Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2014
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1410.8558 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- 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.