Pulsatile Blood Flow in a Channel of Small Exponential Divergence—III. Unsteady Flow Separation

Abstract

Analysis of pulsatile flow through exponentially diverging channels reveals the existence of critical mean Reynolds numbers for which the flow separates at a downstream axial station. These Reynolds numbers vary directly with the frequency of flow oscillation and inversely with the rate of channel divergence. Increasing the Reynolds number above its critical value results in a rapid upstream displacement of the point of separation. For a tube of fixed geometry, periodic unsteadiness causes flow separation to occur at lower Reynolds numbers and upstream of a corresponding steady-state situation. The point of separation moves progressively downstream, however, towards its steady-state location, as the frequency of oscillation increases. These results are discussed as consequences of the nonlinear steady streaming phenomenon described in an earlier paper.