A liquid compound jet

Abstract

The principle and basic physics of a new type of liquid-in-air jet are described. This jet is generated by a primary fluid jet that emerges from a nozzle below the surface of a stationary (secondary) fluid. After breaking the surface, the jet consists of the central primary jet surrounded by a sheath of secondary fluid which has been entrained by the primary jet during its passage through the secondary fluid. Normally the flow in this compound jet is laminar, and it breaks up into drops due to capillary instability.In this paper the generation of compound jets is discussed, and the flow pattern in the jet is studied experimentally both in stable and unstable conditions. Three different types of instabilities can be elicited on the jet. The jet mechanism is described quantitatively, and expressions for the jet velocity and some other parameters are derived.

Nonlinear Instability and Breakup of a Viscous Compound Liquid Jet

“…This is expected to be still valid for the liquid-cored jet. In the following, unless noted otherwise, we take Wb = 47.9, Re = 395, ρ = 1, σ = 2.6, μ = 1,ū 1 =ū 2 = 1,h 1 = 0.485 andh 2 = 1 as the basic parameters according to the experiment for the liquid-cored jet (4) .…”

“…It is also found that the variation of ω c slightly depends upon the phase for both cases and ω c for (I) is a little larger as a whole than for (II). Since we can read ω c to be 1.5 from the experimental data (4) as is shown by the broken lines in Fig.4, it is estimated that this ω c gives η ∼ 0.05 for the case (I) and η ∼ 0.01 for the case (II). Although we cannot know the magnitude and frequencies of disturbances in the experiment in advance because the breakup appears naturally, the above rough estimation shows that the magnitude of velocity disturbances would amount to a few percent of the main…”

“…For a liquid-cored jet, Hertz and Hermanrud (4) observed two different types of encapsulation depending upon the surface tension of the interface between the core and the annular phase.…”

One-dimensional linear analysis of the compound jet

“…As we shall see, T ~ (p a /o°R°ay, where &°, p° and R° are respectively the surface tension, density and radius of the outer jet. Thus 8/R° ~ (p 2 p°/(T 0 R°y -0.16, for the values quoted in Hertz & Hermanrud (1983): a° = 2 x 10~2 N m _1 , p° = 10 3 kg m~3, E" = 3 x 10" 4 m and v = 2 x 10" 6 m 2 s -1 .…”

“…This model has been selected instead of more complicated one-dimensional models (Weber 1931;Green 1976;Entov & Yarin 1984) because, in spite of its relative simplicity, the results obtained are in agreement with experimental evidence, both in the case of single capillary jets (Pimbley & Lee 1977) and in the case of slender liquid bridges (Sanz 1983;Mcseguer & Sanz 1985). Amongst the different types of instability appearing in a compound jet (Hertz & Hermanrud 1983) we analyse capillary instability only, which is the most interesting in ink-jet printing applications in order to predict the size of the resulting drops after the jet breakup. The remaining instabilities (sinuous and varicose instability) are outside the scope of this paper, and they seem to be more easily dealt with by means of an experimental approach rather than a theoretical one.…”