Development of mixing indices for optimization and scale-up of polymer processing equipment

Mixing is an important component of polymer processing operations as material properties are highly influenced by the quality of mixing. New and better mixing criteria are needed to assess dispersive and distributive mixing efficiency in polymer processing equipment and can serve the purpose of process optimization and machine scale-up. In this work new mixing criteria are developed and applied to a twin-flight single screw extruder. Computer simulations based on the finite element method calculate the flow field, and a particle tracking algorithm is used to determine particle positions and trajectories.; The history of flow strength and shear stresses experienced by a number of particles serve as the basis to produce temporal distributions of these parameters. These temporal distributions can characterize the overall dispersive mixing efficiency of the mixer. The histories are also used with a kinetic model of erosion to calculate the parent agglomerate size distribution and average parent agglomerate size. This examines the dispersive mixing capability of a mixing device for a specific polymer/powder pair.; The spatial distribution of particles at the exit of the extruder serve as the basis in developing new distributive mixing indices. We calculate the Renyi entropies, which are a function of a parameter β, using particle concentrations in equal area domains of the mixer 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 and the results show good agreement.; We also examine chaotic features of flow in the extruder via Poincaré sections and Lyapunov exponents. The time evolutions of the Renyi entropy of β = 1 of the 3-D spatial distribution of particles for different initial conditions are followed. Linear and logarithmic curve fits applied to the curves are used to correlate entropy and chaos via the Kolmogorov-Sinai entropy rate and Pesin's theorem.