Stability of initially slow viscous jets driven by gravity

Abstract

The stability of vertically falling viscous liquid jets issuing from a circular orifice with a low fluid velocity where the flow is dominated by viscous effects torn down by gravity leading to a flow dominated by inertia far downstream, is studied by means of linear stability analysis as well as direct numerical simulation of the one-dimensional model. Jet stability is also studied experimentally. Results for marginal stability and critical frequencies are in excellent agreement with our theoretical predictions. A new global instability of a viscous jet is found. This instability is observable whenever a falling liquid jet exhibits a long enough viscosity dominated region. The source of instability is surface tension. In contrast to the Rayleigh capillary instability that is always present, but leads to very long disintegration lengths in highly viscous fluid jets, the instability described here only occurs when the volume flux falls below a certain limit depending on the fluid properties and the nozzle diameter.