Slender jets and thin sheets with surface tension

Simplified equations governing the potential flow and the shape of slender jets and thin sheets of liquid are derived, taking into account surface tension. Families of similarity solutions of these equations are introduced. For jets and for symmetrical sheets they satisfy ordinary differential equations. The properties of these similarity solutions are examined analytically and numerically. They can be used to describe the motion of a liquid sheet on a solid, the thickening and flow following the breaking of jets, the merging of two jets, the formation or closing of holes or slits in sheets, etc. Some applications to such problems are given.