Boundary layer (shear-band) in frustrated viscoplastic flows

Abstract

We show that frustrated creep flows of yield stress fluids give rise to a boundary layer, which takes the form of a liquid region of uniform significant thickness separating two solid regions. In this boundary layer the shear rate is approximately constant for a given flow rate and the layer thickness extremely slowly varies with the flow rate.

Slow flows of yield stress fluids: yielding liquids or flowing solids?

“…Moreover the shear rate in this layer is approximately constant. A similar situation, with similar flow characteristics (after rescaling by the plug velocity) and similar thickness of the sheared layer is observed for different values of the Bingham number as long as it remains larger than 1 (Chevalier et al, 2013), but it seems difficult to predict the size of the sheared layer from simple analytical arguments. …”

“…In particular, for YSF, the thickness ( e ) of the sheared layer is expected theoretically to tend to zero when the velocity tends to zero, or equivalently when the Bingham number tends to infinity. More precisely, for a HB fluid, we have (Chevalier et al (2013)). This poses a serious problem when this thickness falls below the lengthscale of the representative elementary volume of material.…”

Effective rheology of Bingham fluids in a rough channel

“…Lubrication approximations have been investigated extensively for Newtonian fluids in confined geometries (e.g., [32,33]). For visco-plastic fluids, the limit of lubrication has also been investigated by various authors in different geometries (see [34] for film flows, [22][23][24]35] for confined geometries and [36,37] for experiments). In this case, the lubrication hypothesis becomes very restrictive essentially due to rigidity of the plug regions.…”

Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments

“…We are specifically interested in the numerical simulation of recent physical experiments of Chevalier et al [6] and Luu et al [19]. We provide a detailed analysis of the velocity profiles and unyielded zones.…”

“…An impressive range of Bingham numbers, aspect ratios of the geometry and shapes of the cavity (rectangular, sinusoidal wave, triangular, semi-fractal) are presented. But they did not describe in depth the velocity profiles in conjunction with the plug zone, along the lines of the physical experiments of Coussot's and Chambon's groups [6,19].…”