Coalescence of elastic blisters filled with a viscous fluid

TL;DR

This paper investigates the coalescence dynamics of viscous fluid pockets beneath elastic plates, revealing exponential bridge growth and self-similar shapes through experiments, theory, and simulations.

Contribution

It introduces a combined experimental, theoretical, and numerical analysis of elasto-hydrodynamic coalescence, highlighting self-similar behaviors in the process.

Findings

Bridge height grows exponentially over time.

Self-similar shape of the coalescing bridge confirmed.

Lubrication theory accurately models the dynamics.

Abstract

Pockets of viscous fluid coalescing beneath an elastic plate are encountered in a wide range of natural phenomena and engineering processes, spanning across scales. As the pockets merge, a bridge is formed with a height increasing as the plate relaxes. We study the spatiotemporal dynamics of such an elasto-hydrodynamic coalescence process by combining experiments, lubrication theory and numerical simulations. The bridge height exhibits an exponential growth with time, which corresponds to a self-similar solution of the bending-driven thin-film equation. We address this unique self-similarity and the self-similar shape of the bridge, both of which are corroborated in numerical simulations and experiments.