A constitutive equation for the viscosity of stored red cell suspensions: Effect of hematocrit, shear rate, and suspending phase

Abstract

Despite the extensive previous work on the viscosity of red blood cell suspensions, experimental data at very high cell concentrations are limited and scattered, and available constitutive equations for the steady‐state viscosity are unsuitable for numerical calculations that require accurate well‐behaved analytical expressions valid over a wide range of shear rates and which include these very high cell concentrations. The steady‐state viscosity of suspensions of stored red blood cells in both saline and plasma were measured in a coaxial cylinder viscometer at shear rates ranging from below 1–300 s−1 and at cell volume fractions up to 0.98. Emphasis was placed on the evaluation of viscosity at very high cell concentrations because of the lack of available data in this regime and its importance in understanding and modeling cross‐flow microfiltration of red cell suspensions, the application which motivated the current study. This data base was supplemented by additional measurements previously reported in the literature for fresh blood. The data were correlated using a constitutive equation for the viscosity as a function of shear rate that has been used extensively in the development of rheological models for colloidal suspensions. The concentration dependence of the parameters in this model were then described using simple functional forms which incorporate available information on the physical principles governing the rheology of blood. The resulting constitutive equation provides a general expression for the viscosity as a function of shear rate, red cell concentration, and suspending phase viscosity. This equation agrees with available experimental data to within about ±14% for shear rates greater than 1 s−1 and to within ±9% for shear rates greater than 10 s−1, and it is well‐suited for numerical calculations of blood flow.