| Popis: |
A liquid jet originating from a nozzle with radius rt breaks up into droplet; in consequence of disturbances of certain frequencies, depending on the fluid properties and the nozzle geometry. A theoretical model is developed to describe the growth of these disturbances at the jet surface. The model is based on the inviscid and irrotational Bow governed by the Laplace equation together with the kinematical and dynamical conditions at the free surface of the jet A comparison is made between the model and experimental data from literature. The model predicts a dependence on the disturbance-amplitude of the break-off mode. Contrary to other experimental results, the model predicts satellites (i.e. smaller droplets between the main larger ones) at wavelengths exceeding a critical value of (10/7)2lIr,*. The disturbances gr-ow at wavelengths more than the theoretical bound of 2fIrg. Discrepancies with experimental data are possible because of the neglect of the effect of viscosity in the theory. It is shown that the effect of viscosity on the jet can be neglected under cetain conditions. INTRODUCIION A liquid jet originating from a nozzle is sensitive to disturbances. Disturbances of certain frequencies cause the jet to break up into a series of successive droplets. There are two theoretical methods to investi- gate the behaviour of a disturbed liquid jet. The "spatial-instability" method describes the disturbance of the jet surface as a travelling wave in axial direction. The "temporal-instability" method describes the sur- face disturbance of the jet as a standing wave on an infinitely long cylinder with the nozzle at infinity. The model presented in this paper is based on spatial instability and describes the jet form close to the nozzle in the form of travelling waves with har- monic influences. The Laplace equation together with the dynamical and kinematical boundary condition for the free surface are used to describe the radius of the jet and the velocity. The model is mathematically simpli- fied by neglecting both the effects of viscosity and the surroundings. It is possible to approximate the sol- ution of the equations for the radius of the jet by the solution of a simplified fluid dynamical theory, the Cbsserat theory, which is a simplified one-dimensional theory. In this article we present an approximation for radius and velocity by Taylor series expansions with respect to the disturbance-amplitude. The break-up process depends on the surface ten- sion CT*, density p*, nozzle radius 3 and initia1 dis- turbance-amplitude S,*. The disturbances grow with time and distance from the nozzle. Piezo-crystals or mechanical vibrators can be used as sources when applied to the jet surface, the velocity or the pressure distribution in the jet. Previously published theoretical models are of a more limited use as the model presented in this paper, either because the stability analysis ignores higher harmonic effects or because these models are based on a simplified fluid dynamical theory. The spatial-in- stability method describes the physical reality better than the temporal-instability method does, whereas the first method does not impose periodic axial de- mands on the jet. The model based on spatial in- stability shows that satellites can break up before or after a main drop, dependent on the disturbance- amplitude. A condition is derived by which the influ- ences of the viscosity can be estimated and eventually neglected. |
