A quantitative analysis of spatial extensional rate distribution in nonlinear viscoelastic flows

A numerical method is proposed to calculate local extensional rate along arbitrary streamlines measured experimentally. It leads to the calculation of a “local Deborah number” (De) field, which characterizes heterogeneous flows of polymer solutions in a more insightful way than the commonly used nominal Weissenberg number (Wi), defined by an average shear rate. The spatial distribution of non-equilibrium polymer conformation across flow domain could be visualized through an image of the De field for flows of aqueous semi-dilute polyacrylamide (PAAm) solutions through the 4:1:4, 8:1:8 and 16:1:16 planar contraction geometries, over a range of Wi(1.4⩽Wi⩽131.7) and Elasticity numbers (El) (13.3⩽El⩽476.8). The time evolution of these De fields and their profiles near the contraction plane are presented. The correlation between the maximum local De and the nominal Wi is analyzed. The results show that the vortex formation near the contraction entry coincides with shifting the position of the maximum local De away from the centerline. Its actual location is sensitive to flow rate and strongly depends on dynamic flow regime.