Volume-cycled oscillatory flow in a tapered channel

Abstract

Oscillatory viscous flow in a tapered channel is analysed under conditions of fixed stroke volume. A lubrication theory is developed for small taper and the general result is steady bidirectional drift and an induced steady pressure gradient. The characteristics of the drift profiles change significantly as the Womersley parameter is increased. For large values difficulties arise in the matched asymptotics method which are resolved by introducing a steady drift layer that is much thicker than the Stokes layer. This double boundary layer does not arise in pressure-cycled oscillations. Both Eulerian and Lagrangian drift are examined. The results are compared qualitatively to experimental observations which primarily focus on the application to ventilation in the lung.