The Bretherton Problem in Elastic-Walled Channels: Finite Reynolds Number Effects

Heil, Matthias (2001) The Bretherton Problem in Elastic-Walled Channels: Finite Reynolds Number Effects. In: IUTAM Symposium on Free Surface Flows, 10-14 July 2000, Birmingham, UK.

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Abstract

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.

Item Type:	Conference or Workshop Item (Paper)
Uncontrolled Keywords:	Bretherton problem, fluid-structure interaction, pulmonary airway re-opening
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	21 Oct 2009
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1321

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