# A singular perturbation study of the Rolie-Poly model

## TL;DR

This paper analyzes the Rolie-Poly model for entangled polymers using singular perturbation methods, revealing behaviors like yield stress hysteresis and delayed yielding in the large relaxation time limit.

## Contribution

It provides a detailed singular perturbation analysis of the Rolie-Poly model, connecting it to thixotropic yield stress fluid behaviors and identifying dynamic flow regimes.

## Key findings

- Model exhibits yield stress hysteresis and delayed yielding.
- Identification of fast, slow, and yielded flow regimes.
- Long-term viscosity persistence after flow cessation.

## Abstract

We study the Rolie-Poly model for entangled polymers, using a singular perturbation analysis for the limit of large relaxation time. In this limit, it is shown that the model displays the characteristic features of thixotropic yield stress fluids, including yield stress hysteresis, delayed yielding and long term persistence of a decreased viscosity after cessation of flow. We focus on the startup and cessation of shear flow. We identify dynamic regimes of fast, slow and yielded dynamics, and show how the combination of these regimes can be used to describe the flow.