Non-locality and viscous drag effects on the shear localisation in soft-glassy materials

TL;DR

This study investigates how non-locality and viscous drag influence shear localization in soft-glassy materials under shear flow, combining analytical and numerical methods to understand flow behavior near the jamming point.

Contribution

It introduces a combined analytical and numerical framework to analyze shear localization in soft-glassy materials considering wall friction and cooperativity effects.

Findings

Wall friction enhances shear localization near the walls.

Analytical solutions for Bingham fluids match numerical simulations.

Cooperativity effects are robust across different rheological models.

Abstract

We study the Couette flow of a quasi-2d soft-glassy material in a Hele-Shaw geometry. The material is chosen to be above the jamming point, where a yield stress $\sigma_Y$ emerges, below which the material deforms elastically and above which it flows like a complex fluid according to a Herschel-Bulkley (HB) rheology. Simultaneously, the effect of the confining plates is modelled as an effective linear friction law, while the walls aside the Hele-Shaw cell are sufficiently close to each other to allow visible cooperativity effects in the velocity profiles (Goyon et al., Nature 454, 84-87 (2008)). The effects of cooperativity are parametrized with a steady-state diffusion-relaxation equation for the fluidity field $f = \dot{\gamma}/\sigma$, defined as the ratio between shear rate $\dot{\gamma}$ and shear stress $\sigma$. For particular rheological flow-curves (Bingham fluids), the problem is tackled analytically: we explore the two regimes $\sigma \gg \sigma_Y$ and $\sigma \approx \sigma_Y$ and quantify the effect of the extra localisation induced by the wall friction. Other rheo-thinning fluids are explored with the help of numerical simulations based on lattice Boltzmann models, revealing a robustness of the analytical findings. Synergies and comparisons with other existing works in the literature (Barry et al., Phil. Mag. Lett. 91, 432-440 (2011)) are also discussed.