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Evolution of the system for H=0.0395, σ=320. In each picture, the shaded volume represent the fluid; the inner surface is the air–liquid interface and the outer surface is the tube wall. (a) Non-axisymmetric buckling, (b) Azimuthal draining flows develop, t=0.848. (c) Fluid pressure causes thin-film regions to buckle outwards, t=0.8548. (d) Catastrophic collapse, t=0.8549.
From:
Andrew L. Hazel and Matthias Heil, “Surface-tension-induced buckling of liquid-lined elastic tubes: a model for pulmonary airway closure”, The Royal Society Proceedings A, Vol. 461, No. 2058, June 2005,
DOI: 10.1098/rspa.2005.1453
ABSTRACT: 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 destabilizing 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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