Simple model for heterogeneous flows of yield stress fluids.
Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a nonmonotonic local flow curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress Sigma, we find homogeneous flow in the bulk and a hysteretic macroscopic stress-shear-rate curve. Under controlled macroscopic shear rate Gamma;, shear banding is predicted within a range of values of Gamma;. For small shear rates, stick-slip can also be observed. These qualitative behaviors are robust to changes in the boundary conditions.
Picard
Guillemette
G
Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083, ESPCI, 10 Rue Vauquelin, F-75231 Paris Cedex 05, France. guillemette@turner.pct.espci.fr
Ajdari
Armand
A
Bocquet
Lydéric
L
Lequeux
François
F