2014/10/14 by Scagliarini, Andrea, Dollet, Benjamin, Sbragaglia, Mauro
#FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · doi:10.48550/arxiv.1410.3643
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 σY 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 = γ/σ, defined as the ratio between shear rate γ and shear stress σ. For particular rheological flow-curves (Bingham fluids), the problem is tackled analytically: we explore the two regimes σ≫ σY and σ≈ σY 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.