The Influence of Womersley Number on Non-Newtonian Effects: Transient Computational Study of Blood Rheology

Abstract

A properly validated computational fluid dynamics methodology is a valuable predictive tool capable of aiding in the development of new methods for treating cardiovascular disease (CVD). Although blood is a shear-thinning non-Newtonian fluid, a key assumption that remains highly contested is whether non-Newtonian blood can be approximated as a Newtonian fluid. Previously, a preliminary link was established between the effects of non-Newtonian viscosity and the Womersley number, α, which could lend an explanation to the varied conclusions from previous comparison studies. Building upon this foundation, computational fluid dynamics was utilized to perform an in-depth investigation into the link between blood rheology and α for multiple geometries. For the first time in the open literature, the present research sheds definitive light on the source of the diverse results from previous studies. It demonstrates how α can affect the severity of non-Newtonian effects when compared to Newtonian viscosity, while otherwise maintaining the same boundary conditions. These results show that an increase in α reduces the peak global importance factor, a measure of the difference between Newtonian and non-Newtonian models, by upwards of 90%. Additionally, this results in a decrease in the relative difference for disturbed flow factors, parameters linked to the initiation and progression of CVD, from upwards of 34% down to approximately 5%. This study proves that there is a significant relationship between α and blood rheology, with higher α shifting the apparent viscosity of non-Newtonian models further toward the constant Newtonian viscosity.