Elastic and viscous effects on flow pattern of elasto-viscoplastic fluids in a cavity

Inertialess flows of elasto-viscoplastic fluids inside a leaky cavity are numerically analyzed using the finite element technique, with the goal of understanding the influence of both the elastic and viscous effects on the topology of the yield surfaces of an elasto-viscoplastic material. Assuming that the collapse of the material microstructure is instantaneous, a mechanical model is composed of the governing equations of mass and momentum for incompressible fluids, and associated with a hyperbolic equation for the extra-stress tensor based on the Oldroyd-B model (Nassar et al., 2011). The main feature of the model is the consideration of the viscosity and relaxation time as functions of the strain rate to allow the shear-thinning of the viscosity and to restrict the elastic effects to the unyielded regions of the material. The numerical simulations are performed through a three-field Galerkin least-squares-type method in terms of the extra-stress tensor and the pressure and velocity fields. The results indicate that the material yield surfaces are strongly influenced by the interplay between the elastic and viscous effects, in accordance with recent experimental visualization of elasto-viscoplastic flows.