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Title: A thermodynamic study of shear banding in polymer solutions

Abstract

Although shear banding is a ubiquitous phenomenon observed in soft materials, the mechanisms that give rise to shear-band formation are not always the same. In this work, we develop a new two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics. The model is based on the hypothesis that the direct coupling between polymer stress and concentration is the driving mechanism of steady shear-band formation. To obtain smooth banded profiles in the two-fluid framework, a new stress-diffusive term is added to the time evolution equation for the conformation tensor. The advantage of the new model is that the differential velocity is treated as a state variable. This allows a straightforward implementation of the additional boundary conditions arising from the derivative diffusive terms with respect to this new state variable. To capture the overshoot of the shear stress during the start of a simple shear flow, we utilize a nonlinear Giesekus relaxation. Moreover, we include an additional relaxation term that resembles the term used in the Rouse linear entangled polymer model to account for convective constraint release and chain stretch to generate the upturn of the flow curve at large shear rates. Numerical calculations performed formore » cylindrical Couette flow confirm the independency of the solution from the deformation history and initial conditions. Furthermore, we find that stress-induced migration is the responsible diffusive term for steady-state shear banding. Because of its simplicity, the new model is an ideal candidate for the use in the simulation of more complex flows.« less

Authors:
;  [1]
  1. Fluid Dynamics of Complex Biosystems, School of Life Sciences Weihenstephan, Technical University of Munich, Freising 85354 (Germany)
Publication Date:
OSTI Identifier:
22598960
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids; Journal Volume: 28; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; BOUNDARY CONDITIONS; COMPUTERIZED SIMULATION; CONCENTRATION RATIO; COUETTE FLOW; CYLINDRICAL CONFIGURATION; DIAGRAMS; FLUIDS; LIMITING VALUES; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; POLYMERS; QUANTUM ENTANGLEMENT; RELAXATION; SHEAR; STEADY-STATE CONDITIONS; STRESSES; THERMODYNAMICS; TWO-PHASE FLOW

Citation Formats

Hooshyar, Soroush, and Germann, Natalie, E-mail: natalie.germann@tum.de. A thermodynamic study of shear banding in polymer solutions. United States: N. p., 2016. Web. doi:10.1063/1.4953859.
Hooshyar, Soroush, & Germann, Natalie, E-mail: natalie.germann@tum.de. A thermodynamic study of shear banding in polymer solutions. United States. doi:10.1063/1.4953859.
Hooshyar, Soroush, and Germann, Natalie, E-mail: natalie.germann@tum.de. 2016. "A thermodynamic study of shear banding in polymer solutions". United States. doi:10.1063/1.4953859.
@article{osti_22598960,
title = {A thermodynamic study of shear banding in polymer solutions},
author = {Hooshyar, Soroush and Germann, Natalie, E-mail: natalie.germann@tum.de},
abstractNote = {Although shear banding is a ubiquitous phenomenon observed in soft materials, the mechanisms that give rise to shear-band formation are not always the same. In this work, we develop a new two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics. The model is based on the hypothesis that the direct coupling between polymer stress and concentration is the driving mechanism of steady shear-band formation. To obtain smooth banded profiles in the two-fluid framework, a new stress-diffusive term is added to the time evolution equation for the conformation tensor. The advantage of the new model is that the differential velocity is treated as a state variable. This allows a straightforward implementation of the additional boundary conditions arising from the derivative diffusive terms with respect to this new state variable. To capture the overshoot of the shear stress during the start of a simple shear flow, we utilize a nonlinear Giesekus relaxation. Moreover, we include an additional relaxation term that resembles the term used in the Rouse linear entangled polymer model to account for convective constraint release and chain stretch to generate the upturn of the flow curve at large shear rates. Numerical calculations performed for cylindrical Couette flow confirm the independency of the solution from the deformation history and initial conditions. Furthermore, we find that stress-induced migration is the responsible diffusive term for steady-state shear banding. Because of its simplicity, the new model is an ideal candidate for the use in the simulation of more complex flows.},
doi = {10.1063/1.4953859},
journal = {Physics of Fluids},
number = 6,
volume = 28,
place = {United States},
year = 2016,
month = 6
}
  • Recently proposed theories for shear banding in wormlike micellar solutions (WLMs) rely on a shear-induced isotropic-nematic (I-N) phase separation as the mechanism for banding. Critical tests of such theories require spatially-resolved measurements of flow-kinematics and local mesoscale microstructure within the shear bands. We have recently developed such capabilities using a short gap Couette cell for flow-small angle neutron scattering (flow-SANS) measurements in the 1-2 plane of shear with collaborators at the NIST Center for Neutron Research. This work combines flow-SANS measurements with rheology, rheo-optics and velocimetry measurements to present the first complete spatially-resolved study of WLMs through the shear bandingmore » transition for a model shear banding WLM solution near the I-N phase boundary. The shear rheology is well-modeled by the Giesekus constitutive equation, with incorporated stress diffusion to predict shear banding. By fitting the stress diffusivity at the onset of banding, the model enables prediction of velocity profiles in the shear banded state which are in quantitative agreement with measured flow-kinematics. Quantitative analysis of the flow-SANS measurements shows a critical segmental alignment for banding and validates the Giesekus model predictions, linking segmental orientation to shear banding and providing the first rigorous evidence for the shear-induced I-N transition mechanism for shear banding.« less
  • The occurrence of anomalous viscosity behavior of dilute polymer solutions, indicated by increases in shear stress with time at constant shear rate, have been investigated in a cone and plate viscometer. The ionic strengths of the solutions influence the kinetics of increases whereas the presence of small amounts of detergent abolishes the effect. The results are interpreted by assuming the shear-induced development of a structural network of the polymer solute at the air-water interface. (29 refs.)
  • A modification of a viscometer originally proposed by Zimm and Crothers is studied, which may be used to measure ultra low shear viscosity for highly dilute polymer solutions. This may provide useful information on polymer coil dimensions and relaxation time. Use of the low shear viscosity data leads to large value of relaxation time induced by polymer addition to a concentration of only 2 to 3 ppM by wt. This finding is consistent with the marked viscoelastic effects exhibited by these solutions.
  • No abstract prepared.
  • The instability of biaxial stretching leading to the development of shear bands in viscoplastic materials with both isotropic hardening and kinematic hardening is examined. The main issues are to evaluate the effect of anisotropy and inertia on the onset of instability and to examine the development and evolution of an inhomogeneous deformation structure, using both a linear analysis and a nonlinear finite element analysis. It is shown that the back stress and plastic spin, modeling deformation induced anisotropy and texture development, have a significant influence on the critical state at which the first instability occurs. The corotational rate of themore » back stress and its relation to the spin of the substructure produces apparent softening, causing instability at positive strain hardening (in the absence of back stress and corotational rates instability occurs at zero hardening). When decreasing the magnitude of the spin of the substructure by varying the plastic spin parameter the critical value of the hardening parameter decreases towards zero, illustrating again the softening effect of the spin. It is also shown that at the onset of instability, the linear analysis predicts the development of a periodic structure of square cells, implying that although the deformation has become inhomogeneous it is far from being localized. The nonlinear finite element analysis also predicts the formation of a square cell pattern at the onset of instability. This pattern however evolves into localized shear bands far into the post localization regime as shown by the nonlinear analysis. 34 refs., 9 figs.« less