Modeling Three-Dimensional Non-Newtonian Flows in Single-Screw Extruders

Modeling the multidimensional non-Newtonian flow of shear-thinning polymer melts in single-screw extruders generally requires the use of numerical methods. We present a heuristic approach to predicting the three-dimensional, fully developed, isothermal flow of power-law fluids in single-screw extruders that avoids complex and time-consuming numerical simulations. By applying a heuristic optimization algorithm, we approximate numerical results obtained from a comprehensive parametric design study, yielding an analytical relationship for the output-pressure gradient relationship depending on four independent parameters: (i) height-to-width ratio (h/w), (ii) pitch-to-diameter ratio (t/Db), (iii) power-law index (n), and (iv) dimensionless pressure gradient in the down-channel direction (πp,z). The new approach is demonstrated to provide a close approximation to numerical solutions.