Thin polymeric films are usually produced in an extensional flow between an extrusion head and a chill roll. The final product is prone to several defects, such as reduced width and non-uniform thickness, and a better understanding of the whole process can improve the final product quality and reduce wastes. This work revisits the film-casting process by exploring the scaling relation between different variables, with particular focus on the width reduction (neck-in). The numerical simulations are carried out for Newtonian, Upper-Convected Maxwell and Giesekus fluids in isothermal and steady-state conditions, for varying film aspect ratio (AR; film width over length), draw ratio (DR) and Deborah number (De). The governing equations are discretized with finite-volumes in their full form (3D model) and using an approximate 2.5D model. However, the latter has been mainly used in this study, as it offered similar accuracy as the 3D model, at a much lower computational cost. The results show that the normalized film shape is independent of the aspect ratio for sufficiently high values of this parameter and that the film thickness scales with DR according to the theoretical prediction for planar and uniaxial extensional flows, in the centre and edge regions, respectively. The neck-in grows logarithmically with the draw ratio for high AR, with a De-dependent growth rate (higher De leads to lower neck-in and lower dependence on DR). There is a reasonable correlation between the neck-in and the ratio between the planar and uniaxial extensional viscosities, as well as between the neck-in and dimensionless variable M = ln(DR)/(De+δ), where δ is a constant which depends on the fluid rheology. However, none of the correlations offer a perfect fit to the neck-in and the search for such a correlation (or master curve) shall be pursued in future works.

聚合物薄膜通常在挤出头和冷却辊之间的拉伸流中生产。最终产品很容易出现一些缺陷，例如宽度减小和厚度不均匀，更好地了解整个过程可以提高最终产品质量并减少浪费。这项工作通过探索不同变量之间的比例关系重新审视了薄膜流延过程，特别关注宽度减小（缩幅）。在等温和稳态条件下，对牛顿流体、上对流麦克斯韦流体和吉塞库斯流体进行数值模拟，改变薄膜长宽比（AR；薄膜宽度与长度之比）、拉伸比（DR）和德博拉数（De）。控制方程采用完整形式（3D 模型）的有限体积并使用近似 2.5D 模型进行离散化。然而，本研究主要使用后者，因为它提供与 3D 模型相似的精度，但计算成本却低得多。结果表明，对于该参数足够高的值，归一化膜形状与纵横比无关，并且根据分别在中心和边缘区域的平面和单轴拉伸流的理论预测，膜厚度随DR变化。对于高AR ，缩幅随拉伸比呈对数增长，增长率与De相关（较高的De导致较低的缩幅和对DR 的依赖性较低）。颈缩与平面和单轴拉伸粘度之比之间以及颈缩与无量纲变量M  = ln( DR )/( De + δ ) 之间存在合理的相关性，其中δ是常数这取决于流体流变学。然而，没有任何相关性能够完美地拟合颈缩，并且应在未来的工作中寻求这种相关性（或主曲线）。