Interested in the previous work of Walters et al. (Korea Aust Rheol J 21:225–233, 2009) regarding the competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids, rheological studies rarely discuss the relationship between the shear and extension-induced first normal stress differences (N1S and N1E) within a mixed flow for a viscoelastic fluid. One, therefore, derives N1S and N1E related to Weissenberg’s number and Trouton’s ratio. The classic White–Metzner viscoelastic constitutive equation coupled with the recent GNF-X (Generalized Newtonian Fluid eXtended) weighted shear/extension viscosity has the potential to show the typical vortex growth in entry flow simulations. Based on the improved White–Metzner model, demonstrating the opposite effect of N1S and N1E with respect to strain rates is evident. N1S mainly dominates the shell layer near the wall boundary at high strain rates, whereas N1E controls the center core at low strain rates. In contraction flow simulations, the predicted slit-die velocity profile is in good agreement with experimental data. It is significant to conclude that N1E hinders flow and N1S facilitates flow. In addition, a comparison of extensional-thickening and extensional-thinning viscosity curves for the velocity profile is discussed herein.

对 Walters 等人之前的工作感兴趣。(Korea Aust Rheol J 21:225–233, 2009) 关于弹性液体复杂流动中拉伸粘度和法向应力差的竞争作用，流变学研究很少讨论剪切和拉伸引起的第一法向应力差之间的关系 (N1S和 N1E）在粘弹性流体的混合流中。因此，可以推导出与韦森伯格数和特劳顿比相关的 N1S 和 N1E。经典的 White-Metzner 粘弹性本构方程与最近的 GNF-X（广义牛顿流体扩展）加权剪切/拉伸粘度相结合，有可能在入口流模拟中显示典型的涡增长。基于改进的 White-Metzner 模型，N1S 和 N1E 对应变率的相反影响是显而易见的。在高应变率下，N1S 主要控制壁边界附近的壳层，而 N1E 在低应变率下控制中心核心。在收缩流模拟中，预测的狭缝模头速度分布与实验数据非常吻合。N1E 阻碍流动而 N1S 促进流动的结论很重要。此外，本文讨论了速度分布的拉伸增稠和拉伸稀化粘度曲线的比较。