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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 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.

MiS Preprint
72/2010

Occlusion Criteria in Tubes under Transverse Body Forces

Robert Manning, Steven Collicott and Robert Finn

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.

Received:
18.11.10
Published:
24.11.10
MSC Codes:
76B45, 53A10
Keywords:
capillarity, surface tension, mean curvature, bond number, occlusion, nonlinear elliptic pde

Related publications

inJournal
2011 Repository Open Access
Robert Manning, Steven Collicott and Robert Finn

Occlusion criteria in tubes under transverse body forces

In: Journal of fluid mechanics, 682 (2011), pp. 397-414