## 2009.78: The Bretherton Problem in Elastic-Walled Channels: Finite Reynolds Number Effects

2009.78:
Matthias Heil
(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) |
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Uncontrolled Keywords: | Bretherton problem, fluid-structure interaction, pulmonary airway re-opening |

Subjects: | MSC 2000 > 76 Fluid mechanics |

MIMS number: | 2009.78 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 21 October 2009 |

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