Fåhræus–Lindqvist effect

History

The effect was first documented by a German group in 1930. Shortly after, in 1931, it was reported independently by the Swedish scientists Robin Fåhræus (1888–1968) and Johan Torsten Lindqvist (1906–2007), after whom the effect is commonly named. Fåhræus was a pathologist and hematologist, Lindqvist was a physician. Fåhræus and Lindqvist published their article in the American Journal of Physiology in 1931 describing the effect. Their study represented an important advance in the understanding of hemodynamics which had widespread implications for the study of human physiology. They forced blood through fine glass capillary tubes connecting two reservoirs. Capillary diameters were less than 250 μm, and experiments were conducted at sufficiently high shear rates (≥100 1/s) so that a similar flow in a large tube would be effectively Newtonian. After correcting for entrance effects, they presented their data in terms of an effective viscosity, derived from fitting measured pressure drop and volume flow rate to Hagen–Poiseuille equation for a tube of radius R

${\displaystyle Q=\frac{\pi R^4\mathrm{\Delta }P}{8{\mu }_{e}L}}$

where:

${\displaystyle Q}$ is the volumetric flow rate

${\displaystyle \mathrm{\Delta }P}$ is the pressure drop across the capillary

${\displaystyle L}$ is the length of capillary

${\displaystyle {\mu }_e}$ is the effective viscosity

${\displaystyle R}$ is the radius

${\displaystyle \pi }$ is the mathematical constant

Although the Hagen–Poiseuille equation is only valid for a Newtonian fluid, fitting experimental data to this equation provides a convenient method of characterizing flow resistance by a single number, namely ${\displaystyle {\mu }_e}$. In general, ${\displaystyle {\mu }_e}$ will depend on the fluid being tested, the capillary diameter, and the flow rate (or pressure drop). However, for a given fluid and a fixed pressure drop, data can be compared between capillaries of differing diameter. Fahræus and Lindqvist noticed two unusual features of their data. First, ${\displaystyle {\mu }_e}$ decreased with decreasing capillary radius, R. This decrease was most pronounced for capillary diameters < 0.5mm. Second, the tube hematocrit (i.e., the average hematocrit in the capillary) was always less than the hematocrit in the feed reservoir. The ratio of these two hematocrits, the tube relative hematocrit, ${\displaystyle H_R}$, is defined as

${\displaystyle {\mathrm{H}}_{\mathrm{R}}=\frac{\text{tube hematocrit}}{\text{feed reservoir hematocrit}}}$