Modeling Liquid Bridge between Surfaces with Contact Angle Hysteresis

This paper presents the behaviors of a liquid bridge when being compressed and stretched in a quasi-static fashion between two solid surfaces that have contact angle hysteresis (CAR). A theoretical model is developed to obtain the profiles of the liquid bridge given a specific separation between the surfaces. Different from previous models, both contact lines in the upper and lower surfaces were allowed to move when the contact angles reach their advancing or receding values. When the contact angles are between their advancing and receding values, the contact lines are pinned while the contact angles adjust to accommodate the changes in separation. Effects of CAH on both asymmetric and symmetric liquid bridges were analyzed. The model was shown to be able to correctly predict the behavior of the liquid bridge during a quasi-static compression/stretching loading cycle in experiments. Because of CAR, the liquid bridge can have two different profiles at the same separation during one loading and unloading cycle, and more profiles can be obtained during multiple cycles. The maximum adhesion force generated by the liquid bridge is found to be influenced by the CAR of surfaces. CAR also leads to energy cost during a loading cycle of the liquid bridge. In addition, the minimum separation between the two solid surfaces is shown to affect how the contact radii and angles change on the two surfaces as the liquid bridge is stretched.