Stability of oblique liquid curtains with surface tension

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

Automated summary

This article examines non-vertical liquid curtains with large Froude numbers. The structure of these curtains depends on the Weber number. If We < 1 (strong surface tension), the curtains bend upward against gravity. The article shows that these curtains are unstable and give rise to a downstream disturbance near the curtain's terminal point. It is argued that a properly positioned collection nozzle can stabilize the curtain. All curtains with We > 1 bend downward and are stable.