A simple model for heterogeneous flows of yield stress fluids

TL;DR

This paper presents a simple model for heterogeneous flows in yield stress fluids, capturing shear banding, hysteresis, and stick-slip phenomena under different boundary conditions.

Contribution

It introduces a non-monotonous local constitutive curve model to explain heterogeneities and flow behaviors in sheared yield stress fluids.

Findings

Homogeneous flow under controlled stress with hysteresis.

Shear banding occurs under controlled shear rate.

Stick-slip phenomena observed at low shear rates.

Abstract

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 $\Sigma$, we find homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate curve. Under controlled macroscopic shear rate $\dot{\Gamma}$, shear banding is predicted within a range of values of $\dot{\Gamma}$. For small shear rates, stick slip can also be observed. These qualitative behaviours are robust when changing the boundary conditions.