Elongational Flow Mixing

Much of this analysis is aimed at understanding the nature of velocity profiles, shear and elongational flow behaviour of fluid elements experiencing the unique mixing action within internal mixers. Due to their importance in the rubber in-... 

If the mixing device generates a simple shear flow, as shown in Fig. 3.23, the maximum separation forces that act on the particles as they travel on their streamline occur when they are oriented in a 45° position as they continuously rotate during flow. However, if the flow field generated by the mixing device is a pure elongational flow, such as shown in Fig. 3.24, the particles will always be oriented at 0° the position of maximum force. 

The convergent flow at the die entrance provides strong elongational flow. In 1989 Laun and Schuch, derived for Newtonian liquids that P = 1.640j2, The relation is satisfactory for homopolymers, but for the blend, the prediction is about one decade too low. On the other hand, this type of flow provides excellent means for mixing highly viscous dispersed phase. An extensional... 

Better mixing is obtained in the extensional than in the shear flow. The elongational flow field exists anywhere where the streamlines are not parallel. 

Mixing rheology - elongational flow. The above considerations are obviously oversimplified and neglect the particular behaviour of viscoelastic materials. On one hand, we have already pointed out that it is difficult to introduce the more realistic viscosity function n = f ( y> T), and,on the other hand, it is quite clear that the mixing process is not isothermal. Furthermore, Tokita and White (13, 14) demonstrated that the lubrication theory can be applied to a nip of length L and depth H providing that... 

The importance of extensional flow in the mixing process has been pointed out by Gotten (16) and thoroughly analyzed by Nakajima (8) in the case of carbon black-filled compounds. A steady elongational flow can be developed only if the extensional rate increases exponentially (versus time) (17). Nakajima demonstrated that this type of deformation induces an anisotropy of the material, enhanced in highly filled compounds or containing oriented fibers. Therefore, the steady state is nearly impossible and, with polymers, the elongational flow is not a pure deformation and necessarily involves a shear component. 

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