Heil, M. (2000) Finite Reynolds number effects in the propagation of an
air finger into a liquid-filled flexible-walled channel.
Journal of Fluid Mechanics 424, 21-44.
This paper investigates finite Reynolds number effects
in the problem of the propagation of an air finger into a
liquid-filled flexible-walled 2D channel. The study is motivated by
the physiological problem of pulmonary airway reopening.
A fully consistent model of the fluid-structure interaction is
formulated and solved numerically using coupled finite element
discretisations of the free-surface Navier-Stokes equations and the
Lagrangian wall equations. It is shown that for parameter
values which are representative of the conditions in the lung and in
typical laboratory experiments, fluid inertia plays a surprisingly
important role: Even for relatively modest ratios of Reynolds and Capillary
numbers (Re/Ca approx. 5 - 10), the pressure required to drive the
air finger at a given speed increases significantly compared
to the zero Reynolds number case. Fluid inertia leads to significant
changes in the velocity and pressure fields near the bubble tip
and is responsible for a noticeable change in the wall deformation pattern
ahead of the bubble. For some parameter variations (such as
variations in the wall tension), finite Reynolds number effects are
shown to lead to qualitative changes in the system's behaviour.
Finally, the implications of the result for pulmonary airway reopening
Page last modified: July 19, 2000
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