Influence of initial conditions on distributive mixing in a twin flight single screw extruder

Passive advection of light particles carried by a high viscosity fluid in polymer processing equipment exhibits complex behavior due in part to the non-linearity of the equation of motion. The particles motion also exhibits sensitivity to the initial positions. A fundamental understanding of the influence of initial positions of particles on the quality and rate of distributive mixing is essential for the optimization and design of processing equipment. In this work we analyze a twin-flight single screw extruder. Based on a detailed knowledge of the flow patterns, obtained through 3-D FEM numerical simulations, we study particle motion and implicitly mixing in the extruder. In our model particles are massless points that do not affect the flow field or the motion of other particles. We visualize the complexity of the advection by using two-dimensional Poincaré-like sections. We then examine quantitatively distributive mixing for different initial locations of the light particles. Renyi entropies for different values of the parameter β were calculated and related to the various distributive-mixing characteristics they reveal. 1. Background Mixing is an important component of most polymer processing operations. Due to the high viscosity of the polymer melt, flows in such systems are characterized by low Reynolds numbers and lack of turbulence. However, as first pointed out by Aref [1, and references therein] advection of light particles in laminar flows can exhibit chaotic features, due to the geometric and operational complexity present in some systems. Advection in polymer processing equipment provides an important example of such a system. Analysis of the chaotic features and their relevance to mixing is needed for a better understanding of how to improve mixing in processing equipment. Numerical simulations of polymer processing equipment provide an effective means of analyzing the capability of a given machine. There are two types of mixing associated with polymer processing equipment: dispersive mixing and distributive mixing. We restrict this study to distributive mixing. In distributive mixing repeated rearrangement of the minor component enhances system homogeneity by reducing the scale and intensity of segregation of the system. Chaos exhibits itself through sensitivity to initial conditions [2]. Thus initial positions of the tracers should have a profound effect on distributive mixing that warrants study. We use Poincaré-like sections to identify chaotic flow features in a twin-flight single screw extruder and focus on these regions to analyze the influence of initial conditions on the minor component distribution in the system. We quantify distributive mixing by means of Renyi entropies [3, 4]. 2. Procedures and Results 2.1. Numerical simulations: In this project, we first looked at the flow patterns in a twin-flight, single screw extruder [5]. Three dimensional, isothermal Newtonian flow simulations were performed using FIDAP, a commercial computational fluid dynamics package from Fluent Inc. The physical parameters of the extruder are given in consistent dimensionless length units. The radius of the