Modeling Liquid Bridge between Surfaces with Contact Angle Hysteresis

Abstract

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 (CAH). 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 CAH, 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 CAH of surfaces. CAH 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.

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

“…The receding contact angle particularly plays a key role in contact-drop dispensing when the contact line is free 25,35 . Chen et al 33 ,…”

“…Surface imperfections (e.g., heterogeneity and roughness) complicate the equilibrium of gas-liquid-solid contact lines on non-ideal surfaces 25,32,33 . Contact lines remain pinned on non-ideal surfaces as long as the equilibrium contact angle is between the receding and advancing contact angles, and are mobile otherwise 34 .…”

Direct Measurements of Adhesion Forces for Water Droplets in Contact with Smooth and Patterned Polymers

“…They suggested that the total adhesion force consists of two components: a pressure difference DP across the liquid-gas interface and liquid-gas interfacial tension acting along the perimeter of the liquid contact base. More recently, Chen et al [28][29][30][31] demonstrated the importance of contact angles, contact angle hysteresis and the pinning of the contact line in the analysis of capillary and surface tension forces holding a liquid bridge between two surfaces. All studies were restricted, however, to smooth surfaces.…”

“…Specifically, curiosity on the meaning of apparent contact angles, such as advancing and receding contact angles, and contact angle hysteresis drives scientific debate and research in this area. [28][29][30][31][32][33][34] Progress is also driven by the fact that it became possible in recent years to measure the adhesion between a liquid droplet and a solid surface directly using a microbalance or other force-measuring systems. For example, Liu et al 35 studied the interaction between a liquid droplet and a series of gold substrates with wettability gradient by using a microbalance, and they found that the adhesion force decreases as the contact angle increases.…”

Facile manipulation of receding contact angles of a substrate by roughening and fluorination

“…Here  a and  r represent the advancing and receding CAs, respectively. Recently, the receding CA is found to play a paramount role in anti-fingerprint or anti-smudge surfaces and the liquid transfer mechanism between two surfaces [6]. In the process of inflation and deflation of a sessile drop on a real surface, a hysteresis loop can be evidently observed in the plot of CA versus drop volume.…”