Capillary Occlusion of Tubes with Rectangular and Arbitrary Cross-Sections with Transverse Body Forces
The standard Concus-Finn theory for determining critical wetting conditions was extended to include both transverse body forces and some non-cylindrical vessel shapes. This theory predicts the criteria for the existence of bounded capillary solutions, which occludes the vessel. If this condition fails, then no occluding surface exists and the liquid will spread. Three different methods were examined to efficiently apply the theory to arbitrary cross-sections. The transition Bond numbers were calculated for a cylinder under centrifugal and transverse gravitational forces. The theory compares favorably to numerical calculations and experiments. The transition Bond numbers, above which occlusion can not occur, for near-infinite volume liquid plugs were calculated for straight and bent rectangular channels for a range of contact angles, channel aspect ratios, and bend radii. Furthermore, the Surface Evolver code was used to determine the three-dimensional shape of the free surface and the transition Bond number for finite volumes.
Collicott, Purdue University.
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