Breakup processes

Hollow-Cone Sprays. In swid atomizers, the Hquid emerges from the exit orifice ia the form of a cooical sheet. As the Hquid sheet spreads radially outward, aerodyaamic iastabiHty ioimediately takes place and leads to the formation of waves which subsequently disiategrate iato ligaments and droplets. Figure 3 illustrates the breakup process ia an annular Hquid sheet. 

Breakup in a highly turbulent field (L/velocity) ". This appears to be the dominant breakup process in distillation trays in the spray regime, pneumatic atomizers, and high-velocity pipehne contactors. 

Breakup of a low-velocity liquidjet (Ih/elocity) . This governs in special applications like prilling towers and is often an intermediate step in liquid breakup processes. 

Maximum D. This is the largest-sized particle in the population. It is typically 3 to 4 times D39 in turbulent breakup processes, per Walzel [International Chemical Engineering, 33, 46, (1993)]. It is the size directly calculated from the power/mass relationship. D39 is estimated from by... 

Wu, Ruff and Faeth12491 studied the breakup of liquid jets with holography. Their measurements showed that the liquid volume fraction on the spray centerline starts to decrease from unit atZ/<70=150 for non-turbulent flows, whereas the decrease starts at aboutZ/<70=10 for fully developed turbulent flows. Their measurements of the primary breakup also showed that the classical linear wave growth theories were not effective, plausibly due to the non-linear nature of liquid breakup processes. 

In practical fan sheet breakup processes, sheet thickness diminishes as the sheet expands away from the atomizer orifice, and liquid viscosity affects the breakup and the resultant droplet size. Dombrowski and Johns[238] considered these realistic factors and derived an analytical correlation for the mean droplet diameter on the basis of an analysis of the aerodynamic instability and disintegration of viscous sheets with particular reference to those generated by fan spray atomizers ... 

Suddenly exposed to a high-velocity gas stream, a droplet is deformed into a saucer shape with a convex surface to the gas flow. The edges of the saucer shape are drawn out into thin sheets and then fine filaments are sheared from the outer part of the sheets, which subsequently disintegrate into smaller droplets and are swept rapidly downstream by the high-velocity gas. Unstable growth of short wavelength surface waves appears to be involved in the breakup process. 21° This is known as shear breakup (Fig. 3.10)J246f... 

Formulations for SMD of secondary droplets have also been derived by other researchers, for example, O Rourke and Amsden)3101 and Reitz.[316] O Rourke and Amsden[310] used the % -square distri-bution[317] for determining size distribution of the secondary droplets. They speculated that a breakup process may result in a distribution of droplet sizes because many modes are excited by aerodynamic interactions with the surrounding gas. Each mode may produce droplets of different sizes. In addition, during the breakup process, there might be collisions and coalescences of the secondary droplets, giving rise to collisional broadening of the size distribution. 

It should be indicated that a probability density function has been derived on the basis of maximum entropy formalism for the prediction of droplet size distribution in a spray resulting from the breakup of a liquid sheet)432 The physics of the breakup process is described by simple conservation constraints for mass, momentum, surface energy, and kinetic energy. The predicted, most probable distribution, i.e., maximum entropy distribution, agrees very well with corresponding empirical distributions, particularly the Rosin-Rammler distribution. Although the maximum entropy distribution is considered as an ideal case, the approach used to derive it provides a framework for studying more complex distributions. 

Linear stability theories have also been applied to analyses of liquid sheet breakup processes. The capillary instability of thin liquid sheets was first studied by Squire[258] who showed that instability and breakup of a liquid sheet are caused by the growth of sinuous waves, i.e., sideways deflections of the sheet centerline. For a low viscosity liquid sheet, Fraser et al.[73] derived an expression for the wavelength of the dominant unstable wave. A similar formulation was derived by Li[539] who considered both sinuous and varicose instabilities. Clark and DombrowskF540 and Reitz and Diwakar13161 formulated equations for liquid sheet breakup length. 

Current breakup models need to be extended to encompass the effects of liquid distortion, ligament and membrane formation, and stretching on the atomization process. The effects of nozzle internal flows and shear stresses due to gas viscosity on liquid breakup processes need to be ascertained. Experimental measurements and theoretical analyses are required to explore the mechanisms of breakup of liquid jets and sheets in dense (thick) spray regime. 

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. 

Two-phase systems are often exposed to turbulent flow conditions in order to maximize the interfacial area of the fluids being contacted. In addition, turbulence is often present in wind tunnels and other laboratory equipment, as well as in nature where it can influence breakup processes (F5). Prediction of drop or bubble sizes in turbulent contacting equipment for any geometry and operating conditions is a formidable problem, primarily because of the inherent theoretical and experimental diflBculties in treating turbulent flows. To these difficulties, which exist in single phase systems, must be added the complexity of interaction of dispersed particles with turbulent flow fields. 

Figure 9.13. Bubble coalescence and breakup processes (a) Bubble coalescence (b) Bubble breakup.

Park, S.-J., Kim, J. K., Park, )., Chung, S., Chung, C., Chang, ). K., Rapid three-dimensional passive rotation micromixer using the breakup process, J. Micromech. Microeng. 2004, 14, 6-14. 

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