Stretching separation

Fig. 3.2. Typical droplet-droplet collision outcome map with four regimes [88] Bouncing (Bo), Coalescence (Co), Stretching Separation (Ss), and Reflexive Separation (Rs). X denotes the impact factor, and TVe is the Weber number.

Abstract We put together the state of knowledge on binary colUsional interactions of droplets in a gaseous environment. Phenomena observed experimentally after drop collisions, such as coalescence, bouncing, reflexive separation and stretching separation, are discussed. Collisions of drops of the same liquid and of different -miscible or immiscible - liquids, as well as collisions of drops of equal and different size are addressed. Collisions of drops of immiscible liquids may lead to an unstable interaction which is not observed with drops of equal or miscible liquids. Regimes characterized by the various phenomena are depicted in nomograms of the Weber number and the non-dimensional impact parameter. The state-of-the-art in the simulation of binary droplet collisions is reviewed. Overall three different methods are represented in the literature on these simulations. We discuss models derived from numerical simulations and from experiments, which are presently in use for simulations of spray flows to account for the influence of coUisional interactions of the spray droplets on the drop size spectrum of the spray. 

Keywords Binary drop colUsions Bouncing Coalescence Collision model Crossing separation Gaseous environment Immiscible liquids Lattice-Boltzmann simulation Miscible liquids Navier-Stokes simulation Reflexive separation Satellite droplets Spray flow simulation SPH simulation Stretching separation... 

Fig. 7.6 Collisions of a water and an ethanol drop (a) head-on collision with coalescence and separation of one satellite (We =20,X = 0) (b) reflexive separation with formation of a small satellite due to Marangoni forces We = 38.5, X = 0.02) (c) stretching separation with formation of three satellite droplets (We = 82.3, X = 0.82). Droplets move from right to left the water droplet coming from above is marked with w [45] (With kind permission from Springer Science+Busi-ness Media Experiments in Fluids [45], Plates 3, 5 6, Copyright Springer-Verlag 2005)...

Stretching separation is treated accounting for the break-up behavior of the liquid filament formed between the smaller and larger colliding drop bulk masses. The liquid volume in the filament is modeled according to a separation volume coefficient Cvs defined as... 

The domain of stretching separation is slightly shifted to the right with increasing solids mass fraction and then shifted backward again for mass fractions larger than 15 %. 

The collision maps of sucrose solutions are very similar to the ones of K30, except that stretching separation mostly occurs at higher impact parameters for all mass fractions investigated, and reflexive separation disappears at a lower viscosity already. These differences might arise from the non-Newtonian characteristics of the sucrose solutions. 

Fig. 6.9 Comparison of the Jiang et al. [13] model with experimental data for the boundary between coalescence and stretching separation. Left. K30 solutions of mass Iractions of red filled...

The triple point, where botmcing, coalescence, and stretching separation cluster together on the collision map, was experimentally determined. A capillary number of 0.577 was fotmd to be a threshold value below, droplet surface tension governs the outcome of the drop collision, and above, viscous forces govern the outcome of droplet collisions. 

Hence, only coalescence and stretching separation was discovered, whereas bouncing and reflexive separation were absent. 

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