Heil, M. (1998) Minimal Liquid Bridges in Non-Axisymmetrically Buckled Elastic
Journal of Fluid Mechanics 380, 309-337.
This study investigates the existence and stability of static liquid
bridges in non-axisymmetrically buckled elastic tubes. The liquid bridge which
occludes the tube is formed by two menisci which meet the tube
wall at a given contact angle along a contact line whose position is initially
unknown. Geometrically non-linear shell theory is used to describe the
deformation of the linearly elastic tube wall in response to an
external pressure and to the loads due to the surface tension of the
liquid bridge. This highly non-linear problem is solved numerically by Finite
It is found that for a large range of parameters (surface tension,
contact angle and external pressure), the compressive
forces generated by the liquid bridge are strong enough to hold the
tube in a buckled configuration. Typical meniscus shapes
in strongly collapsed tubes are shown and the stability of these
configurations to quasi-steady perturbations is examined. The minimum volume of
fluid required to form an occluding liquid bridge in an elastic tube
is found to be substantially smaller than predicted by estimates based
on previous axisymmetric models. Finally, the implications of the
results for the physiological problem of airway closure are discussed.
Page last modified: November 13, 1998
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