Droplets, breakup splitting

The Rayleigh-Taylor (RT) component has been added to the breakup model by Patterson et al. [11] to improve predictions of the secondary breakup of the droplets. The RT model predicts instabilities on the surface of the drop that grow until a certain characteristic breakup time is reached, when the drop finally breaks up. The RT waves are only allowed to form on droplets with diameters larger than the wavelength of the fastest growing disturbance. When the disturbances exceed the elapsed breakup time, the droplet is split into smaller droplets, with diameters proportional to the wavelength of the disturbances. 

Figure 11 Phenomena connected with drop breakup (a) deformation (splitting) of droplets, (b) deformation into lenticular shape, (c) development and separation of the boundary layer, (d) velocity distribution near the separation point of the boundary layer, (e) Kelvin Helmholtz instability, and (f) Rayleigh Taylor instability, pi < P2-...

A series of articles was published by Utracki et al. [318-322] on the modeling of mixing of immiscible fluids in a twin screw extruder. The fourth paper in the series [321] incorporates several refinements of the earlier model, one of the most important refinements being the incorporation of the effect of coalescence. The model considers two breakup mechanisms, both based on the micro-rheology. One breakup mechanism is the drop fibrillation and disintegration into fine droplets when the Weber number is greater than four times the critical Weber number. The second mechanism is drop splitting that occurs when the Weber number is below four times the critical Weber number. 

It is convenient to express the capillarity number in its reduced form k = k / where represents the minimum value of K sufficient to cause breakup of the deformed drop. Depending on the magnitude of k, drops do not deform, k < 0.1, deform but do not break, 0.1 2. 

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