Heil, M. (2001) The Bretherton problem in elastic-walled channels: Finite Reynolds number effects.

In: IUTAM Symposium on Free Surface Flows, Editors: A.C. King & Y.D. Shikmurzaev.
Kluwer, Dordrecht, Netherlands. pp. 113-120.

This paper investigates the effect of fluid inertia on the propagation of an air finger into a channel with elastic walls, a problem which can be regarded as a generalisation of the classical Bretherton problem. The study is motivated by the physiological problem of pulmonary airway reopening. Numerical results show that fluid inertia plays a surprisingly important role in this problem: Even for relatively modest ratios of Reynolds and Capillary numbers (Re/Ca approximately 5 - 10), the pressure required to drive the air finger at a given speed increases significantly compared to the zero Reynolds number case. Inertial effects are also shown to be responsible for a noticeable change in the wall deformation ahead of the bubble tip. This is analysed by a Karman-Pohlhausen approximation which yields a linear ODE, the eigenvalues of which determine the wavelength and decay rate of the oscillatory wall displacement field in this region.

Page last modified: February 12, 2001

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