Elastohydrodynamics of contact in adherent sheets

TL;DR

This paper investigates the complex dynamics of adhesive contact between a thin elastic sheet and a substrate in a liquid environment, revealing how fluid flow, elasticity, and adhesion interact over time.

Contribution

It introduces a numerical analysis of the coupled elastohydrodynamic equations, providing new insights into the onset and steady propagation of adhesion fronts in such systems.

Findings

Short-time adhesion onset dynamics characterized

Steady-state adhesion front speed determined

Shape of fluid-filled bump ahead of contact identified

Abstract

Adhesive contact between a thin elastic sheet and a substrate in a liquid environment arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long wavelength elastic deformations and microscopic adhesion, and solving the resulting partial differential equation numerically, we uncover the short-time dynamics of the onset of adhesion and the long-time dynamics of a steady propagating adhesion front. Simple scaling laws corroborate our results for characteristic waiting-time for adhesive contact, as well as the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid filled bump ahead of the adhesion zone. Finally, our analysis yields the boundary conditions for the apparent elastohydrodynamic contact line, generalizing the well known conditions for static elastic contact while highlighting how microscale physics regularizes the dynamics of contact.