Geometric scaling of elastic instabilities in the Taylor-Couette geometry: A theoretical, experimental and numerical study

TL;DR

This study explores how curvature affects elastic instabilities in the Taylor-Couette flow through experiments, theory, and simulations, revealing discrepancies with classical models but agreement with the Pakdel-McKinley criterion.

Contribution

It provides a comprehensive analysis combining experiments, advanced modeling, and stability analysis to understand curvature effects on elastic instabilities.

Findings

Experimental critical Weissenberg numbers scale with curvature.

Classical Oldroyd-B model does not match experimental scaling.

Pakdel-McKinley criterion aligns well with observed data.

Abstract

We investigate the curvature-dependence of the visco-elastic Taylor-Couette instability. The radius of curvature is changed over almost a decade and the critical Weissenberg numbers of the first linear instability are determined. Experiments are performed with a variety of polymer solutions and the scaling of the critical Weissenberg number with the curvature against the prediction of the Pakdel-McKinley criterion is assessed. We revisit the linear stability analysis based on the Oldroyd-B model and find, surprisingly, that the experimentally observed scaling is not as clearly recovered. We extend the constitutive equation to a two-mode model by incorporating the PTT model into our analysis to reproduce the rheological behaviour of our fluid, but still find no agreement between the linear stability analysis and experiments. We also demonstrate that that conclusion is not altered by the presence of inertia or viscous heating. The Pakdel-McKinley criterion, on the other hand, shows a very good agreement with the data.