Breakup of droplets

Tjahjadi, M., and Ottino, J. M., Stretching and breakup of droplets in chaotic flows. J. Fluid Mech. 232,191-219 (1991). 

Detailed modeling study of practical sprays has a fairly short history due to the complexity of the physical processes involved. As reviewed by O Rourke and Amsden, 3l() two primary approaches have been developed and applied to modeling of physical phenomena in sprays (a) spray equation approach and (b) stochastic particle approach. The first step toward modeling sprays was taken when a statistical formulation was proposed for spray analysis. 541 Even with this simplification, however, the mathematical problem was formidable and could be analyzed only when very restrictive assumptions were made. This is because the statistical formulation required the solution of the spray equation determining the evolution of the probability distribution function of droplet locations, sizes, velocities, and temperatures. The spray equation resembles the Boltzmann equation of gas dynamics[542] but has more independent variables and more complex terms on its right-hand side representing the effects of nucleations, collisions, and breakups of droplets. 

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. 

Breakup of droplets at the instant that a critical deformation stage has been attained... 

Rumscheidt and Mason [14] described particle deformation in a shear field as a function of viscosity ratio (p). There is a minimum and a maximum viscosity ratio where it becomes impossible to reduce the droplet size. The limits described by Karam and Bellinger [15] are 0.005 and 4. Breakup of droplets readily occurs when the viscosity ratio is of the order of 0.2 1. Intuitively, a ratio of 1 would be best because in this case there is a maximum transfer of energy between the... 

Effect of Flow Velocity. The flow velocity determines the shear rate and the pressure gradient. Therefore, the magnitude of a viscous force acting on a water droplet is directly related to flow velocity. This viscous force determines whether droplets can pass through pore throats smaller than themselves. It is also a factor in breakup of droplets into smaller droplets. 

C. Arcoumanis, D. S. Whitelaw, J. H. Whitelaw Breakup of Droplets of Newtonian and Non-Newtonian Fluids, Atom. Sprays 6, 245-256 (1996). 

The breakup of droplets released from a nozzle into the air mainly can be categorized according the following different regimes. 

The first serious investigations of the breakup of drops of polymer solutions were by Chin and Han [82], who were concerned with the influence of viscoelasticity. Subsequent studies of the breakup of droplets of polymer solutions in liquid fluid matrix were by Elmendorp [52]. Some discrepancies with Tomotika s theory were found and filaments seem generally more stable. Elmendorp also considered experiments with molten polymer filaments in a polymer matrix. Specifically, he looked at the systems (polyethylene)/(polystyrene), (polyethylene)/(polypropylene), and (polyethylene)/(polyamide-6). The filaments exhibited breakup characteristics in agreement with Tomotika s theory (Figure 6.6). 

Stone and Leal found that the surfactant tended to concentrate near the poles of the droplet. This tended to reduce the surface tension at the poles, which, in turn, caused more deformation at the poles. They studied the breakup of droplets and determined critical capillary numbers. 

Kolmogoroff, A. N. (1949). The breakup of droplets in a turbulent stream, Dokl. Akad. Nauk, 66, 825-828. 

Finally, an important aspect for polymer processing is the fact that the uniqueness of Stokes flow is lost when dealing with viscoelastic liquids. As a consequence, the breakup of droplets in systems with a viscoelastic matrix has been found to be largely dependent upon the shear flow history, with more... 

Similar to the breakup of droplets, both the critical breakup time and the critical breakup length should be exceeded in order for fibril breakup to occur. 

Lerdwijitjarud W, Sirivat A, Larson RG. Influence of dispersed-phase elasticity on steady-state deformation and breakup of droplets in simple shearing flow of immiscible polymer blends. J Rheol 2004 48(4) 843-862. 

Various processes take place during emulsification [45] breakup of droplets, adsorption of sinfactant molecules, and droplet collisions (which may lead to coalescence and larger droplets). These processes may occur simultaneously during emulsification, as the time scale for each step is very small (microseconds). Breaking of drops is feasible if the deforming force exceeds the Laplace pressure, / l (the difference between the pressure inside and outside the droplet), which is the interfacial force that acts against droplet deformation ... 

---