A phase-field approach to model evaporation from porous media: Modeling and upscaling
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910540400427008 |
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| author | Ghosh, Tufan Bringedal, Carina Rohde, Christian Helmig, Rainer |
| author_facet | Ghosh, Tufan Bringedal, Carina Rohde, Christian Helmig, Rainer |
| contents | We develop a phase-field model for evaporation from a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases and vapor component), momentum, and energy. In addition, the evolution of the phase field is described by the Allen-Cahn equation. In the limit of vanishing interface width, matched asymptotic expansions reveal that the phase-field model reduces to the sharp-interface model with all the relevant transmission conditions on the moving interface. An energy estimate is derived, which suggests that for the diffusion-dominated regime, energy always decreases with time. However, this is not trivial in the case of other regimes. Through numerical examples, we analyze the efficiency of the developed phase-field formulation in modeling the evaporation process. We observe that our formulation is able to capture shrinking liquid droplet, in other words evaporation. Further, the phase-field model is upscaled to the Darcy scale using periodic homogenization for the diffusion-dominated regime. The effective parameters at the Darcy scale are connected to the pore scale through corresponding cell problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13104 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A phase-field approach to model evaporation from porous media: Modeling and upscaling Ghosh, Tufan Bringedal, Carina Rohde, Christian Helmig, Rainer Analysis of PDEs Mathematical Physics 35C20, 35Q35, 35R35, 76N99, 76R50, 76S05, 76T10 We develop a phase-field model for evaporation from a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases and vapor component), momentum, and energy. In addition, the evolution of the phase field is described by the Allen-Cahn equation. In the limit of vanishing interface width, matched asymptotic expansions reveal that the phase-field model reduces to the sharp-interface model with all the relevant transmission conditions on the moving interface. An energy estimate is derived, which suggests that for the diffusion-dominated regime, energy always decreases with time. However, this is not trivial in the case of other regimes. Through numerical examples, we analyze the efficiency of the developed phase-field formulation in modeling the evaporation process. We observe that our formulation is able to capture shrinking liquid droplet, in other words evaporation. Further, the phase-field model is upscaled to the Darcy scale using periodic homogenization for the diffusion-dominated regime. The effective parameters at the Darcy scale are connected to the pore scale through corresponding cell problems. |
| title | A phase-field approach to model evaporation from porous media: Modeling and upscaling |
| topic | Analysis of PDEs Mathematical Physics 35C20, 35Q35, 35R35, 76N99, 76R50, 76S05, 76T10 |
| url | https://arxiv.org/abs/2112.13104 |