Oscillatory Flow Theory

Abstract

In a stiff tube laminar sinusoidal flow results from a sinusoidal pressure gradient. The velocity depends on the distance from the center of the vessel and varies over the sinusoidal cycle. Viscous and mass effects both contribute. Womersley’s parameter α expresses the relative importance of inertia effects over viscous (frictional) effects. For α < 3, (low frequency, small radius), viscous effects dominate and the profile becomes parabolic, as in Poiseuille’s flow. For α > 10, i.e., high frequency and/or large vessels the profile becomes flat, because inertial effects dominate. The theory is based on sinusoidal oscillations of pressure and flow. This is why Fourier Analysis is required (Appendix 1) in the calculation of wall shear and local flow profiles.