Viscoplastic sheets and threads

A theory is presented for the dynamics of slender sheets of viscoplastic fluid. First a model suitable for relatively small curvature is presented and applied to the fall of a liquid bridge supported at its two ends. Second, order-one curvatures are considered, along with the sagging of a beam with a free end that is either emplaced or extruded horizontally. We then present a theory combining both limits of curvature, and consider the buckling of a nearly vertical column. Analogous models for a circular viscoplastic thread are also discussed.

► A theory is presented for slender viscoplastic sheets and threads.
► Yield stresses are shown to halt the fall of a viscoplastic catenary and the sagging of a horizontal beam.
► The shape of a horizontally extruded sheet is calculated, along with the buckling of a vertically extruded column.