An elastic plate on a thin viscous film
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arXiv
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| Format: | Preprint |
| Published: |
2014
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| _version_ | 1866908369434968064 |
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| author | Trinh, Philippe H. Wilson, Stephen K. Stone, Howard A. |
| author_facet | Trinh, Philippe H. Wilson, Stephen K. Stone, Howard A. |
| contents | We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity, viscosity, surface tension, and pressure forces is derived, and consists of a third-order Landau-Levich equation for the thin film, and a fifth-order beam equation for the plate. A numerical and asymptotic analysis is presented in the relevant limits of the elasticity and Capillary numbers. We demonstrate the emergence of boundary-layer effects near the ends of the plate, which are likely to be a generic phenomenon for singularly perturbed elastocapillary problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1410_8558 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | An elastic plate on a thin viscous film Trinh, Philippe H. Wilson, Stephen K. Stone, Howard A. Fluid Dynamics We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity, viscosity, surface tension, and pressure forces is derived, and consists of a third-order Landau-Levich equation for the thin film, and a fifth-order beam equation for the plate. A numerical and asymptotic analysis is presented in the relevant limits of the elasticity and Capillary numbers. We demonstrate the emergence of boundary-layer effects near the ends of the plate, which are likely to be a generic phenomenon for singularly perturbed elastocapillary problems. |
| title | An elastic plate on a thin viscous film |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/1410.8558 |