Four-roller apparatus

We now come to the final stages of morphology development (for disperse systems). Deformation and breakup of liquid droplets in a liquid matrix was first studied in series of articles by G.I. Taylor [40, 41] in 1932. Taylor first modeled the viscosity of emulsions and in a second article studied the deformation and breakup of liquid droplets. The basis of the work ofTaylor is again the concept of the interfacial tension between immiscible liquid phases (Section 6.3.2.1). Taylor [41] subsequently described experiments with paraUel-band (for shear flow) and four roller apparatus for extensional flow using individual droplets based upon combinations of... 

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. 

Taylor describes experiments with rf jr] having values of0.0003, 0.5, 0.9, and 20. He observed that, in the parallel-band apparatus that produced a shearing flow, when (t] /rf) is 0.0003 (i.e., a very low viscosity drop is placed in a high-viscosity matrix) the drop is elongated indefinitely in flow. However, (L—B)/ L+B) increases less rapidly than Tjay/K, unlike the expectation from Eq. (6.28b). In the four-roller elongational flow apparatus, the deformation of the drop (I—B)/(I + B) was a unique function of tjaE/K and obeyed Eq. (6.28b) at low stretch rates. At higher stretch rates (I—B)/(I+ B) increases less rapidly. The results were quantitatively similar to the shear flow behavior. 

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