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arXiv · 1410.8558

An elastic plate on a thin viscous film

Philippe H. Trinh·Stephen K. Wilson·Howard A. Stone
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Abstract

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.

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Philippe H. Trinh, Stephen K. Wilson, Howard A. Stone. 2014-10-30. An elastic plate on a thin viscous film. https://doi.org/10.1017/jfm.2025.11

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