Opposite wall contact and higher buckling modes

The previous pages demonstrated the existence of small-volume liquid bridges in strongly buckled elastic tubes. Here we investigate what happens if we start with an axisymmetric liquid bridge (formed, e.g., via Halpern & Grotberg's primary axisymmetric instability):

Once the liquid bridge is formed, the system becomes statically unstable to non-axisymmetric perturbations and the tube buckles while spreading out the fluid contained in the liquid bridge. The figure below shows a quasi-static (!) sequence of this buckling process. Note that the intermediate (slightly buckled) states are actually unstable themselves -- only the strongly collapsed configuration with opposite wall contact, shown in (c) and (d), is stable. [For the mathematically inclined readers: This is because the buckling takes place by a subcritical bifurcation.]

For sufficiently high surface tension of the liquid bridge we can also get buckling with higher circumferential wavenumbers. Here's an example of a tube that is buckling into three lobes:

Note that the shape of the air-liquid interface is quite different from that in the two-lobed collapse shown above. Physiological observations suggest that airway closure actually takes place in such multiple lobes.

Back to `Airway Closure'.

Page last modified: September 29, 2000

Back to Matthias Heil's home page..