Abstract
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.
Highlights
Commercial plastics manufacturing has seen outstanding advances in the property profiles of polymeric products in terms of custom tailoring to specific applications with the aim of increased profitability
We present a hybrid approach to modeling stratified co-extrusion flows of two power-law fluids through rectangular ducts
Two major types of co-extrusion techniques – which are slightly adapted to product geom etry and process design – are used in industrial multilayer plastics manufacturing: In feedblock systems, the individual melt streams are combined, and the stratified melt flow is guided through a conventional mono-extrusion die
Summary
Commercial plastics manufacturing has seen outstanding advances in the property profiles of polymeric products in terms of custom tailoring to specific applications with the aim of increased profitability. Yu and Han [8] and Han and Shetty [9] compared the numerically predicted pressure-throughput behavior to results of co-extrusion ex periments involving a rectangular duct They presented further process characteristics, such as velocity distributions and shear stress profiles. Despite the power of numerical methods in the modeling of various polymer-processing steps, their use is often limited in practical appli cations because they require considerable expertise, computational re sources and time This motivated us to develop a hybrid modeling approach to predicting various flow properties of two-layered stratified co-extrusion flows of shear-thinning fluids through rectangular ducts. Symbolic regression modeling based on genetic programming to obtain algebraic relationships between influencing parameters (e.g., geometry, and material parameters) and characteristic process quantities (e.g., pressure drop, interfacial shear stress, and interfacial position), and. Our hybrid modeling approach offers a means of gaining insights into the behavior of various co-extrusion flows in a wide range of industrial fields
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