Oblique liquid curtains with large Froude number and small Reynolds number

This paper examines two-dimensional liquid curtains ejected from a narrow horizontal outlet at an angle to the vertical. Curtains are characterised by the Froude number Fr = U/(gH)^1/2, Reynolds number Re = U H/ν and Weber number We = ρU²H/σ, where U is the ejection velocity, g the gravity, H the outlet’s half-width, ν the kinematic viscosity and σ the surface tension. It is assumed that Fr >>1 (so that the radius of the curtain’s curvature due to gravity exceeds H), Re <<1 (viscosity is strong) and We ∼ 1 (surface tension is on par with inertia). It is shown that steady oblique curtains exist only subject to a constraint of the form We > f (Fr²Re), which is more restrictive than the previously known constraint We > 1. Thus, sufficiently strong viscosity and/or surface tension eliminate the steady regime and make the curtain evolve – typically, rotate around the outlet, eventually producing the teapot effect.