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

Abstract

Morphological transitions here refer to the liquid-body instability of capillary rise as the spacing among cylinders changes and are studied in this paper with both theoretical analysis and experimental verifications for systems composed of two and three equidistant and parallel cylinders systems. The theory predicts cross-sectional shapes of the bounded liquid body in a bundle of cylinders, when gravity is neglected, as a function of the cylinder–cylinder separation, contact angle and the Harkinson/spreading parameter. All these morphological transitions in turn reveal the hysteresis mechanisms in the processes. 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.