Over the last decades, the intensive use of polymer mixtures in Enhanced Oil Recovery (EOR) has led to a great effort in understanding the flow of such fluids through complex porous media. While the macro-scale behavior of these fluids has been actively investigated using core-scale experiments, the link with the micro-scale fundamental physics of the flow remains largely unexplored. A transition from a Newtonian to a non-Newtonian macro-scale regime has been observed. Recently, a simple model has been proposed to characterize the critical Darcy velocity associated to this transition phenomenon. Here, we use computational fluid dynamics, conceptual porous media and experimental datasets provided by the literature to test the robustness this model. We conclude that the model is valid. Furthermore, it allows, via an explicit formulation, a better understanding of the critical Darcy velocity associated to the transition.