A 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 non-monotonous local constitutive curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress $Σ$, we find homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate curve. Under controlled macroscopic shear rate $\dotΓ$, shear banding is predicted within a range of values of $\dotΓ$. For small shear rates, stick slip can also be observed. These qualitative behaviours are robust when changing the boundary conditions.
cond-mat.soft↗