Laminar flow of a viscoelastic shear-thinning liquid over a backward-facing step preceded by a gradual contraction

Abstract

Experimental observations and numerical simulations, based upon the Phan-Thien and Tanner model, are reported for the laminar flow of a series of viscoelastic liquids (0.05%, 0.1%, and 0.4% concentrations of a polyacrylamide) over a symmetrical, double backward-facing step geometry preceded by a short gradual contraction from a long (120 hydraulic diameters in length) square duct. Reynolds numbers are typically between 10 and 100 (i.e., inertia is not negligible) and Deborah numbers of order 100 for the experiments (based on a relaxation time determined from linear viscoelasticity measurements) and order 10 for the viscoelastic simulations. As the polymer concentration is increased, the combined effects of increased shear thinning and viscoelasticity are found to dramatically reduce the length of the recirculation region downstream of the step. The nature of the flow field within the contraction itself is found to be fundamentally different for the viscoelastic liquids to that for a comparable Newtonian fluid flow: large velocity overshoots with very strong gradients appear near to the sidewalls that, due to their appearance, we have dubbed “cat’s ears.” The simulations are able to reproduce these remarkable features, at least qualitatively.