Underwater bubble transport on superhydrophobic cylindrical rod

Abstract

The transport of bubbles along a curved superhydrophobic surface is not governed by buoyancy alone, but also by the interaction between the geometric confinement, the capillary and contact-line resistance, and the hydrodynamic resistance. We systematically investigated the capillary number ($Ca$) and Bond number ($Bo$) of the transported bubble, as well as the size of the rod relative to the bubble. An analytical force-balance model was developed to predict transport velocity, accounting for buoyancy, hydrodynamic drag, and capillary resistance. The transition from transport to detachment was identified. The experiments were carried out sequentially and supplemented by axisymmetric numerical simulations to investigate wake-induced interactions between bubbles. Bubble transport is strongly influenced by rod inclination and the bubble-to-rod size ratio, demonstrating that curvature-induced confinement alters the balance between driving and resistive forces. The analytical model captured the experimental trends with deviations of less than 10\% in most cases. The bubble detaches from the inclined rod at a critical Bond number that depends on rod diameter, facilitating the development of a transport regime map. The study also found that the motion of successive bubbles is strongly coupled. When a following bubble enters the wake of a preceding bubble, it speeds up and attains a higher capillary number than the leading bubble. Both experiments and numerical simulations consistently reproduce this wake-mediated acceleration, which shows that bubble transport is governed by both the force balance on individual bubbles and the hydrodynamic interactions between adjacent bubbles. These findings form the basis for controlling bubble transport, detachment, and collective motion on superhydrophobic interfaces.