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Oscillatory flow and mass transport in a flexible tube

Published online by Cambridge University Press:  26 April 2006

Carolyn A. Dragon  and
James B. Grotberg
Carolyn A. Dragon
Affiliation:
Biomedical Engineering Department. Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA and Department of Anesthesia. Northwestern University Medical School, Chicago, IL 60611, USA
James B. Grotberg
Affiliation:
Biomedical Engineering Department. Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA and Department of Anesthesia. Northwestern University Medical School, Chicago, IL 60611, USA
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 135 - 155
Copyright
© 1991 Cambridge University Press

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