Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch Russian Academy of Sciences, Novosibirsk, Russia, 630090

medvedev@itam.nsc.ru

Abstract. When blood flow in small vessels (less than 300 microns) was observed dependence of rheological properties of blood vessel size – an apparent blood viscosity decreases with decreasing diameter of the blood vessel. To describe the blood flow in small vessels is necessary to establish the equation of state power (except for other parameters) on the diameter of the vessel.
The paper presents a single phase model to describe blood flow in both large and small blood vessels in the. The model yields an equation of the blood – the dependence of viscosity on the diameter of the vessel, and describes the flow characteristics, such as hematocrit and blood velocity. Based on this model was explained long ago known features (effects) of blood flow in vessels: depending on the hematocrit of the diameter of the vessel, the existence of cell-free layer of plasma near the vessel wall, stupid (as compared with the profile of Poiseuille flow) velocity profile of blood, depending on the viscosity blood on the diameter of the vessel. Analytical dependences for the velocity, viscosity and hematocrit blood, depending on the diameter of the blood vessel. A comparison with experimental data.

Key words: hematocrit, Poiseuille flow, mathematical model, two-phase flow, the relative viscosity.