We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
When a tube is occluded by a fluid, the free surface of the fluid becomes a stationary capillary surface spanning the tube. We extend known criteria for existence and non-existence of such a surface. We obtain an occlusion criterion for cylindrical tubes in a transverse body force, based on the force magnitude and contact angle. We show further that for any contact angle γ < π/2, tubes of suitable non-circular section can be designed so as not to occlude regardless of gravity. In addition we derive an analytic occlusion criterion for a circular vessel spinning about its axis.