Asymptotic analysis of die flow for shear‐thinning fluids

The flow in a single‐cavity extrusion die is considered by using 1‐D equations. Since the fluid flow in a well‐performing die does not deviate much from the case of perfect widthwise distribution, linearization of 1‐D governing equations is often justified. It is demonstrated how linearization can lead to significant simplifications in the analysis of die flow. A self‐consistent asymptotic expansion is identified to accomplish this linearization; the expansion can be generalized to obtain higher‐order corrections if necessary. In contrast to previous analyses, which have generally been numerical, analytic solutions are obtained to predict widthwise flow nonuniformities in a die having a specific cavity area variation and in which cavity inertial effects are important; these solutions are valid for power‐law and Newtonian fluids. A novel truncated power‐law approach to modeling the flow of shear‐thinning fluids in a die is proposed that combines, by using analytical criteria, the solutions for purely Newtonian or power‐law flow in the cavity and slot. The validity of this approach is demonstrated through comparison with numerical results of a 1‐D die model for a Carreau constitutive equation.