An interpretation of low strain rate blood viscosity measurements: A continuum approach

Abstract

It is commonly observed that blood shear stress when measured in an instantaneously started Couette viscometer, at low steady state strain rates, initially overshoots its steady state value. The extent of the overshoot and the strain rate range at which the overshoot occurs are evidently strongly dependent on the specific device used for the measurement. The phenomenon is usually explained by recourse to a non-continuum argument which postulates the formation of a cell free plasma skimming layer. It is shown herein that the phenomenon can be qualitatively predicted, in a continuum manner, by accounting for the viscoelastic nature of the fluid. To this end a four constant Oldroyd model equation is solved for the instantaneous start up. The model exhibits both shear thinning and a positive Weissenberg effect. The method of solution is by finite difference approximation. A forward time differencing, centered space differencing technique is applied. It is shown that fluid elasticity is responsible for the initial overshoot, while the increase in the viscous time scale, due to shear thinning, is responsible for the decay and eventual disappearance of the phenomenon with increasing strain rate. Increased shear thinning is shown to heighten the phenomen. The results are shown to be in general agreement with the hypothesis that the stress overshoot is associated with the breakdown with time of shearing of aggregates of red cells.