Coalescence of elastic blisters filled with a viscous fluid

Pockets of a viscous fluid that coalesce underneath a soft elastic plate is a situation encountered in a myriad of natural phenomena and engineering processes, across scales. We study such an elastohydrodynamic coalescence problem by combining experiments, lubrication theory and numerical simulations. As the pockets coalesce, a bridge is formed and further exhibits an exponential growth with time, which corresponds to a self-similar solution of the bending-driven thin-film equation governing the spatio-temporal evolution of the thickness profile. We address this exotic self-similarity, and rationalize in details the observed experimental dynamics, from the numerical simulations and scaling analysis.