Minimal Liquid Bridges in Non-Axisymmetrically Buckled Elastic Tubes

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 Element methods. 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 connguration. Typical meniscus shapes in strongly collapsed tubes are shown and the stability of these conngurations to quasi-steady perturbations is examined. The minimum volume of uid 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.