Pulsatile flow in small blood vessels—I

Abstract

Recent experiments in vivo indicate that there are substantial regions of pulsatile flow throughout the microcirculation. Other experiments, performed with blood in vitro in various viscometric systems, have shown that the steady flow of blood can be represented by the parameters appropriate to a Casson fluid (yield stress, shear-dependent viscosity, power law of one half). The present study draws on these experimental observations, and on our recent mathematical analysis, to illustrate possible pulsatile effects upon the flow of blood in vessels of the scale of venules and arterioles.

In our analysis, it was demonstrated that a quasi-steady theory, valid for small values of α, the Womersley frequency parameter, was a good approximation under conditions of physiological relevance. The results of a mathematical analysis include a thin wall layer having a Newtonian viscosity significantly less than that in the Casson-fluid core. Such a layer can be crucial in determining the flow properties of the system. Illustrations of representative instantaneous velocity and flow rate distributions are presented, and the surprisingly large effects due to the lubricating qualities of a less viscous peripheral layer on the pulsatile flow of the Casson fluid in the core are exhibited.