Abstract
A theoretical tool for the optimum design of a mixer, and visualization and quantification of mixing performance, is presented. Visualization of the mixing performance is based on the kinematic theory of mixing rate proposed by Ottino, and it gives a map of the distribution of local mixing efficiency which illustrates the local mixing information throughout the flow domains. As application examples of the visualization technique, the mixing mechanisms of Couette flow and circulating flow are illustrated and explained, then the geometry optimization of a common pin mixing section used for screw extruders is carried out. The quantification of mixing performance is obtained by tracking and accumulating the local mixing histories of a number of particles to discriminate the mixing ability among several mixers with similar configurations. The influence of the height of a pin in a cavity on mixing is investigated using this approach. The results show that with an increase in the height of the pins, the mixing ability also increases. However, when h changes from 3/4H to 9/10H, an inflection occurs. The results also show that only if these particles are evenly distributed throughout the flow domains will the calculated values of mixing ability in different initial locations start to agree. This tool appears to be generally applicable to mixers but requires knowledge of the velocity field.
