Stability of oblique liquid curtains with surface tension

Oblique (non-vertical) liquid curtains are examined under the assumption that Froude number is large. As shown previously [E. S. Benilov, “Oblique with a large number,” J. Fluid Mech. 861, 328 (2019)], their structure depends on Weber number: if We < 1 (strong surface tension), Navier–Stokes equations admit asymptotic solutions describing bending upward, i.e., against gravity. In present paper, it such unstable respect to small perturbations of flow parameters at outlet: they give rise disturbance traveling downstream and becoming singular near curtain's terminal point (where runs out initial supply kinetic energy). It argued that, since instability spatially localized, curtain can be stabilized by properly positioned collection nozzle. All > bend downward stable.