High-speed breakup

Bubble stability and breakup were reviewed by Hinze (H16). Early stages in the motion and breakup of two-dimensional air bubbles in water have been followed by Rowe and Partridge (R8), using high-speed cinephotography. The initial diameter of their circular bubble was about 4 in. 

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. 

B) have found excellent correlation between the measured sizes of drops atomized by high-velocity gas streams with the equations developed by Nukiyama and Tanasawa (6L), so long as conditions are held within certain limits. The behavior of sprays of 7i-heptane, benzene, toluene, and other fuels has been studied by Garner and Henny (SB) by use of a small air-blast atomizer under reduced pressures. A marked increase in the Sauter mean diameter was obtained for benzene and toluene as compared with n-heptane, which parallels their poor performance in gas turbines. Duffie and Marshall (2B) give a theoretical analysis of the breakup characteristics of a viscous-jet atomizer and show high-speed photographs of the process. 

Joseph DD, Belanger J, Beavers GS. Breakup of a liquid drop suddenly exposed to a high-speed airstream. Int J Multiphase Flow 1999 25 1263-1303. Schlichting H. Boundary Layer Theory. New York Me Graw-Hill, 1979. Taylor GI. The intstability of liquid surfaces when accelerated in a direction perpendicular to their planes. Part I. Proc R Soc Lond 1950 A 201 192-196 also in The Scientific Papers of G.I. Taylor. Vol. 3. In Batchelor GK, eds. Cambridge University Press, 1993. 

Similar experiments were carried out in which drops that were mixtures of /i-decane and various alcohols were injected into dilute solutions of a zwitterionic (amine oxide) surfactant. Here, too, the lamellar phase was the first intermediate phase observed when the system was initially above the PIT. However, with alcohols of intermediate chain length such as /i-heptanol, it formed more rapidly than with oleyl alcohol, and the many, small myelinic figures that developed broke up quickly into tiny droplets in a process resembling an explosion.The high speed of the inversion to hydrophilic conditions was caused by diffusion of n-heptanol into the aqueous phase, which is faster than diffusion of surfactant into the drop. The alcohol also made the lamellar phase more fluid and thereby promoted the rapid breakup of myelinic figures into droplets. Further loss of alcohol caused both the lamellar phase and the remaining microemulsion to become supersaturated in oil, which produced spontaneous emulsification of oil. 

Current spray models may not have the correct physics, may have unknown limits of applicability, and may contain empirical constants. In a recent test conducted by the author and United Technologies Research Center (UTRC), models of primary atomization, secondary atomization, droplet breakup, droplet collision, and turbulent dispersion were applied to an air blast spray. The predictions were compared to experimental data taken at UTRC. The predicted drop size was as much as 35% different from the measured values [8]. In contrast to the typical conference or journal publication, the models were not adjusted to make the agreement as close as possible. They were taken from the literature as is. The conclusion is that physical models of high-speed spray behavior are still lacking, despite years of research in this area. Primary atomization, the beginning of the spray, is one area that is particularly poorly understood. 

In the beginning, the experiments of Savart showed that a laminar flow of a liquid breaks up into droplets. Savart could verify that a circular flow of liquids separates into droplets (and satellite droplets). It was however not yet realized that the surface tension was the reason for the breakup, which was found later only by Plateau. Later Rayleigh was able to enhance this theory, which was further improved by Weber. Nowadays, experimental aids as high-speed camera techniques made it possible to investigate and exploit the breakup of laminar flows in detail. 

In microfluidic devices, generally but not always (e.g., inertial effects can be significant in case of high-speed flows, for high production rates or droplet breakup situations), inertial effects are minimal, meaning that they work in small Reynolds number regimes. 

D. D. Joseph, J. Belanger, G. S. Beavers Breakup of a Liquid Drop Suddenly Exposed to a High-Speed Airstream, Inti. J. Multi. How 25(6-7), 1263-1303 (1999). 

S. S. Hwang, Z. Liu, R. D. Reitz Breakup Mechanisms and Drag Coefficients of High-Speed Vaporizing Liquid Drops, Atom. Sprays 6(3), 353-376 (1996). 

In relatively high-speed atomization, the secondary breakup of a droplet is always followed by the primary breakup. This secondary breakup can also be modeled by a standard two-phase flow procedure of BEM [68]. Murray and Heister [68] identified the three major modes for the secondary breakup, namely, nipple (1.1 < Weg < 2.5), kidney (2.5 < Weg < 3.0), and toroidal (Weg > 3.0) mode. The time required for the breakup of these modes reduces substantially as Weg increases. For the toroidal mode, the droplet rapidly flattens in a plane perpendicular to the imposed acoustic disturbance. With increasing Weg, the overall diameter of the droplet (at the atomization point) increases, while the inner diameter of the torus decreases, as shown in Fig. 18.8. Here, the Weg = 5.78 case is shown at a reduced scale for display purposes. The droplet shapes at high Weg values are consistent with those at aerodynamic shattering, which has been documented by observing the response of a droplet to a shock wave [69]. 

Atomization breakup is mainly characterized by a liquid high-speed jet which disperses into a fine spray of many single droplets directly behind the nozzle exit. A further characteristic is the arising spray cone so that the droplet trajectory is not inevitably in line with the nozzle. The ejected droplets usually exhibit a droplet size distribution rather than a constant droplet volume. The actuation is continuous and very strong which leads to very high velocities inside the nozzle. 

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