Folding fluid curtains

A sheet or ``curtain'' of viscous fluid falling onto a surface forms a pile of regular folds. Using silicone oil falling through a slot at the base of a reservoir, we have performed laboratory experiments to determine how the folding amplitude and frequency depend on the slot geometry, the fall height, the flow rate, and the fluid properties. A scaling analysis of the data that corrects for the surface tension-induced narrowing of the curtain shows that folding can occur in two limiting regimes. At low heights, ``gravitational'' folding occurs in which the viscous forces that resist folding are balanced by gravity. At great heights, the viscous forces are balanced by inertia (``inertial'' folding). At intermediate heights, we observe a transitional regime characterized by frequency multiplicity and hysteresis effects. We interpret these results in terms of the eigenmodes of an oscillating moment-free liquid sheet that is strongly stretched by gravity. We will also present a simple numerical model for the shape of the narrowing curtain, and compare its predictions with our observations.