Minimal Liquid Bridges in Non-Axisymmetrically Buckled Elastic Tubes: Results for Finite Surface Tension

For finite surface tension, the pressure jump over the air-liquid interfaces (the menisci) compresses the tube wall in the region where it is wetted by the liquid bridge. Two parameters control the collapse of the tube: (i) the external pressure, (ii) the surface tension. The figure below shows two strongly collapsed tubes containing a single minimal liquid bridge. The tube collapses symmetrically therefore only one half of the tube wall and one meniscus are shown (the tube was cut in the plane of symmetry at z=0). The large pictures show a detailed view of the most strongly collapsed part of the tube with the meniscus; the smaller pictures show the overall deformation of the tube. Both tubes shown are collapsed to the point where the opposite walls touch for the first time.

For zero external pressure [as in Fig. (a)] the tube is only compressed by the surface tension of the liquid bridge. A relatively large surface tension is required to cause the strong collapse of the tube. The tube re-opens quickly to its undeformed axisymmetric shape as one moves away from the region which is held in the pinched position by liquid bridge.

Conversely, the tube shown in (b) is compressed by a large external pressure. Only a small surface tension is required to deform the tube to the same degree of collapse as in (a). The tube collapses more uniformly, hence the meniscus finger is more pronounced than in case (a) (compare to the computations for zero surface tension).

Back to `Airway Closure'.

Page last modified: February, 23 1998

Back to Matthias Heil's home page..