Applying network theory to the modeling of multilayer flows in slot dies: a use case for symbolic regression-based co-extrusion prediction models

Abstract Slot dies are crucial for shaping operations in flat-film and sheet extrusion processes. For die design and process analysis, modeling of the flow within the die is essential. Alongside computational fluid dynamics (CFD) simulations, network theory – a computationally less expensive, semi-numerical approach – is used to predict, for instance, the pressure-throughput behavior and residence time. In many applications, the products extruded consist of multilayer structures that are formed from stratified flows fed into the slot die. In the absence of explicit expressions for the die conductance of co-extrusion flows, the application of network theory has hitherto been limited to mono-extrusion die flows. In this work, application of network theory was extended to include non-Newtonian two-layer co-extrusion flows in slot dies with rectangular manifold channels. First, a hybrid flow-modeling approach was employed to derive generalized symbolic regression models that predict relevant flow parameters (e.g., pressure-throughput behavior and average shear rates per layer) for two-layer slit flows of power-law fluids. These analytical expressions were then integrated into the flow network. A local power-law approach was chosen to describe the rheological behavior of the melts, for which an additional iterative loop was implemented to evaluate the average shear rate per layer (i.e., representative shear rate) for each network element. Solutions using this extended network approach are both fast and accurate, as confirmed by validation against results from CFD simulations.