Non‐Newtonian Flow of Blood in Arterioles: Consequences for Wall Shear Stress Measurements

Abstract

Our primary goal is to investigate the effects of non-Newtonian blood properties on wall shear stress in microvessels. The secondary goal is to derive a correction factor for the Poiseuille-law-based indirect measurements of wall shear stress. The flow is assumed to exhibit two distinct, immiscible and homogeneous fluid layers: an inner region densely packed with RBCs, and an outer cell-free layer whose thickness depends on discharge hematocrit. The cell-free layer is assumed to be Newtonian, while rheology of the RBC-rich core is modeled using the Quemada constitutive law. Our model provides a realistic description of experimentally observed blood velocity profiles, tube hematocrit, core hematocrit, and apparent viscosity over a wide range of vessel radii and discharge hematocrits. Our analysis reveals the importance of incorporating this complex blood rheology into estimates of WSS in microvessels. The latter is accomplished by specifying a correction factor, which accounts for the deviation of blood flow from the Poiseuille law.