Self-similar solution for laminar bubbly flow evolving from a vertical plate
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929597410443264 |
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| author | Valle, N. Haverkort, J. W. |
| author_facet | Valle, N. Haverkort, J. W. |
| contents | The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees-Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas-specific volume instead of the gas fraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar solution for laminar bubbly flow evolving from a vertical plate Valle, N. Haverkort, J. W. Fluid Dynamics The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees-Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas-specific volume instead of the gas fraction. |
| title | Self-similar solution for laminar bubbly flow evolving from a vertical plate |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2401.13113 |