Predicting the co-extrusion flow of non-Newtonian fluids through rectangular ducts – A hybrid modeling approach

Co-extrusion has become the state-of-the-art process technology in nearly all application areas of polymer processing. By combining different types of polymeric materials within multilayer structures, products with a broad range of property profiles can be obtained for advanced applications. Design of co-extrusion dies and feedblock systems requires extensive knowledge of process and material behavior. To accurately describe the shear-thinning behavior of polymer melts in co-extrusion processes and to predict characteristic process quantities, numerical methods are essential. We present a hybrid approach to modeling stratified co-extrusion flows of two power-law fluids through rectangular ducts. By applying the theory of similarity and transforming the problem into dimensionless representation, we identified four independent influencing parameters that fully describe the flow situation: (i) the power-law index of the first fluid, (ii) the power-law index of the second fluid, (iii) the dimensionless position of the interface, and (iv) the ratio of dimensionless pressure gradients. We varied these input parameters within ranges that cover almost all combinations of industrial relevance, creating in the process a set of more than 44,000 design points. By means of the shooting method, numerical solutions were obtained for (i) pressure-throughput behavior, (ii) interfacial shear stress, (iii) interfacial velocity, and (iv) individual volume flow rates. Finally, we used symbolic regression based on genetic programming to model these target quantities as functions of their influencing parameters and obtain algebraic relationships between them. Our mathematical models thus enable accurate prediction of several characteristic process quantities in two-layer co-extrusion flows of shear-thinning fluids through rectangular ducts. The models are not restricted to the field of polymer processing, but can be used in all industrial applications that involve such co-extrusion flows.