University of Waterloo
Waterloo, Ontario, Canada
The well-known perturbation solution of the equation of motion for blood flow within the Casson theory, first introduced by Aroesty \& Gross, has been re-examined. In this paper, it is shown that the Womersley parameter traditionally associated with blood flow is not the correct perturbation parameter. Instead it is argued that the radius-based Reynolds number should be used. Analysis of the resulting perturbation solution reveals that the first-order correction is significantly smaller than the leading order, as also found by Aroesty \& Gross. In large vessels, where the yield stress tends to zero, the leading behaviour of Newtonian pulsatile flow can be recovered. There is also good agreement of our solution with existing experimental data. Nevertheless, there still remains an intriguing aspect of the perturbation scheme in that it appears not to be uniformly valid.