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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.14049 |
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| _version_ | 1866917148392161280 |
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| author | Bhagat, Rajesh Kumar |
| author_facet | Bhagat, Rajesh Kumar |
| contents | Hydraulic jumps in thin films are traditionally explained through gravity-driven shallow-water theory, with surface tension assumed to play only a secondary role via Laplace pressure. Recent experiments, however, suggest that surface tension can be the primary mechanism. In this work we develop a theoretical framework for surface tension driven hydraulic jumps in planar thin-film flows. Starting from the full interfacial stress conditions, we show that the deviatoric component of the normal stress enters at leading order and fundamentally alters the balance. A dominant-balance analysis in the zero-gravity limit yields parameter-free governing equations, which admit a similarity solution for the velocity profile. Depth-averaged momentum conservation then reveals a singularity at unit Weber number, interpreted as the criterion for hydraulic control. This singularity is regularised by a non-trivial pressure gradient at the jump. This work establishes the theoretical basis for surface-tension-driven hydraulic jumps, providing analytical predictions for the jump location and structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The influence of surface tension in thin-film hydrodynamics: gravity free planar hydraulic jumps Bhagat, Rajesh Kumar Fluid Dynamics Mathematical Physics Hydraulic jumps in thin films are traditionally explained through gravity-driven shallow-water theory, with surface tension assumed to play only a secondary role via Laplace pressure. Recent experiments, however, suggest that surface tension can be the primary mechanism. In this work we develop a theoretical framework for surface tension driven hydraulic jumps in planar thin-film flows. Starting from the full interfacial stress conditions, we show that the deviatoric component of the normal stress enters at leading order and fundamentally alters the balance. A dominant-balance analysis in the zero-gravity limit yields parameter-free governing equations, which admit a similarity solution for the velocity profile. Depth-averaged momentum conservation then reveals a singularity at unit Weber number, interpreted as the criterion for hydraulic control. This singularity is regularised by a non-trivial pressure gradient at the jump. This work establishes the theoretical basis for surface-tension-driven hydraulic jumps, providing analytical predictions for the jump location and structure. |
| title | The influence of surface tension in thin-film hydrodynamics: gravity free planar hydraulic jumps |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2512.14049 |