A phenomenological theory of the sigma effect

Abstract

The sigma effect concerning the flow of blood through a capillary has been discussed in connection with the distribution of the red cells from a phenomenological point of view. The distribution of the red cells is presupposed and the problem is treated by considering that the sigma effect is caused by the axial accumulation of the red cells. It is found that the assumed discontinuous distribution of the red cells across the radius of the tube gives results which most closely correspond to the measured values. A hydrodynamic interaction should exist between a wall and a particle placed near the wall, because a further additional flow due to the wall must be considered in order to satisfy the boundary conditions at the wall. From the analysis of the experimental data we can say that the sigma effect is certainly due to the axial drift of the red cells in the blood in capillary flow, and that while the exact mechanism of the axial accumulation is not yet established, it seems likely that the hydrodynamic wall effect plays an important role in our system.