Fåhræus effect

Should not be confused with "Fåhræus–Lindqvist effect"

The dependence of apparent viscosity of human blood on the capillary size it is flowing through is identified as the Fåhræus–Lindqvist effect. There is a related but different effect called the Fåhræus effect. This is the decrease in average concentration of red blood cells in human blood as the diameter of the glass tube in which it is flowing decreases. In other words, in blood vessels with diameters less than 500 micrometer, both the hematocrit decreases with decreasing capillary diameter. The Fåhræus effect definitely influences the Fåhræus–Lindqvist effect but the former is not the only cause of the later.

Mathematical Model

Considering steady laminar fully developed blood flow in a small tube with radius of $r_{0}$, whole blood separates into a cell-free plasma layer along the tube wall and enriched central core. As a result, the tube hematocrit, $H_{t}$, is smaller than the out flow hematocrit, $H_{0}$. A simple mathematical treatment of the Fåhræus effect was shown in Sutera et al. (1970). This seems to be the earliest analysis:

${\frac {H_{t}}{H_{0}}}={\frac {1}{2-(1-({\frac {\delta }{r_{0}}}))^{2}}}$

where:

$H_{t}$ is the tube hematocrit

$H_{0}$ is the outlet hematocrit

$\delta$ is the cell-free plasma layer thickness

$r_{0}$ is the radius of the tube

Here is a graph based on the functional relationship in the above equation. The graph shows the relationship between tube hematocrit and the plasma layer growth near the capillary wall.