On the in vivo material functions of mammalian blood

The present paper explores the implications of employing time-averaged true continuum fields to investigate blood rheology in "steady viscometric" flows. This approach is in contrast with the spatially-averaged interpretation of field variables which is generally employed. On the basis of four plausible constitutive assumptions it is then possible to deduce the qualitative in vivo behavior of all three of the material functions of whole mammalian blood from inspection of the corresponding velocity profile. Quantitative results, and the evaluation of the material constants for specific constitutive models, can be obtained through curve-fitting procedures, as is illustrated. The development reconfirms, and puts on a formal basis, the earlier conclusion of Bugliarello, et al, that whole blood can have a dilatant response at low rates of shear. In addition, the normal stress forces are shown to have off-axis extrema in tube flow, and to be large enough to influence particle migration across streamlines. The existing data on particle migration in whole blood is reviewed, and shown to be in accord with these results.