Morphological transitions of capillary rise in a bundle of two and three solid parallel cylinders

The problems dealt with cover the full spectrum of wetting behaviors, from complete wetting, to partial wetting and up to the super-hydrophobic surfaces, characterized by the corresponding contact angles and the Harkinson spreading parameters. Unlike the wetting over a flat solid surface, the wetting of bundles of cylinders exhibits much more complexities because of the geometrical curvatures and shapes involved. Various transitions and their criteria are described and derived, extensive parametric studies then followed, and the hysteresis during the transitions is analyzed. Some experimental verifications are provided at the end.