Re-entrant corner for a White-Metzner fluid

Viscoelastic fluids can be difficult to model due to the wide range of different physical behaviors that polymer melts can exhibit. One such feature is the viscous elastic boundary layer. We address the particular problem of a viscoelastic shear-dependent fluid flowing past a corner and investigate how the properties of the boundary layer change for a White-Metzner fluid. The boundary layer equations are derived and the upstream layer is matched with the far-field flow. It was found that if the fluid is sufficiently shear thinning then the viscoelastic boundary layer formulation fails due to the inertial forces becoming dominant. The depth of the boundary layer is controlled by the shear-thinning parameters. These effects are not a feature of other shear-thinning models, such as the Phan-Thien-Tanner model. This study provides insight in the different effects of some commonly used viscoelastic models in corner flows in the upstream boundary layer, the downstream boundary layer is not addressed.