Appyling the Shooting Method to Predict the Co-extrusion Flow of Non-Newtonian Fluids Through Rectangular Ducts

Because of their versatile properties multi-layer polymer products have a high industrial relevance. Process understanding and prediction of the flow characteristics of co-extrusion, hence, is of major importance. When the shear-thinning behavior of polymer melts is to be included in modeling, there is no alternative to numerical solution methods. We present a numerical solver that is based on the shooting method to predict two-layer co-extrusion flows of non-Newtonian fluids within rectangular ducts of infinite width. The pseudo-plastic flow behavior of polymer melts is modeled by the power law according to Ostwald and de Waele. We carried out a dimensional analysis of the governing equations based on the theory of similarity, and identified four independent dimensionless parameters that fully describe the problem. To solve the dimensionless governing equations, we developed a numerical solution procedure. Additionally, we conducted an extensive parametric study by varying these independent dimensionless quantities over a wide range that covers almost all applications in industry. The numerical results offer insights into the influence of the independent parameters on, for instance, pressure gradient, (interfacial) shear stress, velocity profile, and viscosity distribution.