Heil, M. & White, J.P. (2002) Airway Closure: Surface-tension-driven
non-axisymmetric instabilities of liquid-lined elastic rings.
Journal of Fluid Mechanics 462, 79-109.
This paper investigates the stability and large-displacement
post-buckling behaviour of liquid-lined elastic rings. The fluid flow and
the wall deformation are described by the free-surface Navier-Stokes
equations and by geometrically non-linear shell theory, respectively. The
fluid-structure interaction problem is solved numerically by a finite
element method. The compressive load on the ring is a
combination of the external pressure and the effect of surface-tension.
Once this combined load exceeds a critical value, the subsequent
non-axisymmetric collapse of the ring is controlled by the dynamics of the
surface-tension-driven redistribution of fluid in the liquid lining.
It is shown that, for sufficiently large surface tension, the ring can
undergo a catastrophic collapse which leads to a complete occlusion of its
lumen. A novel lubrication theory model, which ensures exact volume
conservation for flows on strongly curved substrates, is developed
and found to be capable of accurately describing the motion of the
air-liquid interface and the fluid-structure interaction in the
large-displacement regime, even in cases where the film thickness is
The findings have important implications for the occurrence
of airway closure in lung diseases (such as oedema) which cause an
increase in the thickness of the airways' liquid lining.
It is shown that under such conditions, airways can
become occluded even if the volume of fluid in their liquid lining
is much smaller than that required to occlude them in
their axisymmetric state.
Page last modified: December 19, 2001
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