Occlusion criteria in tubes under transverse body forces

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 liquid partially filling a circular vessel spinning about its axis.