Droplets, breakup generation

Bentley and Leal have measured droplet shapes and critical conditions for droplet breakup over a wide range of capillary numbers, viscosity ratios, and flow types. The flow type is conveniently controlled in an apparatus called a four-roll mill, in which a velocity field is generated by the rotation of four rollers in a container of liquid (see Fig. 1-15). By varying the rotation rate of one pair of rollers relative to that of a second pair, velocity fields ranging from planar extension to nearly simple shear can be produced near the stagnation point. 

All flows can be decomposed into shear and exten-sional components. The effectiveness of the flow field is dependent on the deformation rate, the relative values of shear and extension, and the micro structure of the fluid. Extensional flows are more effective in microstructure development, such as droplet breakup and mechanochemical reactions. However, such flows are difficult to generate and to maintain and therefore, in practical applications, capillary entrance/exit flows provide a suitable means of achieving extensional flows where the shear component of the flow field changes with the capillary entry-exit angle. Indeed, OFRs also generate extensional flows, which result in efficient droplet breakup in emulsification. Mixers in which the deformation rate and the relative values of shear/extension rates can be controlled are known as controlled deformation mixers. 

Fragment size after droplet breakup is governed by/, the solution of (20.40). The solution is implemented as a numerical code that tracks the droplet and that models the gas phase using LES. Apte et al. [24] showed that the /o generated by this technique is in agreement with available experimental data. 

A review of the past literature on the available correlations on the mean droplet size produced by splash plate nozzles shows that there are large discrepancies between the results. The prediction of the droplet sizes generated by splash plate nozzles is based on the Kelvin-Helmholtz (K-H) instability theory for a liquid sheet. Dombrowski and Johns [14], Dombrowski and Hooper [18] and Fraser et al. [13] developed such a theoretical model to predict droplet sizes from the breakup of a liquid sheet. They considered effects of liquid inertia, shear viscosity, surface tension and aerodynamic forces on the sheet breakup and ligament formation. Dombrowski and Johns [14] obtained the following equation for droplets produced by a viscous liquid sheet ... 

Droplet breakup Droplet generation Droplet motion in microchannels Motion of a deformable drop in microchannels... 

Similar to the droplet breakup model in the previous section, many different vibration modes may be excited on the surface by the acceleration i (f), but the one represented by A in equation is assumed to dominate in the generation of droplets. This assumption is valid at powers just sufficient to cause the generation of droplets, but as the amplitude T is further increased, other modes may become large enough to form droplets, increasing the droplet size distribution and the complexity of analysis. 

Several mixing technologies are commercially available. Depending on the reductant injection, two general types of mixers can be defined (a) Mixers for secondary atomization combined with small scale turbulence for droplet breakup and (b) swirl or vortex generators for large scale distribution [31, 33]. 

The Enhanced-TAB (ETAB) model developed in Tanner [22] maintains the droplet deformation dynamics of the TAB model, that is droplet breakup occurs when the normalized droplet distortion y exceeds the critical value of 1. However, for each breakup event the ETAB model assumes that the rate of product droplet generation is proportional to the number of the product droplets. From this, the rate of droplet creation, in conjunction of with the mass cmiservation principle, leads to the basic ETAB law... 

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