© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.4.1.2 Viscosity of Whole Blood

Human blood is a suspension of cells, in plasma (an aqueous solution of electrolytes and nonelectrolytes; Appendix B). The plasma is ~90% water by weight, 7% plasma proteins, 1% inorganic materials, and 1% other organic substances. The cellular component (Appendix B) is essentially all erythrocytes, or red blood cells (RBCs; Figure 8.43), with white cells of various categories comprising less than 1/600th of the total volume of cells and platelets less than 1/800th.

Pure blood plasma is a Newtonian viscous fluid, with h_plasma = 1.1 x 10^-3 kg/m-sec at 310 K. Blood plasma is the environment normally encountered by micron-sized bloodstream-traversing nanorobots as they move between blood cells.

On the other hand, "whole" blood is the complete natural mixture of blood plasma and blood cells. In blood vessels whose diameters are much larger than the size of blood cells, or in the case of mechanical systems with dimensions much larger than the characteristic sizes of blood cells, whole blood must be treated as an homogenous non-Newtonian fluid. The bulk viscosity of whole blood decreases with rising shear rate and increases with rising hematocrit (Hct), the percentage of blood volume occupied by red cells. (The human male hematocrit has a normal range of Hct = 40%-52%, average Hct = 46%,⁷⁴³ which optimizes oxygen transport.¹³²⁵) As an example, for whole blood at a low shear rate of 'g ~ 0.1 sec^-1, then h_a ~ 0.001 kg/m-sec at Hct = 0%, ~0.1 kg/m-sec at Hct = 45%, and ~1 kg/m-sec at Hct = 90%. At a high shear rate of 'g ~ 100 sec^-1, then h_a ~ 0.001 kg/m-sec at Hct = 0%, ~0.01 kg/m-sec at Hct = 45%, and ~0.1 kg/m-sec at Hct = 90%.³⁶² At still higher shear rates 'g > 100 sec^-1, whole blood behaves almost like a Newtonian fluid with a nearly constant h_a (Fig. 9.12). Viscosity also varies with disease state (if any) and slightly with temperature. For whole blood at normal Hct and 'g = 0.1 sec^-1, then h_a ~ 0.10 kg/m-sec at 310 K and ~0.15 kg/m-sec at 283 K; for 'g = 100 sec^-1, then h_a ~ 0.010 kg/m-sec at 310 K and ~0.015 kg/m-sec at 283 K.³⁶²

For large blood vessels, the effect of hematocrit on viscosity for Hct <~ 45% has been modeled experimentally by Cokelet et al¹³¹⁸ as:

{Eqn. 9.60}

with Hct expressed as a fraction. This formula, which also gives good results for RBC-sized oil/water emulsions in the same volume fraction range,¹³¹⁶ is only useful up to volume fraction of ~10% in the case of rigid-particle suspensions, whose viscosity behaves markedly differently from that of RBC suspensions (see below).

It has long been known¹³¹³ that human red blood cells can form aggregates known as rouleaux, in which the discoid RBCs adhere loosely in a "stack of coins" configuration at shear rates <100 sec^-1.¹³¹⁴ Formation of linear and branched chain aggregates (rouleaux) depends on the presence of the cell-surface cross-linking proteins fibrinogen and globulin in the plasma. The lower the shear rate (e.g., the slower the blood velocity), the more prevalent (larger size and number density) are the aggregates. As the shear rate goes to zero, it is speculated that human blood becomes one big aggregate, which then may behave as a viscoelastic or viscoplastic solid.³⁶²

As shear rate increases, the rouleaux tend to break up. Individual red cells also deform slightly, elongating and lining up with the streamlines. These two effects combine to reduce blood viscosity with rising shear, as illustrated by Figure 9.12 which shows the relative viscosity h_a / h_plasma for human blood at Hct = 45% as a function of shear rate. Note that for rigid particles (including hardened red cells, normal leukocytes, and nondeforming nanorobots), bulk viscosity is essentially independent of shear rate.

Normal blood vessel wall (peripheral zone) shear rates in physiological bloodflow range from 50-700 sec^-1 in the larger arteries to 250-2000 sec^-1 in the smallest arteries and capillaries, and 20-200 sec^-1 in large and small veins.³⁸⁶ At shear rates >100 sec^-1 where RBC aggregation ceases to be important, pure whole blood remains fluid even up to 98% RBC concentration by volume (e.g., Hct = 98% volume fraction).¹³¹⁹

Last updated on 21 February 2003