Occlusion Criteria in Tubes under Transverse Body Forces

Robert Manning, Steven Collicott, and Robert Finn

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Submission date: 18. Nov. 2010
published in: Journal of fluid mechanics, 682 (2011), p. 397-414 
DOI number (of the published article): 10.1017/jfm.2011.230
Bibtex
MSC-Numbers: 76B45, 53A10
Keywords and phrases: capillarity, surface tension, mean curvature, bond number, occlusion, nonlinear elliptic pde

Abstract:
When a fluid in a tube is occluded, one finds a static configuration in which the occluding free surface of the fluid is an equilibrium capillary surface spanning the tube. We extend known criteria for existence and non-existence of such a surface, leading to an explicit mathematically rigorous occlusion criterion for cylindrical tubes in a transverse body force field, depending on the force magnitude and contact angle. For any contact angle γ ≠ π/2, we provide further an explicit design of a tube section, which will not occlude in a downward gravity field, regardless of the field strength. In addition we derive a precise analytic occlusion criterion for a circular vessel spinning about its axis.