Wrinkly fingers: the interaction between fluid- and solid-based instabilities in elastic-walled Hele-Shaw cells

In this fluid dynamics video, we study a two-phase flow in an elastic Hele-Shaw cell that involves two distinct fluid- and solid-based instabilities: viscous fingering and sheet buckling. We show that the relative importance of the two instabilities is controlled by a single non-dimensional parameter, which provides a measure of the elasticity of the flexible wall. We employ numerical simulations to show that for relatively stiff [soft] walls, the system's behaviour is dominated by viscous fingering [sheet buckling]. Strong interactions between the two instabilities arise in an intermediate regime and lead to the development of extremely complex fingering and buckling patterns.