Vorticity breakup

RDC Column. The rotating disc contactor (Fig. 19) provides for redispersion by a series of discs along the shaft, combined with a series of fixed stators. Vortices are formed in each compartment, and the shear of the fluid against the rotor or stator causes the drop breakup. In many instances. 

PIm, power per mass (W/kg). The maximum value for this parameter is calculated for the zone with the highest degree of turbulence. In most cases it takes place in the vortices formed behind the impeller blades. The most important microscale phenomena, such as drop breakup, breaking of crystals, nucleation, and efficient micromixing, take place in these zones. The ratio (P/m) / P/m) is one of the reactor s fingerprints. 

Figure 29.6 shows an example of one of the 2D droplet deformation studies carried out specifically for the purpose of modeling the LnCT by Sarchami et al. [9]. The flow conditions for this case are more extreme than can be handled by the theoretical methods for droplet deformation. As the figure shows, not only can these types of results be used to obtain information about jet deformation and trajectory, but they also provide an estimate for the size of the droplets and ligaments that form due to shear breakup at the tips of the elongated cross section. They also show the pattern of the flow field around the droplet. Of particular interest are the double vortices that form behind the droplet and help stretching it out and into a thin shape. The formation of these vortices can play an important role in the secondary atomization processes of the droplets formed in the lee-side of the jet (2D drop). 

In turbulent flows, large scale eddies with coherent structmes are primarily responsible for the mixing of passive scalars. The large scale eddies embody themselves in the form of identifiable and organized distributions of vorticity. In addition, the mixing process involves all mechanisms typically found in vortex dynamics, such as stretching, breakup, concatenation, and self-induction of... 

Figure 19.6 Microscopy images of droplet breakup in systems with viscoelastic components (a) breakup along the vorticity direction for viscoelastic droplet in Newtonian matrix with p = 0.64. Migler [79]. Reproduced with permission of American Institute of Physics, (b) Parallel sheet breakup for viscoelastic droplet in viscoelastic matrix with p = 8.6. Lin et al. [82]. Reproduced with permission of lohn WUey and Sons, (c) Sheet breakup via tip formation for viscoelastic droplet in viscoelastic matrix atp = 5.1. Lin and Sundararaj [83]. Reproduced with permission of Elsevier, (d) Dropleterosionfor viscoelastic droplet in viscoelastic matrix ip = 8.8. Linetal. [81]. Reproduced with permission of John Wiley and Sons.

Cherdhirankorn T et al. Dynamics of vorticity stretching and breakup of isolated viscoelastic droplets in an immiscible viscoelastic matrix. Rheol Acta 2004 43(3) 246-256. 

The deformation and breakup of Boger-fluid drops in Newtonian liquids under simple shear flow were investigated by direct visualization using a specially designed Couette apparatus which enables visuahzation from two different directions (i.e. to get a 3-D image). Four types of breakup modes were observed. Boger-fluid drops ean break up in simple shear flows along the flow axis or the vorticity axis. The breakup mode was foimd to depend on drop size, viscosity ratio, interfacial tension, matrix viscosity and drop phase viscoelasticity. 

Drop deformation and breakup plays a decisive role in the evolution of polymer blend morphology. The breakup mechanism during polymer blending is very complex and is influenced by many variables, such as shear stress, viscosity ratio, stress ratio, Deborah numbo-and first normal force difference [1-3]. Visualization was used to get realtime information during the drop deformation and breakup process [1-5]. It is shown that drops can break up in simple shear flow via different modes such as breakup in the flow axis, erosion, parallel breakup, tip streaming and breakup along the vorticity axis [1-7]. 

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