Pulsatile Blood Flow in a Channel of Small Exponential Divergence—I. The Linear Approximation for Low Mean Reynolds Number

Abstract

The pulsating flow of a viscous, incompressible fluid through rigid circular channels having walls which diverge at a slow exponential rate is examined analytically. Linearized solutions for low mean Reynolds numbers reveal that viscous effects lead to radially dependent phase shifts between different layers of fluid oscillating in the axial direction, and characteristic phase lags between flow and pressure curves. When the Reynolds number and channel divergence are each small, the flow does not separate, but there is a downstream attenuation of both flow and pressure, together with the appearance of a finite radial velocity component. Utilizing data relevant to basal conditions existing in the major blood vessels of the human coronary circulation, it is found (in the absence of any persistent flow anomalies) that the shear stress at the wall is at least one to two orders of magnitude lower than values reported to be damaging to vascular endothelium.