** Abstract: **

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A. L. Hazel & M. Heil (2005) Surface-tension-induced buckling of
liquid-lined elastic tubes -- a model for pulmonary airway closure.
*Proceedings of the Royal Society* **461**
1847-1868.

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We use a fully-coupled, three-dimensional, finite-element method to
study the evolution of the surface-tension-driven instabilities
of a liquid layer that lines an elastic tube, a simple model for
pulmonary airway closure. The equations of large-displacement
shell theory are used to describe the deformations of
the tube and are coupled to the Navier--Stokes equations, describing
the motion of the liquid.

The liquid layer is susceptible to a capillary instability, whereby
an initially uniform layer can develop a series of axisymmetric
peaks and troughs, analogous to the classical instability
that causes liquid jets to break up into droplets. For sufficiently
high values of the liquid's surface tension,
relative to the bending stiffness of the tube, the additional
compressive load induced by the development of the axisymmetric
instability can induce non-axisymmetric buckling of the tube wall.
Once the tube has buckled, a strong
destabilising feedback between the fluid and solid mechanics leads to an
extremely rapid further collapse and occlusion of the gas-conveying core of
the tube by the liquid. We find that such occlusion
is possible even when the volume of the liquid is too small to
form an occluding liquid bridge in the axisymmetric tube.

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