Pathological Rheology of Non-Stretching Entangled Polymers: Finite-Time Blow-Up Predictions

TL;DR

This paper investigates how the non-stretching approximation in polymer rheology can lead to finite-time blow-up predictions in fast flows, and proposes an extension to improve accuracy.

Contribution

It introduces a second-order extension to the non-stretching approximation to better predict flow behavior in polymer models.

Findings

Fast flows diverge in finite time in the non-stretching model.

Second-order extension aligns non-stretching model with full model behavior.

Disparity between models can be mitigated by higher-order corrections.

Abstract

The non-stretching approximation of polymer rheology simplifies a constitutive equation but fundamentally changes its behavior in fast flows, and the circumstances under which fast flows emerge cannot always be predicted a-priori. In this paper, we consider two simple flows for which shear rates are bounded in the original RP model but diverge to infinity in finite time for the non-stretching RP model. The disparity between the full and non-stretching models can be resolved by extending the non-stretching approximation to second order in accuracy.