Vertical slender jets with surface tension

The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface-tension effects are included and studied. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from three different orifice shapes, which were an ellipse, a square, and an equilateral triangle. Computational results are presented illustrating the effects of different values for the surfacetension coefficient on the shape of the jet and the periodic nature of the cross-sectional shapes.