Effect of Orientation on Distributive Mixing - Erwins Ideal Mixer

1 Effect of Orientation on Distributive Mixing — Erwin s Ideal Mixer 

Erwin [8] developed the theoretical background to assess the effect orientation has on the distributive mixing in single screw extruders. His starting point was the equation that relates the growth of an interface between fluids undergoing shear flow (Fig. 6.43), and described 

For a simple geometry (/ = 0) undergoing simple shear flow, the above equation simplifies to 

Let us consider the best case scenario, where the initial angle a = 0. During shear, the surface is reoriented and will eventually approach 90° hence, the mixing becomes very ineffective as the fluid interfaces are deformed. However, if during the flow, where the total shear, 7, is imposed upon the surfaces, the flow is interrupted in the middle so that the surface can be reoriented back to the initial position, we get 

If the flow is interrupted twice, dividing the total shear into 3 sections we get 

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