Instability and spatiotemporal rheochaos in a shear-thickening fluid model

TL;DR

This paper models a shear-thickening fluid exhibiting complex spatiotemporal behaviors, including oscillations and rheochaos, driven by nonlinear microstructural dynamics rather than inertia, revealing rich phenomena even in simplified models.

Contribution

It introduces a novel model capturing inhomogeneous shear-banded flows and rheochaos in shear-thickening fluids, highlighting mechanisms beyond inertia.

Findings

Rich spatiotemporal dynamics including oscillations and chaos.

Rheochaos occurs even with monotonic flow curves.

Complex behaviors are present in low-dimensional models.

Abstract

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form.