# Numerical study of chain conformation on shear banding using diffusive Rolie-Poly model

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## Abstract

Shear-banding phenomenon in the entangled polymer systems was investigated in a planar Couette cell with the diffusive Rolie-Poly (ROuse LInear Entangled POLYmers) model, a single-mode constitutive model derived from a tube-based molecular theory. The steady-state shear stress *σ* _{s} was constant in the shear gradient direction while the local shear rate changed abruptly, i.e., split into the bands. We focused on the molecular conformation (also calculated from the Rolie-Poly model) around the band boundary. A band was found also for the conformation, but its boundary was much broader than that for the shear rate. Correspondingly, the first normal stress difference (*N* _{1}) gradually changed in this diffuse boundary of the conformational bands (this change of *N* _{1} was compensated by a change of the local pressure). For both shear rate and conformation, the boundary widths were quite insensitive to the macroscopic shear rate but changed with various parameters such as the diffusion constant and the relaxation times (the reptation and the Rouse times). The broadness of the conformational banding, associated by the gradual change of *N* _{1}, was attributed to competition between the molecular diffusion (in the shear gradient direction) and the conformational relaxation under a constraint of constant *σ* _{s}.

## Keywords

Shear banding Rolie-Poly model Velocity band Molecular orientational band Molecular diffusion and relaxation## Notes

### Acknowledgements

This work was partly supported by Grant-in-Aid for Scientific Research on Priority Area “Soft Matter Physics” from the Ministry of Education, Culture, Sports, Science and Technology (grant #18068009). C. Chung thanks a financial support from G-COE program for the stay at ICR.

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