** Abstract: **

###
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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