Stability of a viscous liquid curtain

Abstract

The stability of a viscous liquid curtain falling down steadily under the influence of gravity is investigated. Both spatially and temporally changing disturbances are considered in the linear analysis. Only the spatially growing sinuous disturbances whose group velocity points toward upstream are unstable. The group velocity is in the upstream direction only when the Weber number of the curtain flow exceeds ½. The predicted critical Weber number agrees completely with that found experimentally by Brown (1961). The viscosity is shown to have the dual roles of increasing the amplification rate as well as the damping rate of the disturbances.