A minimal model for chaotic shear banding in shear-thickening fluids

TL;DR

This paper introduces a minimal mathematical model capturing the complex spatiotemporal oscillations and chaos in shear-thickening fluids, highlighting the interplay of shear band formation and structural dynamics at zero Reynolds number.

Contribution

It presents a simplified yet comprehensive model that reproduces rheochaos and oscillatory behaviors, linking shear banding phenomena with neural network dynamics.

Findings

Identification of distinct oscillatory regimes including rheochaos.

Validation that a low-dimensional model captures key physical features.

Mapping of the model onto FitzHugh-Nagumo neural dynamics.

Abstract

We present a minimal model for spatiotemporal oscillation and rheochaos in shear-thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modelled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium `phase diagram' of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, travelling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.