Low Reynolds number equi-bifurcation flow in a two-dimensional channel

Abstract

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.