Abstract
Many problems in elastocapillary fluid mechanics involve the study of elastic structures interacting with thin fluid films in various configurations. In this work, we study the canonical problem of the steady-state configuration of a finite length pinned and flexible elastic plate lying on the free surface of a thin film of viscous fluid. The film lies on a moving horizontal substrate that drives the flow. The competing effects of elasticity, viscosity, surface tension, and fluid pressure are included in a mathematical model consisting of a third-order Landau-Levich equation for the height of the fluid film and a fifth-order Landau-Levich-like beam equation for the height of the plate coupled together by appropriate matching conditions at the downstream end of the plate. The properties of the model are explored numerically and asymptotically in appropriate limits. In particular, we demonstrate the occurrence of boundary-layer effects near the ends of the plate, which are expected to be a generic phenomenon for singularly perturbed elastocapillary problems.
| Original language | English |
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| Journal | Journal of Fluid Mechanics |
| Publication status | Acceptance date - 10 Dec 2024 |
Data Availability Statement
The data supporting the findings of this study are available within the paper.Acknowledgements
We thank Professors Peter Howell and Dominic Vella (University of Oxford) for valuable discussions during the course of the present work. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC-BY) licence to any Author Accepted Manuscript version arising.Funding
PHT thanks Lincoln College, University of Oxford for financial support during the early stages of this work. SKW was partially supported by a Leverhulme Trust Research Fellowship via award RF-2013-355. HAS acknowledges partial support from National Science Foundation (NSF) grant CBET 1132835.