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.

共挤出已成为几乎所有聚合物加工应用领域的最先进工艺技术。通过在多层结构中结合不同类型的聚合物材料，可以获得具有广泛性能特征的产品，用于高级应用。共挤模具和喂料块系统的设计需要广泛的工艺和材料行为知识。为了准确描述共挤出过程中聚合物熔体的剪切稀化行为并预测特征过程量，数值方法必不可少。我们提出了一种混合方法来模拟两种幂律流体通过矩形管道的分层共挤流动。通过应用相似性理论，将问题转化为无量纲表示，我们确定了四个完全描述流动情况的独立影响参数：（i）第一种流体的幂律指数，（ii）第二种流体的幂律指数，（iii）界面的无量纲位置，以及(iv) 无量纲压力梯度的比率。我们在涵盖几乎所有工业相关性组合的范围内改变这些输入参数，在此过程中创建了一组超过 44,000 个设计点。通过射击方法，获得了 (i) 压力-吞吐量行为、(ii) 界面剪切应力、(iii) 界面速度和 (iv) 个体体积流量的数值解。最后，我们使用基于遗传编程的符号回归将这些目标量建模为它们影响参数的函数，并获得它们之间的代数关系。因此，我们的数学模型能够准确预测通过矩形管道的剪切稀化流体的两层共挤出流中的几个特征过程量。这些模型不仅限于聚合物加工领域，还可以用于涉及此类共挤出流的所有工业应用。