Oscillatory flow and mass transport in a flexible tube

Abstract

The mass transport of a diffusible substance during volume-cycled oscillatory flow in a thin-walled viscoelastic tube is studied. A small-amplitude, long-wavelength travelling wave is generated by the oscillatory pressure gradient. Lubrication theory is employed for slow axial variations to derive regular perturbation solutions to the Navier–Stokes equations. The convection–diffusion equation is solved in a similar manner, assuming uniform steady end concentrations and no wall flux. From the velocity and concentration fields, the time-average rate of axial mass transport is calculated, and its dependence on oscillation frequency, tube stiffness, and stroke amplitude is investigated. The general result is that transport is enhanced less for softer tubes than for stiffer ones and that mass flow rate as a function of frequency reaches a local maximal value. The results are related to gas transport in pulmonary airways during high-frequency ventilation.