The flow of human blood through capillary tubes

Abstract

1. The current interpretation of in vivo blood flow is mainly based on the Hagen-Poiseuille equation, although blood is not a Newtonian fluid. In this paper, experimental pressure-flow curves of blood are explained on the basis that the viscosity of the blood is the sum of two components, a Newtonian viscosity term, N, and an anomalous viscosity term equal to A/(B + D), where A and B are constants, and D the shear rate. 2. To a first approximation, blood flow in capillary tubes, comparable to that in vivo, can be deduced if the applied pressure in Poiseuille's equation is reduced by an effective back-pressure, p, equal to 8Al/3R, where l is the length of the capillary tube, and R its radius. 3. The theory explains the progressive change, from a parabolic velocity profile in large vessels, to a flattened profile in small vessels, as observed in vivo. 4. Experimental evidence is given that p is proportional to the length, and increases with decrease of R. The effect of the anomalous viscosity coefficient A was studied by varying the haematocrit, fibrinogen level, erythrocyte flexibility and temperature. 5. As the tube bore is decreased, the Fahraeus-Lindqvist effect decreases N, but this is offset by an increase of the anomalous component, A. This results, at lower pressures, in an increase of the effective blood viscosity in small vessels and of the peripheral resistance, and, at higher pressures, in a decrease of the effective blood viscosity. 5. Blood flow is proportional to the radius to the power n, where n is a variable that increases with increase of A and decrease of the applied pressure.