Periodic folding of viscous sheets

The periodic folding of a sheet of viscous fluid falling upon a rigid surface is a common fluid mechanical instability that occurs in contexts ranging from food processing to geophysics. Asymptotic thin-layer equations for the combined stretching-bending deformation of a two-dimensional sheet are solved numerically to determine the folding frequency as a function of the sheet's initial thickness, the pouring speed, the height of fall, and the fluid properties. As the buoyancy increases, the system bifurcates from forced folding driven kinematically by fluid extrusion to free folding in which viscous resistance to bending is balanced by buoyancy. The systematics of the numerically predicted folding frequency are in good agreement with laboratory experiments.