Stationary Soap Film Bridge Subjected to an Electrostatic Force: The Balanced Case
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912048399515648 |
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| author | Schmitz, Lina Sophie |
| author_facet | Schmitz, Lina Sophie |
| contents | We analytically study a stationary free boundary problem describing a soap film bridge subjected to an electrostatic force. Starting from a cylinder that the soap film forms if its surface tension and the electrostatic force are perfectly balanced, we construct a local branch of stationary solutions. Then, we prove that there is a sharp threshold value for a characteristic model parameter at which the stability behaviour of this branch switches from stable to unstable. Finally, we show that the soap film deflects monotonically outwards if the strength of the electrostatic force is increased. Besides rigorous results, we also discuss a possible balancing effect of the electrostatic force. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stationary Soap Film Bridge Subjected to an Electrostatic Force: The Balanced Case Schmitz, Lina Sophie Analysis of PDEs Dynamical Systems 35R35, 42A32, 35B35, 47J07, 35Q99 We analytically study a stationary free boundary problem describing a soap film bridge subjected to an electrostatic force. Starting from a cylinder that the soap film forms if its surface tension and the electrostatic force are perfectly balanced, we construct a local branch of stationary solutions. Then, we prove that there is a sharp threshold value for a characteristic model parameter at which the stability behaviour of this branch switches from stable to unstable. Finally, we show that the soap film deflects monotonically outwards if the strength of the electrostatic force is increased. Besides rigorous results, we also discuss a possible balancing effect of the electrostatic force. |
| title | Stationary Soap Film Bridge Subjected to an Electrostatic Force: The Balanced Case |
| topic | Analysis of PDEs Dynamical Systems 35R35, 42A32, 35B35, 47J07, 35Q99 |
| url | https://arxiv.org/abs/2409.18784 |