# 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 »

- Authors:

- 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. Wed .
"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 = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}