Huanchen Chen

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 (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.

Fast Liquid Transfer between Surfaces: Breakup of Stretched Liquid Bridges.

In this work, a systematic experimental study was performed to understand the fast liquid transfer process between two surfaces. According to the value of the Reynolds number (Re), the fast transfer is divided into two different scenarios, one with negligible inertia effects (Re ≪ 1) and the other with significant inertia effects (Re > 1). For Re ≪ 1, the influences of the capillary number (Ca) and the dimensionless minimum separation (H(min)* = H(min)/V(1/3), where H(min) is the minimum separation between two surfaces and V is the volume of liquid) on the transfer ratio (α, the volume of liquid transferred to the acceptor surface over the total liquid volume) are discussed. On the basis of the roles of each physical parameter, an empirical equation is presented to predict the transfer ratio, α = f(Ca). This equation involves two coefficients which are affected only by the surface contact angles and H(min)* but not by the liquid viscosity or surface tension. When Re > 1, it is shown for the first time that the transfer ratio does not converge to 0.5 with the increase in the stretching speed.

Stability of a liquid bridge between nonparallel hydrophilic surfaces

Formation of liquid bridges between two solid surfaces is frequently observed in industry and nature, e.g. in printing applications. When the two solid surfaces are not parallel (with a dihedral angle ψ between them), an interesting phenomenon emerges: if ψ exceeds a critical angle (denoted as ψc) the bridge is no longer stable, and propels itself toward the cusp of the surfaces. In this work we performed, for the first time, a systematic study on the parameters influencing ψc by combining experimental, theoretical, and numerical investigations. It was shown that ψc is determined by the advancing contact angle (θa) and Contact Angle Hysteresis (CAH) of the surfaces: it increases as θa or CAH increases, and these two parameters have a nonlinear and interdependent influence on ψc. Based on our quantitative results, an empirical equation is presented to predict the critical angle, ψc=f(θa,CAH) in closed analytical form. This equation can be used to calculate ψc for bridges formed by moving down a pre-tilted surface towards a sessile drop on a stationary lower surface, or bridges between initially parallel surfaces which the top surface tilts after bridge formation.

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 (cfmax) 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 cfmax. 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.