*Article* **A Multi-Rheology Design Method of Sheeting Polymer Extrusion Dies Based on Flow Network and the Winter-Fritz Design Equation**

**Amin Razeghiyadaki <sup>1</sup> , Dongming Wei 1,\*, Asma Perveen <sup>2</sup> and Dichuan Zhang <sup>3</sup>**


**Abstract:** In the polymer sheet processing industry, the primary objective when designing a coathanger die is to achieve a uniform velocity distribution at the exit of the extrusion die outlet. This velocity distribution depends on the internal flow channels of the die, rheological parameters and extrusion process conditions. As a result, coat-hanger dies are often designed for each polymer based on its individual rheological data and other conditions. A multi-rheology method based on a flow network model and the Winter–Fritz equation is proposed and implemented for the calculation, design and optimization of flat sheeting polymer extrusion dies. This method provides a fast and accurate algorithm to obtain die design geometries with constant wall-shear rates and optimal outlet velocity distributions. The geometric design when complemented and validated with fluid flow simulations could be applied for multi-rheological fluid models such as the power-law, Carreau– Yasuda and Cross. This method is applied to sheet dies with both circular- and rectangular-shaped manifolds for several rheological fluids. The designed geometrical parameters are obtained, and the associated fluid simulations are performed to demonstrate its favorable applicability without being limited to only the power-law rheology. The two such designed dies exhibit 32.9 and 21.5 percent improvement in flow uniformity compared to the previous methods for dies with circular and rectangular manifolds, respectively.

**Keywords:** polymer processing; sheet die design; manufacturing process design; coat-hanger die; modeling; rheology; constant shear-rate die; non-Newtonian fluids
