Free liquid jets

Jet trajectory. A free liquid jet in air will describe a trajectory, or path under the action of gravity, with a vertical velocity component which is continually changing. The trajectory is a streamline consequently, if air friction is neglected, Bernoulli s theorem may be applied to it, with all the pressure terms 0. Thus, the sum of the elevation and velocity head must be the same for all points of the curve. The energy gradient is a horizontal line at distance V2/2g above the nozzle, where V is the velocity leaving the nozzle. 

Yarin, A. L. (1993) Free Liquid Jets and Films Hydrodynamics and Rheology, Longman Publishing Group. 

Abstract This chapter deals with capillary instability of straight free liquid jets moving in air. It begins with linear stability theory for small perturbations of Newtonian liquid jets and discusses the unstable modes, characteristic growth rates, temporal and spatial instabilities and their underlying physical mechanisms. The linear theory also provides an estimate of the main droplet size emerging from capillary breakup. Formation of satellite modes is treated in the framework of either asymptotic methods or direct numerical simulations. Then, such additional effects like thermocapiUarity, or swirl are taken into account. In addition, quasi-one-dimensional approach for description of capillary breakup is introduced and illustrated in detail for Newtonian and rheologically complex liquid jets (pseudoplastic, dilatant, and viscoelastic polymeric liquids). 

Keywords Capillary instability of liquid jets Curvature Elongational rheology Free liquid jets Linear stability theory Nonlinear theory Quasi-one-dimensional equations Reynolds number Rheologically complex liquids (pseudoplastic, dilatant, and viscoelastic polymeric liquids) Satellite drops Small perturbations Spatial instability Surface tension Swirl Temporal instability Thermocapillarity Viscosity... 

Summarizing, in the linear stability theory of capillary breakup of thin free liquid jets, the quasi-one-dimensional approach allows for a simple and straightforward derivation of the results almost exactly coinciding with those obtained in the framework of a rather tedious analysis of the three-dimensional equations of fluid mechanics. This serves as an important argument for further applications of the quasi-one-dimensional equations to more complex problems, which do not allow or almost do not allow exact solutions, in particular, to the nonlinear stages of the capillary breakup of straight thin liquid jets in air (considered below in this chapter). 

General Quasi-One-Dimensional Equations of Dynamics of Free Liquid Jets... 

These expressions close the system of the general quasi-one-dimensional equations of free liquid jets moving in air with arbitrary speeds. 

---