Stability of oblique liquid curtains with surface tension

  • Benilov, Eugene (University of Limerick)

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Oblique liquid curtains (those ejected from an orifice at an angle to the vertical) are examined under the assumption that the Froude number is large. As shown by \cite{Benilov19,Benilov21}, their structure depends on the Weber number: if $We<1$ (strong surface tension), the Navier--Stokes equations admit asymptotic solutions describing curtains bending upwards, i.e., against gravity. In the present work, 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 travelling 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 localised, the curtain can be stabilised by a properly positioned collection nozzle. All curtains with $We>1$ bend downwards and are shown to be stable. E. S. Benilov 2019 Oblique liquid curtains with a large Froude number. J. Fluid Mech. 861, 328-348. E. S. Benilov 2021 Paradoxical predictions of liquid curtains with surface tension. J. Fluid Mech. 917, A21.