Blood viscosity in tube flow: dependence on diameter and hematocrit

Since the original publications by Martini et al. (Dtsch. Arch. Klin. Med. 169: 212–222, 1930) and Fahraeus and Lindqvist (Am. J. Physiol. 96: 562–568, 1931), it has been known that the relative apparent viscosity of blood in tube flow depends on tube diameter. Quantitative descriptions of this effect and of the dependence of blood viscosity on hematocrit in the different diameter tubes are required for the development of hydrodynamic models of blood flow through the microcirculation. The present study provides a comprehensive data base for the description of relative apparent blood viscosity as a function of tube diameter and hematocrit. Data available from the literature are compiled, and new experimental data obtained in a capillary viscometer are presented. The combined data base comprises measurements at high shear rates (u > or = 50 s-1) in tubes with diameters ranging from 3.3 to 1,978 microns at hematocrits of up to 0.9. If corrected for differences in suspending medium viscosity and temperature, the data show remarkable agreement. Empirical fitting equations predicting relative apparent blood viscosity from tube diameter and hematocrit are presented. A pronounced change in the hematocrit dependence of relative viscosity is observed in a range of tube diameters in which viscosity is minimal. While a linear hematocrit-viscosity relationship is found in tubes of < or = 6 microns, an overproportional increase of viscosity with hematocrit prevails in tubes of > or = 9 microns. This is interpreted to reflect the hematocrit-dependent transition from single- to multifile arrangement of cells in flow.