Occlusion in fluid conducting tubes transverse to a gravity field (new expanded version)

Robert Manning, Steven Collicott, and Robert Finn

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Submission date: 09. Dec. 2009
Bibtex
MSC-Numbers: 76B45, 76B03
Keywords and phrases: capillarity, surface tension, Flow in tubes

Abstract:
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.