The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the influence of gravity

Abstract

The shape of a two-dimensional liquid curtain issuing from a slot and falling under the influence of gravity is predicted theoretically and verified experimentally for cases where a pressure is applied to the curtain. A set of approximate equations is derived which governs the location of the curtain for a liquid having surface tension σ, density ρ, volumetric flow per unit width Q, and local free-fall velocity V. These equations possess a singularity at the point where the local Weber number, We = ρQV/2σ, is equal to 1. Despite the fact that previous work on the stability of two-dimensional curtains shows that curtains having locations where We < 1 are unstable to small disturbances, our experiments show that these curtains can exist over a wide range of flow conditions. Thus, it is necessary to consider how the singularity is resolved when a pressure is applied.It is found that the singularity can be eliminated from the governing equations if the curtain assumes a definite direction as it leaves the slot. By contrast, if the curtain leaves the slot such that We > 1, there is no such restriction, and experimentally it is found that the curtain leaves parallel to the slot walls. The theoretical predictions of the curtain shapes are in agreement with those measured experimentally for all Weber numbers investigated.