Airway Closure:

Static Liquid Bridges in Axisymmetric Elastic Tubes

The figure below illustrates the formation of an occluding liquid bridge from an initially axisymmetric liquid film of uniform thickness H, inside an elastic cylindrical tube of wall thickness h and radius R0.
  1. The liquid film is unstable to axisymmetric disturbances (indicated by the dashed red line): The initially uniformly distributed fluid drains into the regions of larger film thickness.
  2. Since the fluid pressure is lower in the region where the film thickness grows, the tube wall is pulled radially inwards. This moves the air-liquid interface closer to the tube's centreline. An occluding liquid bridge forms when opposite points on the air-liquid interfaces come into contact.

  3. Following the formation of the liquid bridge, fluid continues to drain from the liquid lining into the liquid bridge. In the final equilibrium state, the liquid bridge is enclosed by two air-liquid interfaces which have the shape of spherical caps and meet the tube wall at a certain contact angle. The pressure jump over the air-liquid interfaces compresses the tube wall in the region that is wetted by the liquid bridge.
This problem was investigated in detail by Halpern & Grotberg [`Fluid-Elastic Instabilities of Liquid-Lined Flexible tubes.' Journal of Fluid Mechanics 244, 615-632 (1992)]. Their study predicted large axisymmetric deformations of the tube wall when the liquid bridge is being formed. This raises the question of the system's stability to non-axisymmetric perturbations since cylindrical tubes tend to buckle when they are compressed too strongly.

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Page last modified: February 13, 1998

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