# Asymptotic regimes in elastohydrodynamic and stochastic leveling on a viscous film

## TL;DR

This paper investigates the long-term behavior of an elastic sheet on a viscous film, identifying different regimes driven by elastic bending or thermal fluctuations, with a focus on how the bump size relative to the film influences the dynamics.

## Contribution

It combines scaling analysis, simulations, and experiments to characterize asymptotic regimes in elastohydrodynamic and stochastic leveling of a surface bump.

## Key findings

- Two distinct asymptotic regimes identified based on bump size.
- Crossover behavior between regimes depending on perturbation-to-film height ratio.
- Different similarity exponents observed for elastic bending and thermal fluctuation-driven flows.

## Abstract

An elastic sheet that deforms near a solid substrate in a viscous fluid is a situation relevant to various dynamical processes in biology, geophysics and engineering. Here, we study the relaxation dynamics of an elastic plate resting on a thin viscous film that is supported by a solid substrate. By combining scaling analysis, numerical simulations and experiments, we identify asymptotic regimes for the elastohydrodynamic leveling of a surface perturbation of the form of a bump, when the flow is driven by either the elastic bending of the plate or thermal fluctuations. In both cases, two distinct regimes are identified when the bump height is either much larger or much smaller than the thickness of the pre-wetted viscous film. Our analysis reveals a distinct crossover between the similarity exponents with the ratio of the perturbation height to the film height.