The investigation of shear banding polymer solutions in die extrusion geometry

This computational study investigates the shear banding phenomenon of semidilute entangled polymer solutions in an extrusion flow. A recently developed nonequilibrium thermodynamic two-fluid model in which shear banding is associated with stress-induced migration was employed. The interfoam solver of the viscoelastic package RheoTool v.2.0, an open-source toolbox based on OpenFOAM v.4.0, was utilized to solve the free-surface flow problem. The PIMPLE algorithm was used for the pressure-velocity coupling, and the convection terms were discretized using the high-resolution scheme CUBISTA. We gradually increased the uniform inlet velocity to reach the shear banding regime. As observed for the Giesekus model, the extrudate swell ratio initially decreases from the Newtonian case with increasing Deborah number. However, the slope's subsequent increase is reduced, which may be due to both the impact of shear banding and the use of a single set of relaxation times. The velocity profiles in the die change from parabolic to plug-like while entering into the shear banding regime. At the die exit region where the die wall meets the free surface, the material's boundary condition is changed from the no-slip surface to free surface, which leads to uniform velocity and stress profiles at the downstream. The polymers are pushed toward the wall in the low-shear-rate regime where Fickian diffusion is dominant. The trend in the shear banding regime is the opposite where the stress-induced migration is dominant. An important observation is that the shear banding effect on the polymer concentration is minor compared to the significant changes occurring in the die expansion region. We suggest using a broader spectrum of relaxation times in future mixed-flow calculations.