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We study the Couette flow of a quasi-2d soft-glassy material in a Hele-Shawgeometry. The material is chosen to be above the jamming point, where a yieldstress $\sigma_Y$ emerges, below which the material deforms elastically andabove which it flows like a complex fluid according to a Herschel-Bulkley (HB)rheology. Simultaneously, the effect of the confining plates is modelled as aneffective linear friction law, while the walls aside the Hele-Shaw cell aresufficiently close to each other to allow visible cooperativity effects in thevelocity profiles (Goyon et al., Nature 454, 84-87 (2008)). The effects ofcooperativity are parametrized with a steady-state diffusion-relaxationequation for the fluidity field $f = \dot{\gamma}/\sigma$, defined as the ratiobetween shear rate $\dot{\gamma}$ and shear stress $\sigma$. For particularrheological 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 simulationsbased on lattice Boltzmann models, revealing a robustness of the analyticalfindings. Synergies and comparisons with other existing works in the literature(Barry et al., Phil. Mag. Lett. 91, 432-440 (2011)) are also discussed.

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