A Two-Phase Model for Analysis of Blood Flow and Rheological Properties in the Elastic Microvessel

The blood in microvascular is seemed as a two-phase flow system composed of plasma and red blood cells (RBCs). Based on hydrodynamic continuity equation, Navier-Stokes equation, Fokker-Planck equation, generalized Reynolds equation and elasticity equation, a two-phase flow transport model of blood in elastic microvascular is proposed. The continuous medium assumption of RBCs is abandoned. The impact of the elastic deformation of the vessel wall, the interaction effect between RBCs, the Brownian motion effect of RBCs and the viscous resistance effect between RBCs and plasma on blood transport are considered. Model does not introduce any phenolmeno-logical parameter, compared with the previous phenolmeno-logical model, this model is more comprehensive in theory. The results show that, the plasma velocity distribution is cork-shaped, which is apparently different with the parabolic shape of the single-phase flow model. The reason of taper angle phenomenon and RBCs “Center focus” phenomenon are also analyzed. When the blood vessel radius is in the order of microns, blood apparent viscosity’s Fahraeus-Lindqvist effect and inverse Fahraeus-Lindqvist effect will occur, the maximum of wall shear stress will appear in the minimum of diameter, the variations of blood apparent viscosity with consider of RBCs volume fraction and shear rate calculated by the model are in good agreement with the experimental values.