Breakup daughter droplets

Consider drops of different sizes in a mixture exposed to a 2D extensional flow. The mode of breakup depends on the drop sizes. Large drops (R > Caa,tal/xcy) are stretched into long threads by the flow and undergo capillary breakup, while smaller drops (R Cacri,oV/vy) experience breakup by necking. As a limit case, we consider necking to result in binary breakup, i.e., two daughter droplets and no satellite droplets are produced on breakup. The drop size of the daughter droplets is then... 

If the hydrodynamic stress is sufficiently high, Ca exceeds a certain value known as the critical capillary number, CacR. Under these conditions no stable shape can persist in the flow, and the droplet deforms continually until it breaks into daughter droplets. These can undergo consequent deformations and breakups until the droplets are so small that the interfadal stress overrules the hydro-dynamic stress. At Ca < Cocr the droplets are deformed into a shape which is stable in the flow and can be also predicted by the theory of Maffetone and Minale [76]. On the other hand, at very high values of Ca (Ca CacR), a quick affine deformation of the droplets occurs and long cylindrical threads are formed which are rather stable in the flow and decay only at very high deformations or even just after the cessation of flow [77,78]. 

All droplets with a size that exceeds this critical value, will break up during flow. However, breakup is not instantaneous and a breakup time is required during which the droplet stretches irreversibly and eventually develops a neck leading to the formation of two daughter droplets and some small satellite droplets in between. This breakup time for near-critical breakup scales as [43] ... 

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