White, J.P. & M. Heil (2004) Three-dimensional instabilities of
liquid-lined elastic tubes -- a lubrication theory model.
Physics of Fluids 17
We develop a theoretical model of surface-tension-driven, three-dimensional
instabilities of liquid-lined elastic tubes --- a model for pulmonary
airway closure. The model is based on
large-displacement shell theory, coupled to the
equations of lubrication theory, modified to ensure the exact
representation of the system's equilibrium configurations.
The liquid film that lines the initially uniform, axisymmetric
tube can become unstable to a surface-tension-driven
instability. We show that, if the surface tension of the liquid lining
is sufficiently large (relative to the tube's bending stiffness),
the axisymmetric redistribution of fluid by this
instability can increase the wall compression to such an extent that
the system becomes unstable to a secondary, non-axisymmetric instability
which causes the tube wall to buckle. We establish
the conditions for the occurrence of the non-axisymmetric instability
by a linear stability analysis and use finite element
simulations to explore the system's subsequent
evolution in the large-displacement regime.
The simulations show that non-axisymmetric instabilities allow the
formation of occluding liquid bridges in situations in which the
volume of fluid is insufficient to occlude the tube in its
axisymmetric state. Finally, we discuss the implications of our
results for the physiological problem of pulmonary airway closure.
Page last modified: October 01, 2003
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