A Theoretical Study of the Flow of Blood in a Capillary with Permeable Wall

Abstract

A hydrodynamical theory of the steady slow motion of blood through a capillary with a permeable wall is presented. It is assumed that the exchange of fluid across the capillary wall obeys Starling's hypothesis, that is, the rate of flow per unit area of the wall surface is proportional to the difference between the pressure of the fluid within and outside of the capillary. It is further assumed that the rate of flow across the capillary wall is very small. Blood is regarded as a homogeneous Newtonian fluid. The expressions for the velocity and pressure distributions within the tube and the volume of the fluid flowing per unit time across a cross section of the tube are obtained. In order to see the motion of the fluid particles, the streamlines are also obtained. Discussions are made from physiological point of view.