Oscillatory Flow and Particle Suspension in a Fluid Through an Elastic Tube

Abstract

Womersley gave a solution for the case of a thin-walled elastic tube, it being assumed that the effect of the inertia term in the equations of viscous fluid motion can be neglected. He did not consider the presence of particles, to account for the blood cells in the blood, within the viscous flow through the tube (artery).

In this paper, the corresponding solution for an oscillatory flow and particle suspension in a fluid (blood), to account for blood cells, through an elastic tube is obtained. This solution is the frequency equation as it was obtained by Womersley but it has a different structure. If the volume fraction particle density , is removed from this solution it collapses to give the same equation as Womersley’s case, without particles.

Keywords: Oscillatory flow, Particle suspension, Elastic tube, Periodic function