Capillary Filling Dynamics in Polygonal Tubes
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911316012171264 |
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| author | Zhao, Chen Huang, Yu Chen, Tingxuan Li, Jiaxuan Zhou, Jiajia Doi, Masao |
| author_facet | Zhao, Chen Huang, Yu Chen, Tingxuan Li, Jiaxuan Zhou, Jiajia Doi, Masao |
| contents | We study the dynamics of capillary filling in tubes of regular polygon cross-section. Using Onsager variational principle, we derive a coupled ordinary differential equation and partial differential equation, which respectively describe time evolution of the bulk flow and the saturation profile of the finger flow. We obtain both numerical solution and self-similar solution to the coupled equations, and the results indicate that the bulk flow and the finger flow both follow the $t^{1/2}$ time-scaling. We show that due to the coupling effect of the finger flow, the prefactor for the bulk flow is smaller than that of the Lucas-Washburn prediction. The reduction effect is more pronounced when the side number $n$ of the regular-polygon is small, while as $n$ increases, the prefactor approaches Lucas-Washburn prediction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Capillary Filling Dynamics in Polygonal Tubes Zhao, Chen Huang, Yu Chen, Tingxuan Li, Jiaxuan Zhou, Jiajia Doi, Masao Fluid Dynamics Soft Condensed Matter We study the dynamics of capillary filling in tubes of regular polygon cross-section. Using Onsager variational principle, we derive a coupled ordinary differential equation and partial differential equation, which respectively describe time evolution of the bulk flow and the saturation profile of the finger flow. We obtain both numerical solution and self-similar solution to the coupled equations, and the results indicate that the bulk flow and the finger flow both follow the $t^{1/2}$ time-scaling. We show that due to the coupling effect of the finger flow, the prefactor for the bulk flow is smaller than that of the Lucas-Washburn prediction. The reduction effect is more pronounced when the side number $n$ of the regular-polygon is small, while as $n$ increases, the prefactor approaches Lucas-Washburn prediction. |
| title | Capillary Filling Dynamics in Polygonal Tubes |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2512.11553 |