Criterion for extensional necking instability in polymeric fluids

TL;DR

This paper identifies a new criterion for predicting necking instability in polymeric fluids during uniaxial extension, emphasizing the role of molecular strain curvature and chain stretching effects.

Contribution

It introduces a novel criterion based on molecular strain curvature for predicting necking, contrasting with the traditional Considere criterion, supported by numerical and analytical analysis.

Findings

Necking onset correlates with downward curvature in molecular strain evolution.

Polymer chain stretching can partially mitigate necking.

The criterion applies broadly across different polymer rheology models.

Abstract

We study the linear instability with respect to necking of a filament of polymeric fluid undergoing uniaxial extension. Contrary to the widely discussed Considere criterion, we find the onset of instability to relate closely to the onset of downward curvature in the time (and so strain) evolution of the zz component of the molecular strain, for extension along the z axis. In establishing this result numerically across five of the most widely used models of polymer rheology, and by analytical calculation, we argue it to apply generically. Particularly emphasized is the importance of polymer chain stretching in partially mitigating necking. We comment finally on the relationship between necking and the shape of the underlying steady state constitutive curve for homogeneous extension.