The Viscosity of Erythrocyte Suspensions: A Review of Theory

Abstract

Blood and erythrocyte suspensions have non-linear pressure-flow curves and so do not possess a unique Newtonian coefficient of viscosity (or its reciprocal, the fluidity) except in the physically unrealizable limits of infinite flow rate and tube radius. However, three coefficients can be defined which are related mathematically to one another and which converge in these infinite limits. They are first, the apparent fluidity, which is proportional to the slope of the line joining any given point on the pressure-flow curve with the origin; second, the differential fluidity, which is proportional to the slope of the pressureflow curve itself at any given point; and third, the generalized fluidity which is proportional to the ratio of the shear rate to the applied stress across any given cylindrical lamina (taken here at the tube wall) within the tube. These three coefficients, which are related mathematically to one another, have been calculated from measured pressure-flow curves for erythrocyte suspensions in glass tubes, and the differential viscosity has been used to develop a simple flow model in which the shear-dependent viscosity is assumed to arise from "structural changes" in the fluid as the flow rate increases. Although the physical basis of such structural changes is uncertain, it is likely that some sort of axial redistribution of the red cells is of greatest importance at normal, physiological hematocrit values.