Non-Darcy flows of elastoviscoplastic fluids in porous media

We study flows of elastoviscoplastic fluids through porous media by numerical simulations. The porous media is made of cylinders arranged in a periodic fashion. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. This study has two main contributions. First, we show that a nonlinear relationship exists between the pressure drop and the flow rate in the porous medium. This nonlinear relationship depends on plastic, elastic, inertial effects and the configuration of the porous field. Second, we study the details of flow as the limiting pressure gradient is approached, particularly showing how the limiting flows of yield stress fluids are affected by the elasticity of the fluid.