Coalescence of viscous blisters under an elastic sheet

TL;DR

This paper investigates how viscous blisters beneath an elastic sheet merge over time, combining experiments, numerical simulations, and a theoretical model to understand the dynamics and predict the coalescence behavior.

Contribution

It introduces a one-dimensional lubrication model and numerical solutions to explain the coalescence process, highlighting the role of elastic bending in the dynamics.

Findings

Coalescence speed relates to the interface curvature.

Elastic bending dominates early-stage coalescence dynamics.

The model accurately predicts the growth of the coalescence neck.

Abstract

We study the coalescence of identical viscous blisters beneath an elastic sheet both experimentally and numerically. Using a time-resolved synthetic schlieren technique, we measure the evolution of the thickness field of the merging blisters and more specifically the dynamics of the coalescence region. To explain this dynamics, we develop a one-dimensional model based on the lubrication approximation, from which we derive scalings to predict the growth of the coalescence neck. We also numerically solve the full non-linear equation to assess the theory and compare to experiments. Our model illustrates that, at short times, the dynamics of coalescence is mainly controlled by the bending of the elastic sheet, leading to a relationship between the coalescence speed and the radius of curvature of the interface at the coalescence neck.