Micromorphic theory as a model for blood in the microcirculation: correction and analysis

Abstract

This paper analyzes the applicability of Eringen’s Generalized Continuum Theories as a model for human blood in the microcirculation. The applied theory considers a fluid with a fully deformable substructure, namely a micromorphic fluid. This analysis is motivated by the fact that blood itself can be considered a suspension of deformable particles, i.e., red blood cells (RBCs), suspended in a Newtonian fluid, i.e., blood plasma. As a consequence, non-Newtonian phenomena such as shear-thinning are observed in blood. To test the micromorphic fluid as a model for blood, the solution for the velocity and the motion of substructure is determined for a cylindrical pipe flow and compared to experimental results of blood flow through narrow glass capillaries representing idealized blood vessels. A similar analysis was also conducted by Kang and Eringen in 1976, but it contains some misprints and minor errors regarding the mathematical expressions and subsequent discussion which are corrected in this paper. For certain material parameters, the micromorphic fluid models capture high-shear blood flow in narrow glass capillaries very well. This concerns both the velocity profiles and the shear-thinning behavior. Furthermore, a parameter study reveals that the flexibility of substructure governs the micromorphic shear-thinning. In this regard, parallels can be drawn to the shear-thinning of human blood, which is also induced by the deformability of RBCs. This makes the micromorphic fluid a complex but accurate model for human blood, at least for the considered experiments.