Contact in fluid-plate interaction: formation and detachment

TL;DR

This paper investigates the dynamics of contact and detachment in fluid-plate interactions, demonstrating conditions under which contact forms or detaches, using a novel variational inequality approach to analyze the problem.

Contribution

It introduces a new variational inequality framework for fluid-structure interaction, proving contact detachment in finite time and the possibility of localized detachment with strong forces.

Findings

Contact can only form on a measure-zero set.

All contact detaches in finite time under certain force conditions.

Localized strong forces can detach contact at any point.

Abstract

In this paper, we study an interaction problem between an elastic plate and a compressible viscous fluid located between the rigid bottom $z=0$ and the plate. First, by utilizing the vertical fluid dissipation, we show that $\ln\eta(t) \in L^1$ for any $t>0$ provided that $\ln\eta_0\in L^1$, ensuring that additional plate contact can form only on a set of a measure zero. Then, by utilizing the expanding capability of compressible fluid pressure, we show that all contact has to detach in finite time provided that the source force acting onto the plate is not pushing down excessively. Finally, we show that contact at any point can be detached in any given time with a strong enough source force localized around that point which is pulling the plate up. The results are based on a novel variational inequality which preserves key information about the total force applied onto the plate, even in presence of contact. This is the first result where detachment of contact is proven in fluid-structure interaction.