Abstract
We study shear banding in a planar 4:1 contraction flow using our recently developed two-fluid model for semidilute entangled polymer solutions derived from the generalized bracket approach of nonequilibrium thermodynamics. In our model, the differential velocity between the constituents of the solution allows for coupling between the viscoelastic stress and the polymer concentration. Stress-induced migration is assumed to be the triggering mechanism of shear banding. To solve the benchmark problem, we used the OpenFOAM software package with the viscoelastic solver RheoTool v.2.0. The convection terms are discretized using the high-resolution scheme CUBISTA, and the governing equations are solved using the SIMPLEC algorithm. To enter into the shear banding regime, the uniform velocity at the inlet was gradually increased. The velocity increases after the contraction due to the mass conservation; therefore, shear banding is first observed at the downstream. While the velocity profile in the upstream channel is still parabolic, the corresponding profile changes to plug-like after the contraction. In agreement with experimental data, we found that shear banding competes with flow recirculation. Finally, the profile of the polymer concentration shows a peak in the shear banding regime, which is closer to the center of the channel for larger inlet velocities. Nevertheless, the increase in the polymer concentration in the region of flow recirculation was significantly larger for the inlet velocities studied in this work. With our two-fluid finite-volume solver, localized shear bands in industrial applications can be simulated.
Highlights
Contraction flow is of great importance in many processing operations, such as molding and extrusion of viscoelastic materials
Experimental evidence has revealed that the vortex enhancement is absent for Boger fluids while it is apparent for shear-thinning fluids [2,3]
The Deborah number is defined as De = λ1 Uout /H, where Uout is the mean velocity at the outlet
Summary
Contraction flow is of great importance in many processing operations, such as molding and extrusion of viscoelastic materials. The lip vortex originates from the re-entrant corner and dominates the flow by vortex enhancement and growth [1]. Experimental evidence has revealed that the vortex enhancement is absent for Boger fluids while it is apparent for shear-thinning fluids [2,3]. Comparisons between strain-hardening low-density polyethylene (LDPE) and strain-softening polystyrene suggest that the size and strength of the vortices are influenced by both extensional and shear properties [4,5]. The vortex size increases if the ratio of the extensional to the shear viscosity increases and vice versa [6]
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