On the geometry of rate independent droplet evolution
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866910642794921984 |
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| author | Feldman, William M Kim, Inwon C. Požár, Norbert |
| author_facet | Feldman, William M Kim, Inwon C. Požár, Norbert |
| contents | We introduce a toy model for rate-independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We consider a notion of energy solutions and show existence by a minimizing movement scheme. The main result of the paper is on the PDE conditions satisfied by general energy solutions: we show that the solutions satisfy the dynamic contact angle condition $\mathcal{H}^{d-1}$-a.e. along the contact line at every time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the geometry of rate independent droplet evolution Feldman, William M Kim, Inwon C. Požár, Norbert Analysis of PDEs 35Q35, 35R35, 35D40, 49Q20 We introduce a toy model for rate-independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We consider a notion of energy solutions and show existence by a minimizing movement scheme. The main result of the paper is on the PDE conditions satisfied by general energy solutions: we show that the solutions satisfy the dynamic contact angle condition $\mathcal{H}^{d-1}$-a.e. along the contact line at every time. |
| title | On the geometry of rate independent droplet evolution |
| topic | Analysis of PDEs 35Q35, 35R35, 35D40, 49Q20 |
| url | https://arxiv.org/abs/2310.03656 |