Hydrodynamic flutter and free-surface breakup of a retracting elastic sheet

Abstract

We study the hydrodynamic flutter and wrinkling of a retracting elastic sheet and the resulting interfacial flow phenomena. A simple experimental model is constructed in which the elastic sheet is initially stretched and floats on a free surface. When the sheet retracts rapidly from the initially stretched state, the imbalance of the shear stresses exerted on the sheet causes the tip to flutter. Because of this tip flutter, the free surface becomes unstable, breaking up into separated liquid ligaments, and the tip flutter wavelength matches the spacing of the liquid ligaments. Furthermore, the contraction of the sheet induces the formation of wrinkles, particularly when the length of the retracting sheet becomes less than its original length. The tip flutter and wrinkle wavelengths increase with the bending rigidity and original length of the sheet, while they decrease with the initial strain of the sheet. A scaling relation between the experimental parameters and wavelengths is also established, using the balance between the dominant forces for each of the retraction and tip flutter/wrinkling processes.