Behavior of a Liquid Bridge between Nonparallel Hydrophobic Surfaces

When a liquid bridge is formed between two nonparallel identical surfaces, it can move along the surfaces. Literature indicates that the direction of bridge movement is governed by the wettability of surfaces. When the surfaces are hydrophilic, the motion of the bridge is always toward the cusp (intersection of the plane of the two bounding surfaces). On the other hand, the movement is hitherto thought to be always pointing away from the cusp when the surfaces are hydrophobic. In this study, through experiments, numerical simulations, and analytical reasoning, we demonstrate that for hydrophobic surfaces, wettability is not the only factor determining the direction of the motion. A new geometrical parameter, i.e., confinement (cf), was defined as the ratio of the distance of the farthest contact point of the bridge to the cusp, and that of the closest contact point to the cusp. The direction of the motion depends on the amount of confinement (cf). When the distance between the surfaces is large (resulting in a small cf), the bridge tends to move toward the cusp through a pinning/depinning mechanism of contact lines. When the distance between the surfaces is small (large cf), the bridge tends to move away from the cusp. For a specific system, a maximum cf value (cf_max) exists. A sliding behavior (i.e., simultaneous advancing on the wider side and receding on the narrower side) can also be seen when a liquid bridge is compressed such that the cf exceeds the cf_max. Contact angle hysteresis (CAH) is identified as an underpinning phenomenon that together with cf fundamentally explains the movement of a trapped liquid between two hydrophobic surfaces. If there is no CAH, however, i.e., the case of ideal hydrophobic surfaces, the cf will be a constant; we show that the bridge slides toward the cusp when it is stretched, while it slides away from the cusp when it is compressed (note sliding motion is different from motion due to pinning/depinning mechanism of contact lines). As such, the displacement is only related to geometrical parameters such as the amount of compression (or stretching) and the dihedral angle between the surfaces.