In this work a new rheological equation of state is presented and its application to blood is studied. The equation considered is a linear combination of Newtonian and non-Newtonian contributions to the apparent viscosity. The general form of the equation is

 T_ij =-(A + Be^{-1/C|(.5)Δi/j:Δj/i|1/2})Δij

Data from the literature were used to test the equation by generating curves of measured torque (T/L) versus applied shear rate (Ω) that would characterize the behavior of blood at all red cell concentrations and all shear rates in the Gilinson, Dauwalter and Merrill viscometer. The constants for the equation were obtained by appropriate curve-fitting using the "Least- Squares Estimation of Non-Linear Parameters" procedure of Marquardt and functions in terms of hematocrit were determined to represent this behavior.

Comparisons of the predicted results with those from the literature indicate considerable deviations at the lowest shear rates. However, it is believed that with more data in the very low shear region (less than 0.5 sec.^-1) to determine the correct values of the constants, better correlation with experimental data may be obtained. The results presented in this work were found to correlate well for shear rates in the intermediate region and low region (greater than 5 sec. ^-1 and less than 50 sec. ^-1).