Shear Banding in 4:1 Planar Contraction

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.

An Experimental Investigation of Viscoelastic Flow in a Contraction Channel

“…Moreover, we observe a large rotating vortex appears in the salient corner of the upstream channel (See Figure 7 b), which is the typical feature of the LDPE melts flowing through a contraction channel. The corner vortex behavior is in agreement with the results of several researchers [ 1 , 13 , 15 ].…”

“…So, a planar 4:1 contraction geometry is constructed in this study for calculating the viscoelastic flow. Because the contraction flow as a benchmark problem [ 1 , 13 , 15 , 17 ] is usually used to evaluate the capability of constitutive models and numerical algorithms. Accordingly, the planar 4:1 contraction viscoelastic flow is also calculated in this study.…”

“…During the past two decades with the developments of numerical algorithm and constitutive model, computational rheology has achieved great progress as an important tool. Many investigators have utilized computational rheology to obtain insight into the complex rheological behaviors of polymers, so as to deeply understand the flow status [ 1 ] and processing mechanisms, such as extrusion swell [ 2 , 3 ], flow instabilities [ 4 ] and secondary flow.…”

“…Numerous studies [ 1 , 13 , 15 , 17 ] were carried out both experimentally and numerically for contraction flow, which is a benchmark problem in computational rheology, because there exists a complex combination flow of both shear flow near the channel wall and extension flow along the centerline in the contraction channel. In practice, similar contraction flows also widely appear in industrial polymer processing, such as extrusion flow, injection molding, fiber spinning process, etc.…”

The Viscoelastic Swirled Flow in the Confusor

“…Here, we consider a viscoelastic flow in a channel with a 4:1 contraction ratio because it has been extensively studied in the literature [ 12 , 15 ] and because it has been defined as benchmark geometry for the workshop on the numerical simulation of viscoelastic flow. For example, planar flow was investigated in [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ], while axisymmetric flow was considered in [ 12 , 26 , 27 , 28 , 29 , 30 ].…”