Body Forces Drive the Apparent Line Tension of Sessile Droplets

Contact Angle Measurements of the Apparent Line Tension Are Spurious

Phenomena in diverse contexts such as wetting, biological assembly, and manufacturing are attributed to the three-phase line tension. However, decades of line tension estimates based on contact angles of droplets controversially span 6 orders of magnitude, raising the question of which measurements are authoritative. Here, we show with experiments and calculations that contact angles fail to estimate line tension regardless of length scale, technique, and measurement quality. Line tension measurements based on contact angles are driven by two distinct and spurious mechanisms: body forces under ideal conditions, and data scatter under noisy conditions.

Size-Dependent Wetting Contact Angles at the Nanoscale Defined by Equimolar Surfaces and Surfaces of Tension

The wetting characteristics of fluids play a crucial role in various fields of interface and surface science. Contact angle serves as a fundamental indicator of wetting behavior. However, accurate quantification of wetting phenomena even at the macroscale often poses challenges, particularly due to the hysteresis between receding and advancing contact angles. The complexity increases further at the nanoscale, where the significant volume of the interphase region causes ambiguity in defining the "dividing surface." In this study, we use molecular dynamics simulations to investigate the wetting dynamics of a "cylindrical nanodroplet" and an argon nanofilm. Through analysis of microscopic density distribution maps and tension tensor distributions within the Gibbs framework, we identified equimolar and tension surfaces at both liquid-gas and liquid-solid interfaces. Our results show over 10% discrepancies between equilibrium contact angles calculated for equimolar surfaces and those based on tension surfaces in the case of the cylindrical nanodroplet. We observed a clear dependence of wetting contact angles on the cross-sectional radius of cylindrical droplets with a straight three-phase contact line. As the radius decreases, the differences between contact angles at equimolar and tension surfaces increase, while for larger droplets, these differences diminish and become negligible.

Wetting Phenomena: Line Tension and Gravitational Effect

An apparent contact angle is formed when a droplet is deposited on a solid substrate. Young's law has been employed to describe the equilibrium contact angle. Often in experiments, the equilibrium contact angle deviates from Young's law and depends on the volume of the droplet, known as the line tension effect. However, the physical origin of the line tension is quite controversial. Especially, the sign and the quantity of the line tension spanning 6 orders of magnitude are unsolved problems. Here, we quantify the line energy in terms of physical parameters and demonstrate that both positive and negative line tensions exist. The results are quantitatively compared with existing experiments as well as with previous theories.

Exploration of contact angle hysteresis mechanisms: From microscopic to macroscopic

Variations from equilibrium Young's angle, known as contact angle hysteresis (CAH), are frequently observed upon droplet deposition on a solid surface. This ubiquitous phenomenon indicates the presence of multiple local surface energy minima for the sessile droplet. Previous research primarily explains CAH via considering macroscopic roughness, such as topographical defects, which alter the effective interfacial energy between the fluid phase and the solid phase, thereby shifting the global surface energy minimum. One typical example is the classic Cassie-Baxter-Wenzel theory. Here, we propose an alternative microscopic mechanism that emphasizes the complexity of molecular rearrangements at the fluid-solid interface, treating their interfacial tensions as variables, which results in multiple local surface energy minima. Our theoretical framework demonstrates that CAH can occur even on chemically homogeneous and mechanically smooth-flat substrates, aligning with previously unexplained experimental observations. In addition, we explore the interplay between macroscopic and microscopic roughness in influencing CAH and clarify the contrasting wetting behaviors-the lotus effect and the rose petal effect-on hierarchical roughness from a thermodynamic perspective. This work provides valuable insights into surface tension determination by restoring the natural physical properties of interfaces and illuminates the multifaceted mechanisms underlying the everyday occurrences of CAH.

Wetting and Contact-Angle Hysteresis: Density Asymmetry and van der Waals Force

A droplet depositing on a solid substrate leads to the wetting phenomenon, such as dew on plant leaves. On an ideally smooth substrate, the classic Young's law has been employed to describe the wetting effect. However, no real substrate is ideally smooth at the microscale. Given this fact, we introduce a surface composition concept to scrutinize the wetting mechanism via considering the liquid-gas density asymmetry and the fluid-solid van der Waals interaction. The current concept enables one to comprehend counterintuitive phenomenon of contact-angle hysteresis on a smooth substrate and increase of contact angle with temperature as well as gas bubble wetting.

Liquid-liquid surfactant partitioning drives dewetting of oil from hydrophobic surfaces

HYPOTHESIS

Sessile droplets solubilizing in surfactant solution are frequently encountered in practice, but the factors governing their non-equilibrium dynamics are not well understood. Here, we investigate mechanisms by which solubilizing, sessile oil droplets in aqueous surfactant solution dewet from hydrophobic substrates and spread on hydrophilic substrates.

EXPERIMENTS

We quantify the dependence of droplet contact line dynamics on drop size and oil, surfactant, and substrate chemistries. We consider halogenated alkane oils as well as aromatic oils and focus on common nonionic nonylphenol ethoxylate surfactants. We correlate these results with measurements of the interfacial tensions.

FINDINGS

Counter-intuitively, under a range of conditions, we observe complete dewetting of oil from hydrophobic substrates but spreading on hydrophilic substrates. The timescales needed to reach a steady-state contact angle vary widely, with some droplets examined taking over a day. We find that surfactant surface adsorption governs the contact angle on shorter timescales, while partitioning of surfactant from water to oil, and oil solubilization into the water, act on longer timescales to facilitate the complete dewetting. Understanding of the role played by surfactant and oil transport presents opportunities for tailoring sessile droplet behaviors and controlling droplet dynamics under conditions that would previously not have been considered.

Line tension of sessile droplets: Thermodynamic considerations

We deduce a thermodynamically consistent diffuse interface model to study the line tension phenomenon of sessile droplets. By extending the standard Cahn-Hilliard model via modifying the free energy functional due to the spatial reflection asymmetry at the substrate, we provide an alternative interpretation for the wall energy. In particular, we find the connection of the line tension effect with the droplet-matrix-substrate triple interactions. This finding reveals that the apparent contact angle deviating from Young's law is contributed by the wall energy reduction as well as the line energy minimization. Besides, the intrinsic negative line tension resulting from the curvature effect is observed in our simulations and shows good accordance with recent experiments [Tan et al. Phys. Rev. Lett. 130, 064003 (2023)0031-900710.1103/PhysRevLett.130.064003]. Moreover, our model sheds light upon the understanding of the wetting edge formation which results from the vying effect of wall energy and line tension.