Paradoxical predictions of liquid curtains with surface tension

This paper examines two-dimensional liquid curtains ejected at an angle to the horizontal and affected by gravity surface tension. The flow is, leading order, shearless viscosity, negligible. Froude number is large, so that radius of curtain's curvature exceeds its thickness. Weber close unity, forces inertia tension are almost perfectly balanced. An asymptotic equation derived under these assumptions, steady solutions explored. It shown that, for a given pair ejection velocity/angle, infinitely many exist, each representing curtain with stationary capillary wave superposed on it. These describe rich variety behaviours: in addition arching downwards, can zigzag self-intersect, even rise until initial supply liquid's kinetic energy used up. last type corresponds separatrix between upward- downward-bending -- both cases, self-intersecting (such meaningful only first intersection, after which just splashes down). Finally, suggestions made as how existence upward-bending be tested experimentally.