such phase field models for a few selected mobility operators and free energies to show how boundary dynamics impart changes to bulk dynamics and vice verse. As an example, we show numerically how reactive transport on the boundary impacts the dynamics in the bulk using a reactive transport model for binary reactive fluids by adopting a structure-preserving algorithm to solve the model equations in a rectangular domain.https://www.mdpi.com/1099-4300/24/11/1683thermodynamically consistent modelbinary phase field modeldynamic boundary conditionsenergy dissipation |
| spellingShingle | Xiaobo Jing Qi Wang Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics Entropy thermodynamically consistent model binary phase field model dynamic boundary conditions energy dissipation |
| title | Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics |
| title_full | Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics |
| title_fullStr | Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics |
| title_full_unstemmed | Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics |
| title_short | Thermodynamically Consistent Models for Coupled Bulk and Surface Dynamics |
| title_sort | thermodynamically consistent models for coupled bulk and surface dynamics |
| topic | thermodynamically consistent model binary phase field model dynamic boundary conditions energy dissipation |
| url | https://www.mdpi.com/1099-4300/24/11/1683 |
| work_keys_str_mv | AT xiaobojing thermodynamicallyconsistentmodelsforcoupledbulkandsurfacedynamics AT qiwang thermodynamicallyconsistentmodelsforcoupledbulkandsurfacedynamics |