Characterization of Distributive Mixing in Polymer Processing Equipment Using Renyi Entropies

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International Polymer Processing


A new method for characterization of distributive mixing in processing equipment, based on Renyi entropies, was developed. This method was applied to a twin-flight single screw extruder, in which tracer positions were determined through computer simulations of the flow field. The various entropies were calculated using particle concentrations in equal area domains of the mixer. Renyi entropies, which are function of a parameter β were calculated for extruders of different lengths. We discuss the merit of using Renyi entropies for different values of β by pointing to the different mixing characteristics they probe. The relative Renyi entropy varies between 0 and 1 and represents a measure of distributive mixing quality, with 1 corresponding to perfect mixing and 0 corresponding to poorest mixing. We compare this new method of distributive mixing characterization to traditional ones based on the concepts of Scale and Intensity of Segregation, and the calculations based on Pairwise Correlations and Correlation Sums. The results show good agreement between the relative Renyi entropy and the traditional methods. Other advantages of the Renyi entropy such as reduced calculation time and geometric independence are discussed. For the case of a twin-flight single screw extruder, it is shown that a longer extruder is not necessarily more beneficial to distributive mixing.


Wang and Manas-Zloczover acknowledge the financial support of this work by the National Science Foundation under grant DMI-9812969.