Nonequilibrium thermodynamic investigation of the shear banding phenomenon in entangled polyacrylamide solutions
Final Report Abstract
In this project, we have developed a two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics to study shear bands. The model is based on the hypothesis that stress-induced migration is responsible for shear band formation. This particular type of diffusion process is described by a term in the time evolution equation of the differential velocity. The conformational tensor equation includes a nonlinear Giesekus relaxation that accounts for the overshoot of stress during the rapid onset of simple shear flow and the hydrodynamic interactions between the solution and the polymeric constituents. To capture the upturn of the flow curve at high shear rates, a nonlinear relaxation term similar to the term in the Rolie-Poly model was added to account for convective release of constraints and chain stretching. An additional stress diffusive term was added to the equation of the conformation tensor to control the smoothness of the profiles. The new model qualitatively captures the basic experimental features of the shear bands, which supports the validity of our hypothesis. Yet, it is relatively simple and can even be solved in two dimensions within a reasonable computational time. Another advantage is that microstructural information about the constituents (e.g., concentration, orientation, and orientation) can be obtained directly as a result. To analyze the model behavior, we solved the model for four benchmark problems, namely a cylindrical Couette flow, a pressure-driven channel flow, a 4:1 contraction flow, and an extrusion flow. We found that the steady-state solution is unique for different initial conditions and independent of the applied deformation history. Moreover, the value of the local diffusivity constant has no significant effect on the steady-state solution. The steady-state solution was more uniform when we used a larger nonlocal diffusivity constant. The channel flow results showed a plug-like profile of the velocity and concentration bands. We also investigated the effects of wall slip using the linear Navier slip model to illustrate how slip can be accounted for in our two-fluid framework, as it has been shown experimentally to be an important feature. The contraction flow results show that the size of the corner vortices increases with increasing inflow velocity due to shear thinning, but decreases after the onset of shear band formation. The axial velocity profile forms a plug-like shape in the shear band region after contraction. The extrusion flow study revealed a local minimum in the swelling ratio profile versus the Deborah number, a dimensionless measure of elasticity, immediately after the Newtonian case, followed by a positive slope that is very small as a result of shear band formation. Due to the change in boundary conditions from non-slip at the wall to free surface, the velocity evolves to a uniform profile after the nozzle exit. In the linear viscoelastic regime, the polymers were more concentrated near the centerline because the predominant diffusion process is a Fickian process. However, in the shear band regime, the opposite trend is observed as stress-induced migration dominates. The results and simplicity of the new model encourage us to analyze the model behavior for more complicated types of inhomogeneous flows, such as nozzles used in polymer and food processing. The model parameters can be defined as a function of polymer concentration and molecular weight. To add more relaxation times to the model for quantitative experimental comparison, an integral version of the model should be considered in the future. Since edge fracture has been observed in some rheometric experiments with polyacrylamide and may be an additional cause of shear bands, this phenomenon should also be considered in the future when simulating processing with free surfaces.
Publications
-
A two-fluid model for semidilute entangled polymer solutions. XI International Conference on Computational Heat, Mass, and Momentum Transfer, Cracow, Poland, May 21-24, 2018
Hooshyar, S. & Germann, N.,
-
Benchmark calculations of shear-banding polymer solutions. 13th World Congress on Computational Mechanics, New York, USA, July 22-27, 2018
Hooshyar, S. & Germann, N.
-
Multiscale simulation of shear banding in industrial flows. ProcessNet Annual Meeting and DECHEMA Biotechnology Annual Meeting, Aachen, Germany, September 10-13, 2018
Hooshyar, S. & Germann, N.
-
Numerical study of shear banding in pressure-driven channel and 4:1 contraction flow. Annual European Rheology Conference, Portorož, Slovenia, April 8-11, 2019, Invited keynote
Hooshyar, S. & Germann, N.,
-
Shear Banding in 4:1 Planar Contraction. Polymers, 11(3), 417.
Hooshyar, Soroush & Germann, Natalie
-
Shear banding in semidilute entangled polymer solutions. Current Opinion in Colloid & Interface Science, 39, 1-10.
Germann, Natalie
-
The investigation of shear banding polymer solutions in die extrusion geometry. Journal of Non-Newtonian Fluid Mechanics, 272, 104161.
Hooshyar, Soroush & Germann, Natalie
-
Thesis, 2020, Modeling of semidilute entangled polymer solutions and numerical simulation of industrially relevant benchmark flows to study shear banding
Hooshyar, S.
-
Experimental-based modeling of complex mixtures. Science Talks, 3, 100055.
Germann, Natalie
